Evidence Law and Audit Program Essay - 879 Words

As corporate controller for Apollo Shoes, you are tasked to find and explain any irregularities in the Apollo Shoes Case. Resource: Apollo Shoes Casebook Define the process you will use and address the following assessed classroom discussion questions: What procedures will be used to collect accounting evidence? What sampling tools and techniques will be used for the examination? How will you use analytical and inferential tools to evaluate accounting evidence? Submit your assignment to the facilitator. Note. APA formatting is not required for this assignment. Use a title and reference page where appropriate. Consider using a checklist or flowchart to outline your process. There are many irregularities that can arise†¦show more content†¦79-80). Substantive procedures for detecting irregularities in cash receipts include the following: ââ€" ª review the cash receipts journal and master file for unusual transactions; ââ€" ª trace cash receipts entries from the cash receipts journal entries to the bank statement; ââ€" ª prepare a proof of cash receipts; ââ€" ª obtain a... Although every investigation case is unique, the investigation process is similar for most cases and usually consists of four stages: Goal Setting, Planning, Investigation and Evaluation. The investigation process starts with goal setting. Goal Setting sets the expectation and identifies the complainant’s goals as well as obtainable results and acceptable outcomes. â€Å"The effectiveness of every fraud investigator, in pursuing either criminal or civil fraud investigations, is ultimately judged by how closely—and consistently—she reaches or exceeds her investigative goals.† Once the goals and expectation have been clearly defined, then an investigative plan is developed. Financial fraud investigations usually involves large amounts of data and information, an investigative plan focuses and controls the investigation and helps to manages the volumes of data gathered in an investigation. The investigation process begins with intelligence gathering, these procedures includes database searches,Show MoreRelatedFinancial Statements And On Design Internal Control Systems895 Words   |  4 Pagesprovides opinions on the reliability of the report and the effectiveness of the internal control. 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Cluster Analysis Free Essays

Chapter 9 Cluster Analysis Learning Objectives After reading this chapter you should understand: – The basic concepts of cluster analysis. – How basic cluster algorithms work. – How to compute simple clustering results manually. We will write a custom essay sample on Cluster Analysis or any similar topic only for you Order Now – The different types of clustering procedures. – The SPSS clustering outputs. Keywords Agglomerative and divisive clustering A Chebychev distance A City-block distance A Clustering variables A Dendrogram A Distance matrix A Euclidean distance A Hierarchical and partitioning methods A Icicle diagram A k-means A Matching coef? cients A Pro? ing clusters A Two-step clustering Are there any market segments where Web-enabled mobile telephony is taking off in different ways? To answer this question, Okazaki (2006) applies a twostep cluster analysis by identifying segments of Internet adopters in Japan. The ? ndings suggest that there are four clusters exhibiting distinct attitudes towards Web-enabled mobile telephony adoption. Interestingly, freelance, and highly educated professionals had the most negative perception of mobile Internet adoption, whereas clerical of? ce workers had the most positive perception. Furthermore, housewives and company executives also exhibited a positive attitude toward mobile Internet usage. Marketing managers can now use these results to better target speci? c customer segments via mobile Internet services. Introduction Grouping similar customers and products is a fundamental marketing activity. It is used, prominently, in market segmentation. As companies cannot connect with all their customers, they have to divide markets into groups of consumers, customers, or clients (called segments) with similar needs and wants. Firms can then target each of these segments by positioning themselves in a unique segment (such as Ferrari in the high-end sports car market). While market researchers often form E. Mooi and M. Sarstedt, A Concise Guide to Market Research, DOI 10. 1007/978-3-642-12541-6_9, # Springer-Verlag Berlin Heidelberg 2011 237 238 9 Cluster Analysis market segments based on practical grounds, industry practice and wisdom, cluster analysis allows segments to be formed that are based on data that are less dependent on subjectivity. The segmentation of customers is a standard application of cluster analysis, but it can also be used in different, sometimes rather exotic, contexts such as evaluating typical supermarket shopping paths (Larson et al. 2005) or deriving employers’ branding strategies (Moroko and Uncles 2009). Understanding Cluster Analysis Cluster analysis is a convenient method for identifying homogenous groups of objects called clusters. Objects (or cases, observations) in a speci? c cluster share many characteristics, but are very dissimilar to objects not belonging to that cluster. Let’s try to gain a basic understanding of the cluster analysis procedure by looking at a simple example. Imagine that you are interested in segmenting your customer base in order to better target them through, for example, pricing strategies. The ? rst step is to decide on the characteristics that you will use to segment your customers. In other words, you have to decide which clustering variables will be included in the analysis. For example, you may want to segment a market based on customers’ price consciousness (x) and brand loyalty (y). These two variables can be measured on a 7-point scale with higher values denoting a higher degree of price consciousness and brand loyalty. The values of seven respondents are shown in Table 9. 1 and the scatter plot in Fig. 9. 1. The objective of cluster analysis is to identify groups of objects (in this case, customers) that are very similar with regard to their price consciousness and brand loyalty and assign them into clusters. After having decided on the clustering variables (brand loyalty and price consciousness), we need to decide on the clustering procedure to form our groups of objects. This step is crucial for the analysis, as different procedures require different decisions prior to analysis. There is an abundance of different approaches and little guidance on which one to use in practice. We are going to discuss the most popular approaches in market research, as they can be easily computed using SPSS. These approaches are: hierarchical methods, partitioning methods (more precisely, k-means), and two-step clustering, which is largely a combination of the ? rst two methods. Each of these procedures follows a different approach to grouping the most similar objects into a cluster and to determining each object’s cluster membership. In other words, whereas an object in a certain cluster should be as similar as possible to all the other objects in the Table 9. 1 Data Customer x y A 3 7 B 6 7 C 5 6 D 3 5 E 6 5 F 4 3 G 1 2 Understanding Cluster Analysis 7 6 A C D E B 239 Brand loyalty (y) 5 4 3 2 1 0 0 1 2 G F 3 4 5 6 7 Price consciousness (x) Fig. 9. 1 Scatter plot same cluster, it should likewise be as distinct as possible from objects in different clusters. But how do we measure similarity? Some approaches – most notably hierarchical methods – require us to specify how similar or different objects are in order to identify different clusters. Most software packages calculate a measure of (dis)similarity by estimating the distance between pairs of objects. Objects with smaller distances between one another are more similar, whereas objects with larger distances are more dissimilar. An important problem in the application of cluster analysis is the decision regarding how many clusters should be derived from the data. This question is explored in the next step of the analysis. Sometimes, however, we already know the number of segments that have to be derived from the data. For example, if we were asked to ascertain what characteristics distinguish frequent shoppers from infrequent ones, we need to ? nd two different clusters. However, we do not usually know the exact number of clusters and then we face a trade-off. On the one hand, you want as few clusters as possible to make them easy to understand and actionable. On the other hand, having many clusters allows you to identify more segments and more subtle differences between segments. In an extreme case, you can address each individual separately (called one-to-one marketing) to meet consumers’ varying needs in the best possible way. Examples of such a micro-marketing strategy are Puma’s Mongolian Shoe BBQ (www. mongolianshoebbq. puma. com) and Nike ID (http://nikeid. nike. com), in which customers can fully customize a pair of shoes in a hands-on, tactile, and interactive shoe-making experience. On the other hand, the costs associated with such a strategy may be prohibitively high in many 240 9 Cluster Analysis Decide on the clustering variables Decide on the clustering procedure Hierarchical methods Select a measure of similarity or dissimilarity Partitioning methods Two-step clustering Select a measure of similarity or dissimilarity Choose a clustering algorithm Decide on the number of clusters Validate and interpret the cluster solution Fig. 9. 2 Steps in a cluster analysis business contexts. Thus, we have to ensure that the segments are large enough to make the targeted marketing programs pro? table. Consequently, we have to cope with a certain degree of within-cluster heterogeneity, which makes targeted marketing programs less effective. In the ? nal step, we need to interpret the solution by de? ning and labeling the obtained clusters. This can be done by examining the clustering variables’ mean values or by identifying explanatory variables to pro? le the clusters. Ultimately, managers should be able to identify customers in each segment on the basis of easily measurable variables. This ? nal step also requires us to assess the clustering solution’s stability and validity. Figure 9. 2 illustrates the steps associated with a cluster analysis; we will discuss these in more detail in the following sections. Conducting a Cluster Analysis Decide on the Clustering Variables At the beginning of the clustering process, we have to select appropriate variables for clustering. Even though this choice is of utmost importance, it is rarely treated as such and, instead, a mixture of intuition and data availability guide most analyses in marketing practice. However, faulty assumptions may lead to improper market Conducting a Cluster Analysis 241 segments and, consequently, to de? cient marketing strategies. Thus, great care should be taken when selecting the clustering variables. There are several types of clustering variables and these can be classi? d into general (independent of products, services or circumstances) and speci? c (related to both the customer and the product, service and/or particular circumstance), on the one hand, and observable (i. e. , measured directly) and unobservable (i. e. , inferred) on the other. Table 9. 2 provides several types and examples of clustering variables. Ta ble 9. 2 Types and examples of clustering variables General Observable (directly Cultural, geographic, demographic, measurable) socio-economic Unobservable Psychographics, values, personality, (inferred) lifestyle Adapted from Wedel and Kamakura (2000) Speci? c User status, usage frequency, store and brand loyalty Bene? ts, perceptions, attitudes, intentions, preferences The types of variables used for cluster analysis provide different segments and, thereby, in? uence segment-targeting strategies. Over the last decades, attention has shifted from more traditional general clustering variables towards product-speci? c unobservable variables. The latter generally provide better guidance for decisions on marketing instruments’ effective speci? cation. It is generally acknowledged that segments identi? ed by means of speci? unobservable variables are usually more homogenous and their consumers respond consistently to marketing actions (see Wedel and Kamakura 2000). However, consumers in these segments are also frequently hard to identify from variables that are easily measured, such as demographics. Conversely, segments determined by means of generally observable variables usually stand out due to their identi? ability but often lack a unique response structure. 1 Consequently, researchers often combine different variables (e. g. , multiple lifestyle characteristics combined with demographic variables), bene? ing from each ones strengths. In some cases, the choice of clustering variables is apparent from the nature of the task at hand. For example, a managerial problem regarding corporate communications will have a fairly well de? ned set of clustering variables, including contenders such as awareness, attitudes, perceptions, and media habits. However, this is not always the case and researchers have to choose from a set of candidate variables. Whichever clustering variables are chosen, it is important to select those that provide a clear-cut differentiation between the segments regarding a speci? c managerial objective. More precisely, criterion validity is of special interest; that is, the extent to which the â€Å"independent† clustering variables are associated with 1 2 See Wedel and Kamakura (2 000). Tonks (2009) provides a discussion of segment design and the choice of clustering variables in consumer markets. 242 9 Cluster Analysis one or more â€Å"dependent† variables not included in the analysis. Given this relationship, there should be signi? cant differences between the â€Å"dependent† variable(s) across the clusters. These associations may or may not be causal, but it is essential that the clustering variables distinguish the â€Å"dependent† variable(s) signi? antly. Criterion variables usually relate to some aspect of behavior, such as purchase intention or usage frequency. Generally, you should avoid using an abundance of clustering variables, as this increases the odds that the variables are no longer dissimilar. If there is a high degree of collinearity between the variables, they are not suf? ciently unique to identify distinct market segments. If highly correlated variables are used for cluster analysis, speci? c aspects covered by thes e variables will be overrepresented in the clustering solution. In this regard, absolute correlations above 0. 90 are always problematic. For example, if we were to add another variable called brand preference to our analysis, it would virtually cover the same aspect as brand loyalty. Thus, the concept of being attached to a brand would be overrepresented in the analysis because the clustering procedure does not differentiate between the clustering variables in a conceptual sense. Researchers frequently handle this issue by applying cluster analysis to the observations’ factor scores derived from a previously carried out factor analysis. However, according to Dolnicar and Grâ‚ ¬n u (2009), this factor-cluster segmentation approach can lead to several problems: 1. The data are pre-processed and the clusters are identi? ed on the basis of transformed values, not on the original information, which leads to different results. 2. In factor analysis, the factor solution does not explain a certain amount of variance; thus, information is discarded before segments have been identi? ed or constructed. 3. Eliminating variables with low loadings on all the extracted factors means that, potentially, the most important pieces of information for the identi? ation of niche segments are discarded, making it impossible to ever identify such groups. 4. The interpretations of clusters based on the original variables become questionable given that the segments have been constructed using factor scores. Several studies have shown that the factor-cluster segmentation signi? cantly reduces the success of segment recovery. 3 Consequently , you should rather reduce the number of items in the questionnaire’s pre-testing phase, retaining a reasonable number of relevant, non-redundant questions that you believe differentiate the segments well. However, if you have your doubts about the data structure, factorclustering segmentation may still be a better option than discarding items that may conceptually be necessary. Furthermore, we should keep the sample size in mind. First and foremost, this relates to issues of managerial relevance as segments’ sizes need to be substantial to ensure that targeted marketing programs are pro? table. From a statistical perspective, every additional variable requires an over-proportional increase in 3 See the studies by Arabie and Hubert (1994), Sheppard (1996), or Dolnicar and Grâ‚ ¬n (2009). u Conducting a Cluster Analysis 243 observations to ensure valid results. Unfortunately, there is no generally accepted rule of thumb regarding minimum sample sizes or the relationship between the objects and the number of clustering variables used. In a related methodological context, Formann (1984) recommends a sample size of at least 2m, where m equals the number of clustering variables. This can only provide rough guidance; nevertheless, we should pay attention to the relationship between the objects and clustering variables. It does not, for example, appear logical to cluster ten objects using ten variables. Keep in mind that no matter how many variables are used and no matter how small the sample size, cluster analysis will always render a result! Ultimately, the choice of clustering variables always depends on contextual in? uences such as data availability or resources to acquire additional data. Marketing researchers often overlook the fact that the choice of clustering variables is closely connected to data quality. Only those variables that ensure that high quality data can be used should be included in the analysis. This is very important if a segmentation solution has to be managerially useful. Furthermore, data are of high quality if the questions asked have a strong theoretical basis, are not contaminated by respondent fatigue or response styles, are recent, and thus re? ect the current market situation (Dolnicar and Lazarevski 2009). Lastly, the requirements of other managerial functions within the organization often play a major role. Sales and distribution may as well have a major in? uence on the design of market segments. Consequently, we have to be aware that subjectivity and common sense agreement will (and should) always impact the choice of clustering variables. Decide on the Clustering Procedure By choosing a speci? c clustering procedure, we determine how clusters are to be formed. This always involves optimizing some kind of criterion, such as minimizing the within-cluster variance (i. e. , the clustering variables’ overall variance of objects in a speci? c cluster), or maximizing the distance between the objects or clusters. The procedure could also address the question of how to determine the (dis)similarity between objects in a newly formed cluster and the remaining objects in the dataset. There are many different clustering procedures and also many ways of classifying these (e. g. , overlapping versus non-overlapping, unimodal versus multimodal, exhaustive versus non-exhaustive). 4 A practical distinction is the differentiation between hierarchical and partitioning methods (most notably the k-means procedure), which we are going to discuss in the next sections. We also introduce two-step clustering, which combines the principles of hierarchical and partitioning methods and which has recently gained increasing attention from market research practice. See Wedel and Kamakura (2000), Dolnicar (2003), and Kaufman and Rousseeuw (2005) for a review of clustering techniques. 4 244 9 Cluster Analysis Hierarchical Methods Hierarchical clustering procedures are characterized by the tree-like structure established in the course of the analysis. Most hierarchical techniques fall into a category called agglomerative clustering. In this category, clusters are consecutively formed from objects. Initially, this type of procedure starts with each object representing an individual cluster. These clusters are then sequentially merged according to their similarity. First, the two most similar clusters (i. e. , those with the smallest distance between them) are merged to form a new cluster at the bottom of the hierarchy. In the next step, another pair of clusters is merged and linked to a higher level of the hierarchy, and so on. This allows a hierarchy of clusters to be established from the bottom up. In Fig. 9. 3 (left-hand side), we show how agglomerative clustering assigns additional objects to clusters as the cluster size increases. Step 5 Step 1 A, B, C, D, E Agglomerative clustering Step 4 Step 2 Divisive clustering A, B C, D, E Step 3 Step 3 A, B C, D E Step 2 Step 4 A, B C D E Step 1 Step 5 A B C D E Fig. 9. 3 Agglomerative and divisive clustering A cluster hierarchy can also be generated top-down. In this divisive clustering, all objects are initially merged into a single cluster, which is then gradually split up. Figure 9. 3 illustrates this concept (right-hand side). As we can see, in both agglomerative and divisive clustering, a cluster on a higher level of the hierarchy always encompasses all clusters from a lower level. This means that if an object is assigned to a certain cluster, there is no possibility of reassigning this object to another cluster. This is an important distinction between these types of clustering and partitioning methods such as k-means, which we will explore in the next section. Divisive procedures are quite rarely used in market research. We therefore concentrate on the agglomerative clustering procedures. There are various types Conducting a Cluster Analysis 245 of agglomerative procedures. However, before we discuss these, we need to de? ne how similarities or dissimilarities are measured between pairs of objects. Select a Measure of Similarity or Dissimilarity There are various measures to express (dis)similarity between pairs of objects. A straightforward way to assess two objects’ proximity is by drawing a straight line between them. For example, when we look at the scatter plot in Fig. 9. 1, we can easily see that the length of the line connecting observations B and C is much shorter than the line connecting B and G. This type of distance is also referred to as Euclidean distance (or straight-line distance) and is the most commonly used type when it comes to analyzing ratio or interval-scaled data. In our example, we have ordinal data, but market researchers usually treat ordinal data as metric data to calculate distance metrics by assuming that the scale steps are equidistant (very much like in factor analysis, which we discussed in Chap. 8). To use a hierarchical clustering procedure, we need to express these distances mathematically. By taking the data in Table 9. 1 into consider ation, we can easily compute the Euclidean distance between customer B and customer C (generally referred to as d(B,C)) with regard to the two variables x and y by using the following formula: q Euclidean ? B; C? ? ? xB A xC ? 2 ? ?yB A yC ? 2 The Euclidean distance is the square root of the sum of the squared differences in the variables’ values. Using the data from Table 9. 1, we obtain the following: q p dEuclidean ? B; C? ? ? 6 A 5? 2 ? ?7 A 6? 2 ? 2 ? 1:414 This distance corresponds to the length of the line that connects objects B and C. In this case, we only used two variables but we can easily add more under the root sign in the formula. However, each additional variable will add a dimension to our research problem (e. . , with six clustering variables, we have to deal with six dimensions), making it impossible to represent the solution graphically. Similarly, we can compute the distance between customer B and G, which yields the following: q p dEuclidean ? B; G? ? ? 6 A 1? 2 ? ?7 A 2? 2 ? 50 ? 7:071 Likewise, we can compute the distance between all other pairs of objects. All these distances are usually expressed by means of a distance matrix. In this distance matrix, the non-diagonal elements express the distances between pairs of objects 5 Note that researchers also often use the squared Euclidean distance. 246 9 Cluster Analysis and zeros on the diagonal (the distance from each object to itself is, of course, 0). In our example, the distance matrix is an 8 A 8 table with the lines and rows representing the objects (i. e. , customers) under consideration (see Table 9. 3). As the distance between objects B and C (in this case 1. 414 units) is the same as between C and B, the distance matrix is symmetrical. Furthermore, since the distance between an object and itself is zero, one need only look at either the lower or upper non-diagonal elements. Table 9. 3 Euclidean distance matrix Objects A B A 0 B 3 0 C 2. 236 1. 414 D 2 3. 606 E 3. 606 2 F 4. 123 4. 472 G 5. 385 7. 071 C D E F G 0 2. 236 1. 414 3. 162 5. 657 0 3 2. 236 3. 606 0 2. 828 5. 831 0 3. 162 0 There are also alternative distance measures: The city-block distance uses the sum of the variables’ absolute differences. This is often called the Manhattan metric as it is akin to the walking distance between two points in a city like New York’s Manhattan district, where the distance equals the number of blocks in the directions North-South and East-West. Using the city-block distance to compute the distance between customers B and C (or C and B) yields the following: dCityAblock ? B; C? ? jxB A xC j ? jyB A yC j ? j6 A 5j ? j7 A 6j ? 2 The resulting distance matrix is in Table 9. 4. Table 9. 4 City-block distance matrix Objects A B A 0 B 3 0 C 3 2 D 2 5 E 5 2 F 5 6 G 7 10 C D E F G 0 3 2 4 8 0 3 3 5 0 4 8 0 4 0 Lastly, when working with metric (or ordinal) data, researchers frequently use the Chebychev distance, which is the maximum of the absolute difference in the clustering variables’ values. In respect of customers B and C, this result is: dChebychec ? B; C? max? jxB A xC j; jyB A yC j? ? max? j6 A 5j; j7 A 6j? ? 1 Figure 9. 4 illustrates the interrelation between these three distance measures regarding two objects, C and G, from our example. Conducting a Cluster Analysis 247 C Brand loyalty (y) Euclidean distance City-block distance G Chebychev distance Price consciousness (x) Fig. 9. 4 Distance measures There are other d istance measures such as the Angular, Canberra or Mahalanobis distance. In many situations, the latter is desirable as it compensates for collinearity between the clustering variables. However, it is (unfortunately) not menu-accessible in SPSS. In many analysis tasks, the variables under consideration are measured on different scales or levels. This would be the case if we extended our set of clustering variables by adding another ordinal variable representing the customers’ income measured by means of, for example, 15 categories. Since the absolute variation of the income variable would be much greater than the variation of the remaining two variables (remember, that x and y are measured on 7-point scales), this would clearly distort our analysis results. We can resolve this problem by standardizing the data prior to the analysis. Different standardization methods are available, such as the simple z standardization, which rescales each variable to have a mean of 0 and a standard deviation of 1 (see Chap. 5). In most situations, however, standardization by range (e. g. , to a range of 0 to 1 or A1 to 1) performs better. 6 We recommend standardizing the data in general, even though this procedure can reduce or in? ate the variables’ in? uence on the clustering solution. 6 See Milligan and Cooper (1988). 248 9 Cluster Analysis Another way of (implicitly) standardizing the data is by using the correlation between the objects instead of distance measures. For example, suppose a respondent rated price consciousness 2 and brand loyalty 3. Now suppose a second respondent indicated 5 and 6, whereas a third rated these variables 3 and 3. Euclidean, city-block, and Chebychev distances would indicate that the ? rst respondent is more similar to the third than to the second. Nevertheless, one could convincingly argue that the ? rst respondent’s ratings are more similar to the second’s, as both rate brand loyalty higher than price consciousness. This can be accounted for by computing the correlation between two vectors of values as a measure of similarity (i. . , high correlation coef? cients indicate a high degree of similarity). Consequently, similarity is no longer de? ned by means of the difference between the answer categories but by means of the similarity of the answering pro? les. Using correlation is also a way of standardizing the data implicitly. Whether you use correlation or one of the distance measures depends on wh ether you think the relative magnitude of the variables within an object (which favors correlation) matters more than the relative magnitude of each variable across objects (which favors distance). However, it is generally recommended that one uses correlations when applying clustering procedures that are susceptible to outliers, such as complete linkage, average linkage or centroid (see next section). Whereas the distance measures presented thus far can be used for metrically and – in general – ordinally scaled data, applying them to nominal or binary data is meaningless. In this type of analysis, you should rather select a similarity measure expressing the degree to which variables’ values share the same category. These socalled matching coef? ients can take different forms but rely on the same allocation scheme shown in Table 9. 5. Table 9. 5 Allocation scheme for matching coef? cients Number of variables with category 1 a c Object 1 Number of variables with category 2 b d Object 2 Number of variables with category 1 Number of variables with category 2 Based on the allocation scheme in Table 9. 5, we can compute different matching coef? cients, such as t he simple matching coef? cient (SM): SM ? a? d a? b? c? d This coef? cient is useful when both positive and negative values carry an equal degree of information. For example, gender is a symmetrical attribute because the number of males and females provides an equal degree of information. Conducting a Cluster Analysis 249 Let’s take a look at an example by assuming that we have a dataset with three binary variables: gender (male ? 1, female ? 2), customer (customer ? 1, noncustomer ? 2), and disposable income (low ? 1, high ? 2). The ? rst object is a male non-customer with a high disposable income, whereas the second object is a female non-customer with a high disposable income. According to the scheme in Table 9. , a ? b ? 0, c ? 1 and d ? 2, with the simple matching coef? cient taking a value of 0. 667. Two other types of matching coef? cients, which do not equate the joint absence of a characteristic with similarity and may, therefore, be of more value in segmentation studies, are the Jaccard (JC) and the Russel and Rao (RR) coef? cients. They are de? ned as follows: a JC ? a? b? c a RR ? a? b? c? d These matching coef? cients are – just like the distance measures – used to determine a cluster solution. There are many other matching coef? ients such as Yule’s Q, Kulczynski or Ochiai, but since most applications of cluster analysis rely on metric or ordinal data, we will not discuss these in greater detail. 7 For nominal variables with more than two categories, you should always convert the categorical variable into a set of binary variables in order to use matching coef? cients. When you have ordinal data, you should always use distance measures such as Euclidean distance. Even though using matching coef? cients would be feasible and – from a strictly statistical standpoint – even more appropriate, you would disregard variable information in the sequence of the categories. In the end, a respondent who indicates that he or she is very loyal to a brand is going to be closer to someone who is somewhat loyal than a respondent who is not loyal at all. Furthermore, distance measures best represent the concept of proximity, which is fundamental to cluster analysis. Most datasets contain variables that are measured on multiple scales. For example, a market research questionnaire may ask about the respondent’s income, product ratings, and last brand purchased. Thus, we have to consider variables measured on a ratio, ordinal, and nominal scale. How can we simultaneously incorporate these variables into one analysis? Unfortunately, this problem cannot be easily resolved and, in fact, many market researchers simply ignore the scale level. Instead, they use one of the distance measures discussed in the context of metric (and ordinal) data. Even though this approach may slightly change the results when compared to those using matching coef? cients, it should not be rejected. Cluster analysis is mostly an exploratory technique whose results provide a rough guidance for managerial decisions. Despite this, there are several procedures that allow a simultaneous integration of these variables into one analysis. 7 See Wedel and Kamakura (2000) for more information on alternative matching coef? cients. 250 9 Cluster Analysis First, we could compute distinct distance matrices for each group of variables; that is, one distance matrix based on, for example, ordinally scaled variables and another based on nominal variables. Afterwards, we can simply compute the weighted arithmetic mean of the distances and use this average distance matrix as the input for the cluster analysis. However, the weights have to be determined a priori and improper weights may result in a biased treatment of different variable types. Furthermore, the computation and handling of distance matrices are not trivial. Using the SPSS syntax, one has to manually add the MATRIX subcommand, which exports the initial distance matrix into a new data ? le. Go to the 8 Web Appendix (! Chap. 5) to learn how to modify the SPSS syntax accordingly. Second, we could dichotomize all variables and apply the matching coef? cients discussed above. In the case of metric variables, this would involve specifying categories (e. g. , low, medium, and high income) and converting these into sets of binary variables. In most cases, however, the speci? ation of categories would be rather arbitrary and, as mentioned earlier, this procedure could lead to a severe loss of information. In the light of these issues, you should avoid combining metric and nominal variables in a single cluster analysis, but if this is not feasible, the two-step clustering procedure provides a valuable alternative, which we will discuss later. Lastly, the choice of the (dis)similarity measure is not extremely critical to recovering the underlying cluster structure. In this regard, the choice of the clustering algorithm is far more important. We therefore deal with this aspect in the following section. Select a Clustering Algorithm After having chosen the distance or similarity measure, we need to decide which clustering algorithm to apply. There are several agglomerative procedures and they can be distinguished by the way they de? ne the distance from a newly formed cluster to a certain object, or to other clusters in the solution. The most popular agglomerative clustering procedures include the following: l l l l Single linkage (nearest neighbor): The distance between two clusters corresponds to the shortest distance between any two members in the two clusters. Complete linkage (furthest neighbor): The oppositional approach to single linkage assumes that the distance between two clusters is based on the longest distance between any two members in the two clusters. Average linkage: The distance between two clusters is de? ned as the average distance between all pairs of the two clusters’ members. Centroid: In this approach, the geometric center (centroid) of each cluster is computed ? rst. The distance between the two clusters equals the distance between the two centroids. Figures 9. 5–9. 8 illustrate these linkage procedures for two randomly framed clusters. Conducting a Cluster Analysis Fig. 9. 5 Single linkage 251 Fig. 9. 6 Complete linkage Fig. 9. 7 Average linkage Fig. 9. 8 Centroid 252 9 Cluster Analysis Each of these linkage algorithms can yield totally different results when used on the same dataset, as each has its speci? c properties. As the single linkage algorithm is based on minimum distances, it tends to form one large cluster with the other clusters containing only one or few objects each. We can make use of this â€Å"chaining effect† to detect outliers, as these will be merged with the remaining objects – usually at very large distances – in the last steps of the analysis. Generally, single linkage is considered the most versatile algorithm. Conversely, the complete linkage method is strongly affected by outliers, as it is based on maximum distances. Clusters produced by this method are likely to be rather compact and tightly clustered. The average linkage and centroid algorithms tend to produce clusters with rather low within-cluster variance and similar sizes. However, both procedures are affected by outliers, though not as much as complete linkage. Another commonly used approach in hierarchical clustering is Ward’s method. This approach does not combine the two most similar objects successively. Instead, those objects whose merger increases the overall within-cluster variance to the smallest possible degree, are combined. If you expect somewhat equally sized clusters and the dataset does not include outliers, you should always use Ward’s method. To better understand how a clustering algorithm works, let’s manually examine some of the single linkage procedure’s calculation steps. We start off by looking at the initial (Euclidean) distance matrix in Table 9. 3. In the very ? rst step, the two objects exhibiting the smallest distance in the matrix are merged. Note that we always merge those objects with the smallest distance, regardless of the clustering procedure (e. g. , single or complete linkage). As we can see, this happens to two pairs of objects, namely B and C (d(B, C) ? 1. 414), as well as C and E (d(C, E) ? 1. 414). In the next step, we will see that it does not make any difference whether we ? rst merge the one or the other, so let’s proceed by forming a new cluster, using objects B and C. Having made this decision, we then form a new distance matrix by considering the single linkage decision rule as discussed above. According to this rule, the distance from, for example, object A to the newly formed cluster is the minimum of d(A, B) and d(A, C). As d(A, C) is smaller than d(A, B), the distance from A to the newly formed cluster is equal to d(A, C); that is, 2. 236. We also compute the distances from cluster [B,C] (clusters are indicated by means of squared brackets) to all other objects (i. e. D, E, F, G) and simply copy the remaining distances – such as d(E, F) – that the previous clustering has not affected. This yields the distance matrix shown in Table 9. 6. Continuing the clustering procedure, we simply repeat the last step by merging the objects in the new distance matrix that exhibit the smallest distance (in this case, the newly formed cluster [B, C] and object E) and calculate the distance from this cluster to all other objects. The result of this step is described in Table 9. 7. Try to calculate the remaining steps yourself and compare your solution with the distance matrices in the following Tables 9. 8–9. 10. Conducting a Cluster Analysis Table 9. 6 Distance matrix after ? rst clustering step (single linkage) Objects A B, C D E F G A 0 B, C 2. 36 0 D 2 2. 236 0 E 3. 606 1. 414 3 0 F 4. 123 3. 162 2. 236 2. 828 0 G 5. 385 5. 657 3. 606 5. 831 3. 162 0 253 Table 9. 7 Distance matrix after second clustering step (single linkage) Objects A B, C, E D F G A 0 B, C, E 2. 236 0 D 2 2. 236 0 F 4. 123 2. 828 2. 236 0 G 5. 385 5. 657 3. 606 3. 162 0 Table 9. 8 Distance matrix after third clustering step (single linkage) Objects A, D B, C, E F G A, D 0 B, C, E 2. 236 0 F 2. 236 2. 828 0 G 3. 606 5. 657 3. 162 0 Table 9. 9 Distance matrix after fourth clustering step (single linkage) Objects A, B, C, D, E F G A, B, C, D, E 0 F 2. 236 0 G 3. 06 3. 162 0 Table 9. 10 Distance matrix after ? fth clustering step (single linkage) Objects A, B, C, D, E, F G A, B, C, D, E, F 0 G 3. 162 0 By following the single linkage procedure, the last steps involve the merger of cluster [A,B,C,D,E,F] and object G at a distance of 3. 162. Do you get the same results? As you can see, conducting a basic cluster analysis manually is not that hard at all – not if there are only a few objects in the dataset. A common way to visualize the cluster analysis’s progress is by drawing a dendrogram, which displays the distance level at which there was a ombination of objects and clusters (Fig. 9. 9). We read the dendrogram from left to right to see at which distance objects have been combined. For example, according to our calculati ons above, objects B, C, and E are combined at a distance level of 1. 414. 254 B C E A D F G 9 Cluster Analysis 0 1 2 Distance 3 Fig. 9. 9 Dendrogram Decide on the Number of Clusters An important question we haven’t yet addressed is how to decide on the number of clusters to retain from the data. Unfortunately, hierarchical methods provide only very limited guidance for making this decision. The only meaningful indicator relates to the distances at which the objects are combined. Similar to factor analysis’s scree plot, we can seek a solution in which an additional combination of clusters or objects would occur at a greatly increased distance. This raises the issue of what a great distance is, of course. One potential way to solve this problem is to plot the number of clusters on the x-axis (starting with the one-cluster solution at the very left) against the distance at which objects or clusters are combined on the y-axis. Using this plot, we then search for the distinctive break (elbow). SPSS does not produce this plot automatically – you have to use the distances provided by SPSS to draw a line chart by using a common spreadsheet program such as Microsoft Excel. Alternatively, we can make use of the dendrogram which essentially carries the same information. SPSS provides a dendrogram; however, this differs slightly from the one presented in Fig. 9. 9. Speci? cally, SPSS rescales the distances to a range of 0–25; that is, the last merging step to a one-cluster solution takes place at a (rescaled) distance of 25. The rescaling often lengthens the merging steps, thus making breaks occurring at a greatly increased distance level more obvious. Despite this, this distance-based decision rule does not work very well in all cases. It is often dif? cult to identify where the break actually occurs. This is also the case in our example above. By looking at the dendrogram, we could justify a two-cluster solution ([A,B,C,D,E,F] and [G]), as well as a ? ve-cluster solution ([B,C,E], [A], [D], [F], [G]). Conducting a Cluster Analysis 255 Research has suggested several other procedures for determining the number of clusters in a dataset. Most notably, the variance ratio criterion (VRC) by Calinski and Harabasz (1974) has proven to work well in many situations. 8 For a solution with n objects and k segments, the criterion is given by: VRCk ? ?SSB =? k A 1 =? SSW =? n A k ; where SSB is the sum of the squares between the segments and SSW is the sum of the squares within the segments. The criterion should seem familiar, as this is nothing but the F-value of a one-way ANOVA, with k representing the factor levels. Consequently, the VRC can easily be computed using SPSS, even though it is not readily available in the clustering procedures’ outputs. To ? nally determine the appropriate number of segments, we compute ok for each segment solution as follows: ok ? ?VRCk? 1 A VRCk ? A ? VRCk A VRCkA1 ? : In the next step, we choose the number of segments k that minimizes the value in ok. Owing to the term VRCkA1, the minimum number of clusters that can be selected is three, which is a clear disadvantage of the criterion, thus limiting its application in practice. Overall, the data can often only provide rough guidance regarding the number of clusters you should select; consequently, you should rather revert to practical considerations. Occasionally, you might have a priori knowledge, or a theory on which you can base your choice. However, ? rst and foremost, you should ensure that your results are interpretable and meaningful. Not only must the number of clusters be small enough to ensure manageability, but each segment should also be large enough to warrant strategic attention. Partitioning Methods: k-means Another important group of clustering procedures are partitioning methods. As with hierarchical clustering, there is a wide array of different algorithms; of these, the k-means procedure is the most important one for market research. The k-means algorithm follows an entirely different concept than the hierarchical methods discussed before. This algorithm is not based on distance measures such as Euclidean distance or city-block distance, but uses the within-cluster variation as a Milligan and Cooper (1985) compare various criteria. Note that the k-means algorithm is one of the simplest non-hierarchical clusteri ng methods. Several extensions, such as k-medoids (Kaufman and Rousseeuw 2005) have been proposed to handle problematic aspects of the procedure. More advanced methods include ? ite mixture models (McLachlan and Peel 2000), neural networks (Bishop 2006), and self-organizing maps (Kohonen 1982). Andrews and Currim (2003) discuss the validity of some of these approaches. 9 8 256 9 Cluster Analysis measure to form homogenous clusters. Speci? cally, the procedure aims at segmenting the data in such a way that the within-cluster variation is minimized. Consequently, we do not need to decide on a distance measure in the ? rst step of the analysis. The clustering process starts by randomly assigning objects to a number of clusters. 0 The objects are then successively reassigned to other clusters to minimize the within-cluster variation, which is basically the (squared) distance from each observation to the center of the associated cluster. If the reallocation of an object to another cluste r decreases the within-cluster variation, this object is reassigned to that cluster. With the hierarchical methods, an object remains in a cluster once it is assigned to it, but with k-means, cluster af? liations can change in the course of the clustering process. Consequently, k-means does not build a hierarchy as described before (Fig. . 3), which is why the approach is also frequently labeled as non-hierarchical. For a better understanding of the approach, let’s take a look at how it works in practice. Figs. 9. 10–9. 13 illustrate the k-means clustering process. Prior to analysis, we have to decide on the number of clusters. Our client could, for example, tell us how many segments are needed, or we may know from previous research what to look for. Based on this information, the algorithm randomly selects a center for each cluster (step 1). In our example, two cluster centers are randomly initiated, which CC1 (? st cluster) and CC2 (second cluster) in Fig. 9. 10 A CC 1 C B D E Brand loyalty (y) CC2 F G Price consciousness (x) Fig. 9. 10 k-means procedure (step 1) 10 Note this holds for the algorithms original design. SPSS does not choose centers randomly. Conducting a Cluster Analysis A CC1 C B 257 D E Brand loyalty (y) CC2 F G Price consciousness (x) Fig. 9. 11 k-means procedure (step 2) A CC1 CC1? C B Brand loyalty (y) D E CC2 CC2? F G Price consciousness (x) Fig. 9. 12 k-means procedure (step 3) 258 A CC1? 9 Cluster Analysis B C Brand loyalty (y) D E CC2? F G Price consciousness (x) Fig. 9. 13 k-means procedure (step 4) epresent. 11 After this (step 2), Euclidean distances are computed from the cluster centers to every single object. Each object is then assigned to the cluster center with the shortest distance to it. In our example (Fig. 9. 11), objects A, B, and C are assigned to the ? rst cluster, whereas objects D, E, F, and G are assigned to the second. We now have our initial partitioning of the objects into two clusters. Based on this i nitial partition, each cluster’s geometric center (i. e. , its centroid) is computed (third step). This is done by computing the mean values of the objects contained in the cluster (e. . , A, B, C in the ? rst cluster) regarding each of the variables (price consciousness and brand loyalty). As we can see in Fig. 9. 12, both clusters’ centers now shift into new positions (CC1’ for the ? rst and CC2’ for the second cluster). In the fourth step, the distances from each object to the newly located cluster centers are computed and objects are again assigned to a certain cluster on the basis of their minimum distance to other cluster centers (CC1’ and CC2’). Since the cluster centers’ position changed with respect to the initial situation in the ? st step, this could lead to a different cluster solution. This is also true of our example, as object E is now – unlike in the initial partition – closer to the ? rst cluster center (CC1’) than to the second (CC2’). Consequently, this object is now assigned to the ? rst cluster (Fig. 9. 13). The k-means procedure now repeats the third step and re-computes the cluster centers of the newly formed clusters, and so on. In other 11 Conversely, SPSS always sets one observation as the cluster center instead of picking some random point in the dataset. Conducting a Cluster Analysis 59 words, steps 3 and 4 are repeated until a predetermined number of iterations are reached, or convergence is achieved (i. e. , there is no change in the cluster af? liations). Generally, k-means is superior to hierarchical methods as it is less affected by outliers and the presence of irrelevant clustering variables. Furthermore, k-means can be applied to very large datasets, as the procedure is less computationally demanding than hierarchical methods. In fact, we suggest de? nitely using k-means for sample sizes above 500, especially if many clustering variables are used. From a strictly statistical viewpoint, k-means should only be used on interval or ratioscaled data as the procedure relies on Euclidean distances. However, the procedure is routinely used on ordinal data as well, even though there might be some distortions. One problem associated with the application of k-means relates to the fact that the researcher has to pre-specify the number of clusters to retain from the data. This makes k-means less attractive to some and still hinders its routine application in practice. However, the VRC discussed above can likewise be used for k-means clustering an application of this index can be found in the 8 Web Appendix ! Chap. 9). Another workaround that many market researchers routinely use is to apply a hierarchical procedure to determine the number of clusters and k-means afterwards. 12 This also enables the user to ? nd starting values for the initial cluster centers to handle a second problem, which relates to the procedure’s sensitivity to the initial classi? cation (we will follow this approach in the example application). Two-Step Clustering We have already discussed the issue of analyzing mixed variables measured on different scale levels in this chapter. The two-step cluster analysis developed by Chiu et al. (2001) has been speci? cally designed to handle this problem. Like k-means, the procedure can also effectively cope with very large datasets. The name two-step clustering is already an indication that the algorithm is based on a two-stage approach: In the ? rst stage, the algorithm undertakes a procedure that is very similar to the k-means algorithm. Based on these results, the two-step procedure conducts a modi? ed hierarchical agglomerative clustering procedure that combines the objects sequentially to form homogenous clusters. This is done by building a so-called cluster feature tree whose â€Å"leaves† represent distinct objects in the dataset. The procedure can handle categorical and continuous variables simultaneously and offers the user the ? exibility to specify the cluster numbers as well as the maximum number of clusters, or to allow the technique to automatically choose the number of clusters on the basis of statistical evaluation criteria. Likewise, the procedure guides the decision of how many clusters to retain from the data by calculating measures-of-? t such as Akaike’s Information Criterion (AIC) or Bayes 2 See Punji and Stewart (1983) for additional information on this sequential approach. 260 9 Cluster Analysis Information Criterion (BIC). Furthermore, the procedure indicates each variable’s importance for the construction of a speci? c cluster. These desirable features make the somewhat less popular two-step clustering a viable alternative to the traditional methods. Y ou can ? nd a more detailed discussion of the two-step clustering procedure in the 8 Web Appendix (! Chap. 9), but we will also apply this method in the subsequent example. Validate and Interpret the Cluster Solution Before interpreting the cluster solution, we have to assess the solution’s stability and validity. Stability is evaluated by using different clustering procedures on the same data and testing whether these yield the same results. In hierarchical clustering, you can likewise use different distance measures. However, please note that it is common for results to change even when your solution is adequate. How much variation you should allow before questioning the stability of your solution is a matter of taste. Another common approach is to split the dataset into two halves and to thereafter analyze the two subsets separately using the same parameter settings. You then compare the two solutions’ cluster centroids. If these do not differ signi? cantly, you can presume that the overall solution has a high degree of stability. When using hierarchical clustering, it is also worthwhile changing the order of the objects in your dataset and re-running the analysis to check the results’ stability. The results should not, of course, depend on the order of the dataset. If they do, you should try to ascertain if any obvious outliers may in? ence the results of the change in order. Assessing the solution’s reliability is closely related to the above, as reliability refers to the degree to which the solution is stable over time. If segments quickly change their composition, or its members their behavior, targeting strategies are likely not to succeed. Therefore, a certain degree of stability is necessary to ensure that marketing strategies can be implemented and produce adequate results. This can be evaluated by critically revisiting and replicating the clustering results at a later point in time. To validate the clustering solution, we need to assess its criterion validity. In research, we could focus on criterion variables that have a theoretically based relationship with the clustering variables, but were not included in the analysis. In market research, criterion variables usually relate to managerial outcomes such as the sales per person, or satisfaction. If these criterion variables differ signi? cantly, we can conclude that the clusters are distinct groups with criterion validity. To judge validity, you should also assess face validity and, if possible, expert validity. While we primarily consider criterion validity when choosing clustering variables, as well as in this ? al step of the analysis procedure, the assessment of face validity is a process rather than a single event. The key to successful segmentation is to critically revisit the results of different cluster analysis set-ups (e. g. , by using Conducting a Cluster Analysis 261 different algorithms on the same data) in terms of managerial relevance. This underlines the exploratory charact er of the method. The following criteria will help you make an evaluation choice for a clustering solution (Dibb 1999; Tonks 2009; Kotler and Keller 2009). l l l l l l l l l l Substantial: The segments are large and pro? able enough to serve. Accessible: The segments can be effectively reached and served, which requires them to be characterized by means of observable variables. Differentiable: The segments can be distinguished conceptually and respond differently to different marketing-mix elements and programs. Actionable: Effective programs can be formulated to attract and serve the segments. Stable: Only segments that are stable over time can provide the necessary grounds for a successful marketing strategy. Parsimonious: To be managerially meaningful, only a small set of substantial clusters should be identi? ed. Familiar: To ensure management acceptance, the segments composition should be comprehensible. Relevant: Segments should be relevant in respect of the company’s competencies and objectives. Compactness: Segments exhibit a high degree of within-segment homogeneity and between-segment heterogeneity. Compatibility: Segmentation results meet other managerial functions’ requirements. The ? nal step of any cluster analysis is the interpretation of the clusters. Interpreting clusters always involves examining the cluster centroids, which are the clustering variables’ average values of all objects in a certain cluster. This step is of the utmost importance, as the analysis sheds light on whether the segments are conceptually distinguishable. Only if certain clusters exhibit signi? cantly different means in these variables are they distinguishable – from a data perspective, at least. This can easily be ascertained by comparing the clusters with independent t-tests samples or ANOVA (see Chap. 6). By using this information, we can also try to come up with a meaningful name or label for each cluster; that is, one which adequately re? ects the objects in the cluster. This is usually a very challenging task. Furthermore, clustering variables are frequently unobservable, which poses another problem. How can we decide to which segment a new object should be assigned if its unobservable characteristics, such as personality traits, personal values or lifestyles, are unknown? We could obviously try to survey these attributes and make a decision based on the clustering variables. However, this will not be feasible in most situations and researchers therefore try to identify observable variables that best mirror the partition of the objects. If it is possible to identify, for example, demographic variables leading to a very similar partition as that obtained through the segmentation, then it is easy to assign a new object to a certain segment on the basis of these demographic 262 9 Cluster Analysis characteristics. These variables can then also be used to characterize speci? c segments, an action commonly called pro? ling. For example, imagine that we used a set of items to assess the respondents’ values and learned that a certain segment comprises respondents who appreciate self-ful? lment, enjoyment of life, and a sense of accomplishment, whereas this is not the case in another segment. If we were able to identify explanatory variables such as gender or age, which adequately distinguish these segments, then we could partition a new person based on the modalities of these observable variables whose traits may still be unknown. Table 9. 11 summarizes the steps involved in a hierarchical and k-means clustering. Whi le companies often develop their own market segments, they frequently use standardized segments, which are based on established buying trends, habits, and customers’ needs and have been speci? ally designed for use by many products in mature markets. One of the most popular approaches is the PRIZM lifestyle segmentation system developed by Claritas Inc. , a leading market research company. PRIZM de? nes every US household in terms of 66 demographically and behaviorally distinct segments to help marketers discern those consumers’ likes, dislikes, lifestyles, and purchase behaviors. Visit the Claritas website and ? ip through the various segment pro? les. By entering a 5-digit US ZIP code, you can also ? nd a speci? c neighborhood’s top ? ve lifestyle groups. One example of a segment is â€Å"Gray Power,† containing middle-class, homeowning suburbanites who are aging in place rather than moving to retirement communities. Gray Power re? ects this trend, a segment of older, midscale singles and couples who live in quiet comfort. http://www. claritas. com/MyBestSegments/Default. jsp We also introduce steps related to two-step clustering which we will further introduce in the subsequent example. Conducting a Cluster Analysis 263 Table 9. 11 Steps involved in carrying out a factor analysis in SPSS Theory Action Research problem Identi? ation of homogenous groups of objects in a population Select clustering variables that should be Select relevant variables that potentially exhibit used to form segments high degrees of criterion validity with regard to a speci? c managerial objective. Requirements Suf? cient sample size Make sure that the relationship between objects and clustering variables is reasonable (rough guideline: number of obse rvations should be at least 2m, where m is the number of clustering variables). Ensure that the sample size is large enough to guarantee substantial segments. Low levels of collinearity among the variables ? Analyze ? Correlate ? Bivariate Eliminate or replace highly correlated variables (correlation coef? cients 0. 90). Speci? cation Choose the clustering procedure If there is a limited number of objects in your dataset or you do not know the number of clusters: ? Analyze ? Classify ? Hierarchical Cluster If there are many observations ( 500) in your dataset and you have a priori knowledge regarding the number of clusters: ? Analyze ? Classify ? K-Means Cluster If there are many observations in your dataset and the clustering variables are measured on different scale levels: ? Analyze ? Classify ? Two-Step Cluster Select a measure of similarity or dissimilarity Hierarchical methods: (only hierarchical and two-step clustering) ? Analyze ? Classify ? Hierarchical Cluster ? Method ? Measure Depending on the scale level, select the measure; convert variables with multiple categories into a set of binary variables and use matching coef? cients; standardize variables if necessary (on a range of 0 to 1 or A1 to 1). Two-step clustering: ? Analyze ? Classify ? Two-Step Cluster ? Distance Measure Use Euclidean distances when all variables are continuous; for mixed variables, use log-likelihood. ? Analyze ? Classify ? Hierarchical Cluster ? Choose clustering algorithm Method ? Cluster Method (only hierarchical clustering) Use Ward’s method if equally sized clusters are expected and no outliers are present. Preferably use single linkage, also to detect outliers. Decide on the number of clusters Hierarchical clustering: Examine the dendrogram: ? Analyze ? Classify ? Hierarchical Cluster ? Plots ? Dendrogram (continued) 264 Table 9. 11 (continued) Theory 9 Cluster Analysis Action Draw a scree plot (e. g. , using Microsoft Excel) based on the coef? cients in the agglomeration schedule. Compute the VRC using the ANOVA procedure: ? Analyze ? Compare Means ? One-Way ANOVA Move the cluster membership variable in the Factor box and the clustering variables in the Dependent List box. Compute VRC for each segment solution and compare values. k-means: Run a hierarchical cluster analysis and decide on the number of segments based on a dendrogram or scree plot; use this information to run k-means with k clusters. Compute the VRC using the ANOVA procedure: ? Analyze ? Classify ? K-Means Cluster ? Options ? ANOVA table; Compute VRC for each segment solution and compare values. Two-step clustering: Specify the maximum number of clusters: ? Analyze ? Classify ? Two-Step Cluster ? Number of Clusters Run separate analyses using AIC and, alternatively, BIC as clustering criterion: ? Analyze ? Classify ? Two-Step Cluster ? Clustering Criterion Examine the auto-clustering output. Re-run the analysis using different clustering procedures, algorithms or distance measures. Split the datasets into two halves and compute the clustering variables’ centroids; compare ce How to cite Cluster Analysis, Essay examples

Evolution and Pragmatism free essay sample

Pragmatic Ethics As a Descriptive Theory 2. Pragmatic Ethics As a Normative Ethics 3. Conclusions PRAGMATISM Recently development shows us the Pragmatism is likely the theory of a meaning, an inquiry, a truth and an ethics. In that aspect Pragmatism can be declared as cohesion between different opinions. Furthermore Pragmatism can be a bridge which balances those differences and get those theories in to synthesis. It IS be against of Preconception, Dogmatism and Authoritative solutions. But in a contrary way, Pragmatism considers importance of pluralism, collective notion and humanism. Thus Pragmatism is being as an evolutionary liberal philosophy. Pragmatism is being developed mainly by Charles Sanders Pierce, William James and John Dewey. In generally Pragmatism considered in a different way as a Person do anything whatever he/she wants in manner of his profit. But that phenomenon cannot be defined in one sentence. Actually Pragmatism can be divided into 4 different kind of theory as considered above in the first paragraph. Therefore meaning of Pragmatism considered in that different kind of aspects. PRAGMATISM AS A THEORY OF MEANING Pragmatism discussed as a theory of meaning by one of its developer from Charles Sanders Price. According to him, any opinion of us about stuff comes from the noticeable effects of that stuff. As an example a book of Kerchief which has been published with name of Analytical Mechanics being criticized by Price. In that book according to Kerchief a Person can understand the effects Of power but it is invisible.But Price said that if we truly know about the effects of Power, we therefore know the entire happening situation which is mentioned by existence of Power and nothing more required to know. Therefore according to Pragmatist meaning of a concept appears by the help of action, situation or etc.. . It doesnt make a cost that whatever we thought/designed about a concept. So the real worth of that concept will be defined by help of relationship of a Person with its environment. Result of our experiments will tell us about the real worth of those concepts.Although Price was the founder of Pragmatism, actually that philosophy became a famous over the World by contribution of William James. Sesames Pragmatism is differing from Pierces in 3 manners. First of all according to Price, Pragmatism is not totally but as essentially consists of a theory of meaning. But this vision didnt accept by James due to his implementation of Pragmatism into metaphysical aspects. Those different opinions depend on transferring of Sesames attention from meanings into affects.As an example he didnt only think about scalded hand under the fire also he thought that how should be reacted when a fire been seen. PRAGMATISM AS A THEORY OF INQUIRY Pragmatism can be seen as a theory of inquiry. According to Pragmatist, a Person interrogates the meaning of concepts only when some other influences/threats affects into its opinion. In that situation that Person who has threatened from its environment starts to adopt against those threats. Therefore inquiry being defined by Price as transferring effort from suspicion into belief. He says; if suspicion has been started a state of belief has also been started. Therefore according to him purpose of inquiry is a settlement of opinion. As happens in the aspect of meaning theory, James and Dewey thinks not the same as Price in inquiry theory. Dewey tells us about the steps which should be taken from a Person who has a suspicion. So according to Dews Pragmatism slight, inquiries should find solution for the problems which happens in environment The difference slight between James and Dewey is considered by a scientist.He said that; Pierces inquiry comprehension depends on defining satisfactions but as a contrary Dewey aims to fixing its position. As an understood from that debate, starting point of Pragmatism is not suspicion also it is about established principles/beliefs. According to Price by defining the beliefs 3 different ways is being used as a traditionally. But he suggests handling a new scientific technique. Those 3 different ways are; the first one People dont want to see what happens in their environment. Price calls that way as tenacity.The second way calls as n authority. In that situation beliefs are been defined by any corporations. Price thinks that the first and the second methods are unsuccessful due to beliefs of a Person cannot be controlled by whatsoever corporations. The third and also the last way calls as a priori. It is not differ from the method of authority but according to that method acting of a Person depends on established principles. Judgments like people are good or Nature of all People are bad defines how a Person act and beliefs into what.If those beliefs doesnt support by the truth they wont be counted as a rue from Pragmatist, albeit suitably. Price says that if a Person realizes that his belief has been shaped by an insubstantial situation/case, he gets doubt on its belief. After that point those beliefs lose their attributes. Therefore, according to Price by making a decision and creating some of our beliefs we shouldnt take care of those above given 3 different traditionally methods. Instance of considering those traditionally methods, method of science can be used to define our beliefs.That science method consists of 3 different phase. In first phase a Person should create some hypothesis to decide which f its belief take roll on. This called as abduction. After that a Person makes some inferences from its hypothesis. This called deduction. At last phase a Person acts likely to that result and defines whether its inferences happen or not. That is called induction. PRAGMATISM AS A THEORY OF TRUTH According to Pragmatist the not only important thing is how getting our beliefs also at same time the truth of those beliefs are much important.About the reality Price says that; truth is any of idea which can be accepted by a person who has investigated. But according to James and Dewey; the truth of NY beliefs can be measured by success of solving some problems in our lives. In that aspects Price and James have nearly the same slight about the truth. PRAGMATISM AS A THEORY OF ETHICS Pragmatism can be measured as a theory of ethics. So far we can easily predict what actually Pragmatism defending on. First of all, Pragmatism refuses dogmatic approach into ethics and there is not any rule which forces a Person acting in a pre-definite boundary.According to James none of an ethic philosophy is being created in a dogmatic way and he adds that being suitable to humanism and interactions ontology, Pragmatism declares that ACH problems has own quality and therefore, different solutions methods must be approved to get solution for each problems. Thus, according to theory Of pragmatism creating ethical philosophy is not being completed yet, perhaps it will never be accomplished. James says that; final truth can never be reached until a Person, who the latest one in this World is, gets some experiences and telling what its inferences from those experiences.Pragmatism aims to placing sophistication in a daily life of a Person. Firstly, Pragmatism refuses two identical approaches to events and objects like a goal-tool distinction. As an example Dewey says that we cannot realize the final g oals of our behaviors, on the contrary goals which are so close to us can be realized much easily. From that aspect, according to Pragmatism, to ensure solving so many problems in our environment principles of ethics must be defined as an induction phase by the help of our brains.Ethic comprehension of Pragmatism is differing from ethic comprehension of both deontological and utilitarianism approaches. By deciding the quality of a behavior deontological approaches emphasize the importance Of tools and morality but utilitarianism approaches emphasize only goals and their results. But according to Pragmatism nor tools neither goals should become count on because they both influences each others. Hence, Pragmatist thinks that ethical behaviors must consist of both morality and successfully results. But dont remember that thus opinions only define the general boundary of ethic comprehension.The precise definition of ethical behavior for each situation depends on type of situation. To get successfully results human experiences and brains needed according to specification of situation. PRAGMATIC ETHICS AS A DESCRIPTIVE THEORY Price provides a teleological framework for pragmatic ethics drawn from two important intellectual developments of the 19th century: the central limit theorem and Darnings theory of evolution, both of which continue to be counted as fundamental theorems of statistics and biology. Price is also keen to show how they complement one another.The central limit theorem states that random processes, such as rolling dice, the velocity of gas molecules in a closed container, or sampling arbitrarily from a population, will express itself by the Gaussian power law-?the familiar bell-shaped curve, or normal distribution as Price originally coined the term. Price likes to say hat this theorem proves chance begets order. More generously interpreted, the central limit theorem suggests that phenomena have a tendency towards self-morning, or as Price would put it, .. . All things have a tendency to take habits.For Every conceivable real object, there is a greater probability of acting as on a former like occasion than otherwise.. . Price calls these pinions processes, in that direction emerges in and through their interactive behavior. The central limit theorem had enormous import for Price. One important sense is derived from his work on calculating observation errors in astronomy. If all observations of a star are assumed wrong, it is possible to determine the approximately correct position of the star, based on the central limit theorem and the method of least squares.All observations are subject to error, but get self-corrected in comparison with more observations; the larger the sample of observations, the more likely the resultant line of best fit is the correct position of the star. Thus, truth emerges from the self, correction of error through a sufficiently long process of inquirythe central theme of Pierces theory of inquiry. The second import of the central limit hurry is that it shows all laws are habits with variations. Their indurate character is measured by the range of deviations.Dynamic variations from the norm and can lead to subtle, sometimes dramatic changes in habits. This requires some mechanism of selection that allows for the prosperity of the central tendency, or some of its deviations. For example, when this concept is applied to thermodynamic concepts such as the gas behavior in a closed container-?the second law argues that velocities of the gas molecules will settle around a normative, I. E. , uniform velocity, best expressed by the Gaussian power curve. Yet, as Maxwell showed, precisely because it is a central tendency, there are variations in that velocity and, in principle, mechanisms;such as Maxwell could select molecules in a manner that take advantage of those deviations. Price notes the linkage to evolution theoryselection of variations from a norm will result in subtle, sometimes radical shifts and, cumulatively, over time, could result in a significant change in the fabric of things. The hypothesis suggested by the present writer is that all laws are results of evolution; that underlying all other laws The tendency of all things to take habits.. .. If law is a result of evolution It follows that no law is absolute. That is, we must suppose that the phenomena themselves involve departures from law analogous to errors of observation. . In so far as evolution follows a law, the law of habit, instead of being a movement from homogeneity to heterogeneity, is growth from deformity to uniformity. But the chance divergences from law are perpetually acting to increase the variety of the world, and are checked by a sort of natural selection.The central limit theorem and the theory of evolution are implementers in the sense that the former permits the possibility of variation, and the latter provides selection devices which perpetuate variations. As we know, Darnings theory accounts elegantly for the variety of species through relatively simple processes of variation and selection. The development of genetics provided, auspiciously, the detailed mechanisms for transmission of traits and their variations.Although Price recognized the power of Darnings theory, he believed that the evolution of certain phenomena-?especially cultural and technological onescould not be fully explained by the fortuitous processes of natural selection alone. The development in the history of thought seems to outpace any form of biological evolution. Compared to the biological evolution from homo sapiens to homo sapiens sapiens in a period of roughly 200,000 years, innovations in technology have changed rapidly in a mere 4,000 yearsa factor of 50. For this reason, Price believed that Lamarckian evolution was an appropriate explanation Of cultural evolution.In this respect he stands in good company with several contemporary thinkers. As we know Lamarckian theory fails as n account of biological evolution. It claims there can be genotypes inheritance of acquired phenotypes characteristics in the evolutionary process. In Darwinian theory, the phenotype is an expression of a genotype; environmental pressures select phenotypes which reproduce the information expressed in their genotype to a next generation; mutations and fortuitous variations are passed on and feed into the success or failure of selection.As Price knew, Wassermann (1883) showed that acquired changes to the body of an organism during its lifetime did not affect the gametes or sex cells of an organism, demonstrating a biological barrier to the transmission of acquired traits to the next generation. However, Lamarckian evolution more easily explains rapid evolutionary changes in culture. According to Geoffrey Hodgkin, Lamarckian, as an account of social evolution, is not incompatible with Darwinian-based biotic evolution. Darwinism could account for th e emergence of learning capacity, which in turn feeds into the possibility of a Lamarckian-like process. For Hodgkin, the notion of habit is a key concept in the theoretical explanation of such change, and recognizes the contribution of the pragmatists to this action (Hodgkin, forthcoming). The notion of habit provides an alternative to Dianna explanations of cultural change, such as Disdains memorial. Although this debate cannot be pursued here, it is important to note that even a strong critic of Lamarckism, Daniel Detente, argues that the theory is a plausible account of non-genetic inheritances (Detente 1995).As Price says, Lamarckian evolution is Evolution by the force of habit. Habit Forces [new elements] to take practical shapes, compatible with the structure they affect, and in the form of heredity and otherwise, gradually replaces the pantones energy that sustains them. Thus, habit plays a double part; it serves to establish the new features, and also to bring them into harmony with the general morphology and function of the animals and plants. Habits are bridging mechanisms between the biological and socio-cultural domains.The purposive drive of individuals contributes directly to the reinforcement or change of certain habits, which are then passed on generational in the form of local institutionalized practices. Habits are not dispositions, but as Dewey argues, The cooperation of organism and environment. Walking implicates the ground as well as the legs. They are things done by the environment by means of organic structures or acquired dispositions. Price says the stream of water that wears a bed for itself is forming a habit The point is that, even if the capacity for a habit is immanent to an organism, habits are not.They are formed in the interstices between organism and its habitat. Virtues and vices, Dewey says, are working adaptations of personal capacities with environing forces. Dewey believes habits start as an activity by someone which sets up reaction in the surroundings others approve, sportive, protest, encourage, share and resent. So, in this respect, conduct is always shared. As shared, habits are formed through the convergence of the behavior of individuals within their environment, so is a pinions process.Brushing ones teeth is not a disposition in the person but, rather-?figuratively speaking-?a channel dug into the fabric of peoples immediate internal and external environment. The very presence of equipment and the establishment of habitat for brushing suggests a history and effort of institutionalizing, offices for its practice, and teaching for ourselves and our children. In effect, the brushing habit is a capacity realized in the organization of the environment in which it is exercised, its institutionalizing in the larger culture. This easily translates to moral habits. Moral agents are already habituated. Although it is always possible to deviate from these moral habits, they constitute the bulwark of the working part Of moral life, and are ingrained in institutions and practices. In a well-ordered society, most people are not in the habit of killing; practices and institutions are established to mollify frustrations, anger, conflict, and, individuals have acquired mental and emotional habits that do the same thing-?- reinforcing and being reinforced by institutions and practices.Habits provide us with an ethical tens, a ready-made repertoire of actions and conduct. As Pierce says the pursuit of a conscience, if one hasnt one already.. . Seems to me an aimless and hypochondriac pursuit. If a man finds himself under no sense of obligation, let him congratulate himself. For such a man to hanker after a bondage to conscience, is as if a man with a good digestion should cast about for a regiment of food. A conscience, too, is not a theorem or a piece of information Acquired by reading a book; it must be bred in a man from infancy or it will be a poor imitation of the genuine article.If a man has a conscience, it may be an article of faith with him that he should reflect upon that conscience, and thus Receive a further development. But it never will do him the least good to get up a make-believe skepticism and pretend to himself not to believe what he really does believe. Most people act morally on the basis of existing habits; it is only when habits fail to address novel situations, or external and internal conflicts that genuine moral deliberation sakes place. Deliberation, however, is not a monotonic process, but eclectic.Dewey says we are not consistently rational maximizes, or even satisfiers, but use methods appropriate to our sense of ourselves as moral agents, conceptualized to the practice and situation The office of deliberation is not to supply an inducement to act by figuring out where the most advantage is to be procured. It is to resolve entanglements in existing activity, restore continuity, recover harmony, utilize loose impulse and redirect habit. Analogous to the behavior of gas particles, moral agents fitted by the ability of self-correction are similarly pinions.Their interaction Will produce a morning, and under the assumption that everyone is wrong, yet capable Of correction, a vector will emerge, not determinately, but in the very process of morning -?what Dewey calls the mutual modification of habits. This is not a natural selection theory, butt conscious selection theorythe tendency towards a result is itself the re sult of controlled selection by agents. In practical terms, norms result from an effort by communities of moral agents to select for better norms, to engage in a process of the fixation of habits. Deer the right conditions the tendency is for those agents to select better. In this regard there is a parallel, for Price, between convergence towards a true belief and a right norm. This Lamarckian-process thereby distinguishes itself from Darwinian ones by this contact for improvement which Price sometimes whimsically calls evolutionary love, and which captures Cants original sense of pragmatic: pragmatic knowledge aims at improvement, according to self-adopted purposes, and which the human species can work Only through continuous progress within an endless sequence of many generations.Living in the milieu of social Darwinism, Price characterized its ethos as a competition among individuals for survival, the selection process prospering the fittest, and foregoing the less fit. Price depicts Darwinism as a zero-sum game among gamblers in which each generation will become smaller but, at the same time, richer. Lamarckian processes emphasize cooperation instead as the primary mode of inheritance because of the very nature of the formation of habits-?which requires the behavior of individuals converge to some degree.Darwinian processes only require individuals to successfully reproduce. For Alarmists the lack of cooperation is the anomaly to be explained; for Darwinism, cooperation is the anomaly. PRAGMATIC ETHICS AS A NORMATIVE ETHICS Pragmatic ethics is in part a descriptive theory arguing that ethical norms emerge through a pinions process created when norms correct against each other, a process parallel to Pierces convergence theory of truth: just as the history of thought shows fixation of belief, human history shows the fixation of habits.But in order for pragmatic ethics to be effective, it must also provide a normative theory, establishing criteria fo r the evaluation of habits and emerging norms. Dews rather vague criteria is not very helpful: we should promote habits that simply promote the development of habits. Nor are his followers much more helpful. La Foliate, for example, attempts the trick of suggesting that pragmatic ethics employs criteria but is not criteria, which is patently paradoxical.In effect, the descriptive aspect of pragmatic ethics says that self-morning happens; that-?comparable to Newtons first lawhabits have a tendency to remain in place until met with a force that opposes them; and that the result of such disruptions is that a second, self- morning process results. If this is the case Pragmatic Ethics is in danger of being committed to these morally doubtful claims: 1 . Whatever dominant norm emerges is the right norm. 2. Whatever norm persists is the right norm. TO counter their obvious flaws, it must be supposed that: 1 .The right norm will eventually emerge as a central tendency, but not all central tendencies will be right. 2. The right norm will persist, but not everything that persists should be counted as right. Thus, although the presence of central tendency and persistence is a necessary condition for the rightness of norms, they are not sufficient conditions. Some of this criteria for the sufficient conditions can be found in Pierces theory of inquiry. If there is a parallel between the fixation of beliefs and the fixation of ethical habits, then the methods by which morning takes place matters. Following his ideas in The Fixation of Belief, morning by exclusion, authoritative domination, and dogmatic morning allow us to discount certain kind of norms that happen to achieve dominance. In scientific observation, this would be comparable to excluding observations of stars by fiat, or by the fact that they happen to disagree with yours. Second, the scope Of such norms should tater. Analogous to scientific practice, the smaller the sample, the less reliable the results. The law of large numbers suggests that the results of sampling become more accurate as the sample increases in size.Thus, the more inclusive the morning process, the more likely the results will be the right norm. Both Price and Dewey share the normative ideals of a certain type of community necessary for proper inquiry-?both scientifically and ethically. However, Dews notion of the public, and the proper constitution of public discourse may be a more appropriate substitute for the more extractive sense of scientific community found in Price The connection here with Haberdashers and Apples notions of discourse ethics are also worth exploring.CONCLUSION All of investigation show us that Pragmatism isnt imitative and cannot be defined so easily as a utilitarianism. It was founded towards the 20th century in United States of America and nearly all the root of sciences have been affected by that philosophy. Depending on the theory of meaning, the real worth of any concept is being formed from its perceivable affects. Therefore those meaning will not appear in theoretical meaning, contrary will appear in NY case or happens. Pragmatic approach is not only helpful for appearing that meaning also helps for how to elicit for those.As an example if we thought about the war, it is not meaningful that thinking of war only a victory. Also one of perceivable affects of war is death and destroying. Namely if facet of wars are also well-known about that reality of death and destroying, they will able to realized a more sensational behavior like a rationalism. Depending on the theory of inquiry, Pragmatism emphasizes passing through from suspicion into beliefs. If the beliefs of Person are threatened by its environment, incompatibility between a Persons own beliefs and its environment will increases.Therefore some of its conviction/satisfaction will be out, and new suspicious will be appeared. Here comes the most important question; how can a Person define its own conviction situation? As an answer, according to Pragmatism scientific methods must take a place in this moment. Those methods should be helpful for a Person whose beliefs have been threatened by environment. Because a Person will be orientated by the factor of human in the methods of tenacity, authority and priorities. So he/ she will again believe into full of mistakes.But on the other hand science is an objective and only science has a capacity to realize its own mistakes and fix it back. So according to Pragmatism convictions and beliefs must be formed by an external continuity. Depending on the theory of truth, Pragmatism defines the truth as an inevitable thing that cannot be refused by the investigators in the future. In that definition accent held in the future terms. In that time none of the investigators may not be likened in a certain tasks, but in the future phase they will be met in a special point where all of investigators opinion will coincide. By the help of that coincide, opinion of that objective will be proved. This is like an evolutionary ontology. So with the contribution Of evolutionary truth comprehension, Pragmatism is placed in the opposite side of both absolutism and skepticism. Depending on the theory of ethics, Pragmatism refuses the existence of ethics concepts which forces a Person to act in a certain boundary. Seeing that the truth will be defined in the future phase and depending that People believes into different things and acts also in different way from each others. If so, according to Pragmatism the existence of unchangeable ethics concepts cannot be defended.Each Person will reach his/her own truths and will define ethics concepts which will suitable for him/ her. So Pragmatism defends pluralism. That pluralism concept tries to make some equilibrium been personal values and social values. Improvement on the ethics depends on defining cohesion between values as well as possible and after getting definition should do some analysis on it. By the way Pragmatism refuses to think about any certain happen just only looking for tools and goals. However tools and goals are also important but before making a decision should have searched for interactions between those incepts.As a conclusion Pragmatism refuses demonology approaches and utilitarianism. As we understood from this essay, Pragmatism is an evolutionary liberal philosophy and aims to evolutionary improvement by the help of changes. Explicitly refuses about radical opinions. In that aspect Pragmatism can be seen as a bridge which balances the opposite slights and getting analyze them. Also Pragmatism is optimist for thinking about our World is getting a greater place to live it on. As a last word on Pragmatism; it will be helpful philosophy when it is fully-learned from the investigators.