A Step by Step Guide for SPSS and Exercise Studies

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Statistical tests 133 4. Homogeneity of variance-covariance matrices. This assumption states that variance-covariance matrices in each predicted group should be similar (i.e., come from similar populations). Results of classification analysis (see below) may well be affected by violations of this assumption. The homogeneity of variance-covariance matrices assumption can be tested by using the Box’s M test (see below). However, this test is very sensitive and is likely to produce significant results (i.e., indicate that the homogeneity assumption cannot be accepted). You can also check this assumption by looking at the separate group plots (see below). Scatterplots of scores which are roughly equal in size indicate homogeneity of variance-covariance matrices. You can also request the separate group covariance matrices (see below) to examine whether the covariances between the predictor variables are considerably different among the predicted groups. Tabachnick and Fidell (1996) argue that discriminant analysis is relatively robust to violations of this assumption, provided that the group sizes are equal or large. How to carry out the test Suppose you have coded a group of gymnasts as qualifiers (code 1) and nonqualifiers (code 2) for a national competition. Also, suppose you have measured gymnasts’ confidence, relaxation, and anxiety levels prior to the trials. You are interested to examine whether these three measures can distinguish between qualifiers and non-qualifiers. If they are good predictors, they will be able to maximise the differences between the two groups and classify correctly a large number of cases (gymnasts) into their appropriate groups (Figure 40). Select the dependent variable qualific and move it into the Grouping Variable box. Click Define Range to define the two groups. Move the predictor variables into the Independents box. If you want to carry out the analysis for a subset of the sample only (e.g., females), click Select, identify the selection variable (i.e., gender) and type the appropriate value (e.g., 1 if this value has been used in the data file to identify females). There are two main methods of analysis: the forced entry method (enter independents together) and the stepwise. For a discussion of the advantages and disadvantages of each method, you should consult appropriate statistical texts. In Dialog box 88, the forced entry method is used. Click on Statistics to open Dialog box 89. Select Means to produce a table with the mean scores and standard deviations of all independent variables in each group and in the whole sample. Univariate ANOVAs perform one-way ANOVA tests to examine whether the two groups have the same mean on each of the predictor variables. A different ANOVA is produced for each predictor in the discriminant model. The major discriminant predictors should have significantly different group means (i.e., the F value of the ANOVA should be significant). The Box’s M is a test of the equality of the group covariance matrices (see assumptions of discriminant analysis above). The average of the covariance matrices of all groups can be requested by ticking the within-groups covariance matrix. Alternatively, you can ask SPSS to display the covariance matrix of each group separately (separate-group covariance matrix).
134 Statistical tests Figure 40 Dialog box 88 In Dialog box 88 click on Classify to open Dialog box 90. Usually, you expect that participants have equal probabilities to belong to one of the two groups, therefore you select the All groups equal option. However, if you want to base the calculation of probabilities on the number of cases in each group, select the Compute from group sizes option. Display Casewise Results will produce a table with the actual and predicted group membership for each case. It will also
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A Step-by-Step Guide to SPSS for Sp
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First published 2001 by Routledge 1
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Contents Preface Acknowledgements x
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Contents 4 Chart and table options
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Preface This book intends to fill i
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Acknowledgements The comments and s
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2 Introduction variety of options a
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4 Introduction Data Entry Each row
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252 Index discriminant analysis 2,
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