Correlation and Regression with SPSS – Problem 8.3: Correlation Matrix for Several Variables

If you have more than two ordinal or normally distributed variables that you want to correlate, the program will produce a matrix showing the correlation of each selected variable with each of the others. You could print a matrix scatterplot to check the linear relationship for each pair of variables (see Fig. 8.1). We

Correlation and Regression with SPSS – Problem 8.4: Internal Consistency Reliability With Cronbach’s Alpha

A very common measure of reliability in the research literature is Cronbach’s alpha. It usually is used to assess the internal consistency reliability of several items or scores that the researcher wants to add together to get a summary or summated scale score. Alpha is based on a correlation matrix and is interpreted similarly

Correlation and Regression with SPSS – Problem 8.5: Bivariate or Simple Linear Regression

As stated earlier, the Pearson correlation is the best choice for a statistic when you are interested in the association of two variables that have normal or scale level measurement for the two variables. Correlations do not indicate prediction of one variable from another; however, there are times when researchers wish to make such

Correlation and Regression with SPSS – Problem 8.6: Multiple Regression

The purpose of multiple regression is similar to bivariate regression, but with more predictor variables. Multiple regression attempts to predict a normal (i.e., scale) dependent variable from a combination of several normally distributed and/or dichotomous independent/predictor variables. In this problem, we will see if math achievement can be predicted well from a combination of

Comparing Two Groups with SPSS – Problem 9.1: One-Sample t Test

Sometimes you want to compare the mean of a sample with a hypothesized population mean to see if your sample is significantly different. For example, the scholastic aptitude test was originally standardized so that the mean was 500 and the standard deviation was 100. In our modified HSB data set, we made up mock

Comparing Two Groups with SPSS – Problem 9.2: Independent Samples t Test

When investigating the difference between two unrelated or independent groups (in this case males and females) on an approximately normal dependent variable, it is appropriate to choose an independent samples t test if the following assumptions are not markedly violated. Assumptions of the Independent Samples t Test: The variances of the dependent variable in

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Comparing Two Groups with SPSS – Problem 9.3: The Nonparametric Mann-Whitney U Test

What should you do if the t test assumptions are markedly violated (e.g., what if the dependent variable data are grossly skewed, otherwise non-normally distributed, or are ordinal)? One answer is to run the appropriate nonparametric statistic, which in this case is called the Mann-Whitney (M-W) U test. The M-W is used with a

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Comparing Two Groups with SPSS – Problem 9.4: Paired Samples t Test

In this problem, you will compare the average scores of each HSB student’s father’s and mother’s scores on the same measure, namely, their educational level. Because father’s and mother’s education are not independent of each other, the paired t test is the appropriate test to perform. The paired samples t test is also used

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Comparing Two Groups with SPSS – Problem 9.5: Using the Paired t Test to Check Reliability

In addition to comparing the means for two paired or matched samples, the paired t can be used in connection with checking reliability, especially test-retest or parallel (equivalent) forms reliability. These reliability measures are usually done using a correlation coefficient, so we could have demonstrated test-retest reliability for the visualization test scores in the

Comparing Two Groups with SPSS – Problem 9.6: Nonparametric Wilcoxon Test for Two Related

Let’s assume that education levels and visualization test scores are not normally distributed and/or other assumptions of the paired t test are violated. In fact, mother’s education was quite skewed (see Chapter 4). Let’s run the Wilcoxon signed-ranks nonparametric test to see if fathers have significantly higher educational levels than the mothers and to

Analysis of Variance with SPSS – Problem 10.1: One-Way (or Single Factor) ANOVA

In this problem, you will examine a statistical technique for comparing two or more independent groups on the dependent variable. The appropriate statistic, called One-Way ANOVA, compares the means of the samples or groups in order to make inferences about the population means. One­way ANOVA also is called single factor analysis of variance because

Analysis of Variance with SPSS – Problem 10.2: Post Hoc Multiple Comparison Tests

Now we will introduce the concept of post hoc multiple comparisons, sometimes called follow­up tests. When you compare three or more group means, you know that there will be a statistically significant difference somewhere if the ANOVA F (sometimes called the overall F or omnibus F) is significant. However, we would usually like to

Analysis of Variance with SPSS – Problem 10.3: Nonparametric Kruskal-Wallis Test

What else can you do if the homogeneity of variance assumption is violated (or if your data are ordinal or highly skewed)? One answer is a nonparametric statistic. Let’s make comparisons similar to Problem 10.1, assuming that the data are ordinal or the assumption of equality of group variances is violated. Remember that the

Analysis of Variance with SPSS – Problem 10.4: Two-Way (or Factorial) ANOVA

In previous problems, we compared two or more groups based on the levels of only one independent variable or factor using t tests (Chapter 9) and one-way ANOVA (this chapter). These were called single factor designs. In this problem, we will compare groups based on two independent variables. The appropriate statistic for this is

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Several Measures of Reliability with SPSS – Problem 3.1: Cronbach’s Alpha for the Motivation Scale

The motivation score is composed of six items that were rated on four-point Likert scales, from very atypical (1) to very typical (4). Do the scores for these items go together (interrelate) well enough to add them together for future use as a composite variable labeled motivation? What is the internal consistency reliability of

Several Measures of Reliability with SPSS – Problems 3.2 and 3.3: Cronbach’s Alpha for the Competence and Pleasure Scales

Again, is it reasonable to add the scores for these items together to form summated measures of the concepts of competence and pleasure? What is the internal consistency reliability of the competence scale? What is the internal consistency reliability of the pleasure scale? Let’s repeat the same steps as before to check the reliability

Several Measures of Reliability with SPSS – Problem 3.4: Test-Retest Reliability Using Correlation

Is there support for the test-retest reliability of the two visualization test scores? Let’s do a Pearson r for visualization test and visualization retest scores. Click on Analyze → Correlate → Bivariate. Move variables visualization and visualization retest into the variable box. Do not select flag significant correlations because statistical significance is not important for reliability

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Several Measures of Reliability with SPSS – Problem 3.5: Intraclass Correlation Coefficients (ICC)

ICC performs a reliability analysis for two or usually more judges or observers who have rated the same somewhat subjective behavior. In our example, the mosaic pattern test was given to students; then responses to the test were scored by three different observers, raters, or judges. The scores these judges recorded were called mosaic,

Several Measures of Reliability with SPSS – Problem 3.6: Cohen’s Kappa With Nominal Data

When we have two nominal categorical variables with the same values (usually two raters’ observations or scores using the same codes), we can compute Cohen’s kappa to check the reliability or agreement between the measures. Cohen’s kappa is preferable over simple percentage agreement because it corrects for the probability that raters will agree due

Problem 4.1: Factor Analysis on Math Attitude Variables with SPSS

In Problem 4.1, we perform a principal axis factor analysis on the math attitude variables. Factor analysis is more appropriate than PCA when one has the belief that there are latent variables underlying the variables or items measured. In this example, we have beliefs about the constructs underlying the math attitude questions; we believe

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