Inferential Statistics in SPSS: Writing About Your Outputs

One of the goals of this book is to help you write a research report or thesis using the outputs. Thus, we have provided an example later that could be two paragraphs from a research paper based on the expanded HSB data used in the assignments in this book. Before demonstrating how you might

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Problem 7.1: Chi-Square and Phi (or Cramer’s V) with SPSS

The statistics discussed in this first problem are designed to analyze two nominal or dichotomous variables. Remember, nominal variables are variables that have distinct unordered levels or categories; each subject is in only one level (you can only be male or female). Chi-square (x2) or phi/Cramer’s V are good choices for statistics when analyzing

Problem 7.2: Risk Ratios and Odds Ratios with SPSS

When you have two dichotomous variables and thus a 2 x 2 contingency table or cross-tabulation, you can compute risk ratios and odds ratios instead of chi-square and phi. These ratios are commonly used to report results in medical, applied health, and prevention science fields. The assumptions for odds ratios are listed under Problem

Problem 7.3: Other Nonparametric Associational Statistics with SPSS

In addition to phi and Cramer’s V, there are several other nonparametric measures of association that we could have chosen in Fig. 7.2. They attempt, in different ways, to measure the strength of the association between two variables. If both variables are nominal and you have a 2 x 2 cross­tabulation, like the one

Problem 7.4: Cross-Tabulation and Eta with SPSS

There is an important associational statistic, eta, that is used when one variable is nominal and the other is approximately normal or scale. We will use this statistic to describe the association between gender and math courses taken (an approximately normal variable with six levels). Eta squared will be an important statistic in later

Problem 7.5: Cohen’s Kappa for Reliability With Nominal Data with SPSS

When we have two nominal variables with the same values (usually two raters’ observations or scores using the same codes), you can compute Cohen’s kappa to check the reliability or agreement between the measures. Kappa has a few assumptions about the underlying nature of the data: 1) Participants are independent of each other, 2)

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Correlation and Regression with SPSS – Problem 8.1: Scatterplots to Check Assumptions

A scatterplot is a plot or graph of two variables that shows how the score for an individual on one variable associates with his or her score on the other variable. If the correlation is high positive, the plotted points will be close to a straight line (the linear regression line) from the lower

Correlation and Regression with SPSS – Problem 8.2: Bivariate Pearson and Spearman Correlations

The Pearson product moment correlation is a bivariate parametric statistic used when both variables are approximately normally distributed (i.e., scale data). When you have ordinal data or when assumptions are markedly violated, one should use a nonparametric equivalent of the Pearson correlation coefficient. One such nonparametric, ordinal statistic is the Spearman rho (another is

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