SAGE Journal Articles
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Goodman and Kruskal’s τ measure of categorical association is advanced as a replacement for conventional measures of effect size for r × c contingency tables. Goodman and Kruskal’s τ is an asymmetric measure of categorical association which is based entirely on the observed data and possesses a clear interpretation in terms of proportional reduction in error. Comparisons with conventional measures of effect size based on chi-square such as Pearson’s ϕ2, Tschuprow’s T2 and Cramér’s V2 demonstrate the advantages of employing τ as a measure of effect size.
Questions to Consider
1. What do the authors posit as a replacement for conventional measures of effect size for r × c contingency tables?
Cognitive Domain: Comprehension
Difficulty Level: Medium
2. Summarize and briefly explain Goodman and Kruskal’s τ as an asymmetric measure of categorical association.
Cognitive Domain: Knowledge
Difficulty Level: Hard
3. Compare and contrast Goodman and Kruskal’s τ with conventional measures of effect size based on chi-square such as Pearson’s ϕ2, Tschuprow’s T2 and Cramér’s V2.
Cognitive Domain: Comprehension, Analysis
Difficulty Level: Hard
The label “Pearson r” is legitimately used both for the standard Pearson r calculated on continuous variables and for its other varieties in the form of the point biserial or the phi coefficient. This fact is often ignored by psychologists and psychiatrists.
Questions to Consider
1. Summarize and point out what the authors consider a frequent error made by many when referring to Pearson r.
Cognitive Domain: Comprehension
Difficulty Level: Medium
2. Explain how it happens that the errors associated with Pearson r take place and what the significance is of the correlation matrix and the errors being made.
Cognitive Domain: Comprehension, Analysis
Difficulty Level: Hard
3. What do the authors propose as a solution to avoid the errors of reporting and reviewing Pearson r calculations?
Cognitive Domain: Comprehension, Knowledge
Difficulty Level: Medium
In this study, Monte Carlo resampling methods to obtain probability values for chi-squared and likelihood-ratio test statistics for multiway contingency tables are presented. A resampling algorithm provides random arrangements of cell frequencies in a multiway contingency table, given fixed marginal frequency totals. Probability values are obtained from the proportion of resampled test statistic values equal to or greater than the observed test statistic value.
Questions to Consider
1. Briefly summarize the Monte Carlo resampling methods to obtain probability values for the χ2.
Cognitive Domain: Comprehension
Difficulty Level: Medium–Hard
2. Why do the authors posit that resampling probability values for χ2 and G2 are recommended?
Cognitive Domain: Comprehension, Analysis
Difficulty Level: Medium–Hard
3. Explain what the authors contend is the advantage of the resampling approach over the asymptotic approach for a sparse three-way contingency table.
Cognitive Domain: Analysis
Difficulty Level: Hard
The present study examined relationship status, psychological orientation toward sexual risk taking, and other characteristics as potential correlates of risky sexual behavior in a sample of 223 heterosexual African American college students. Risky sexual behavior was investigated as a multinomial variable (i.e., abstinence, consistent condom use, inconsistent condom use, or noncondom use) to determine whether differentiation of levels of risky sexual behavior yielded meaningful psychological or demographic patterns. The hypotheses were (a) students who are in a long-term relationship are more likely to engage in risky sexual behavior, and (b) students who report inconsistent condom use differ from those who report noncondom use on demographic and psychological variables. The first hypothesis was partially supported. The second hypothesis was supported. The findings suggest that HIV/AIDS interventions need to take into consideration different levels of sexual risk taking with regard to condom use behavior among African American college students.
Questions to Consider
1. Interpret the significant chi-square statistic comparing condom use among participants with different relationship status states.
Learning Objective: Statistical significance
Cognitive Domain: Comprehension
Difficulty Level: Medium
2. Based on the degrees of freedom and four condom use categories, how many different categories of relationship status did the authors include in their test: (a) 2, (b) 3, (c) 4, (d) 222.
Learning Objective: Chi-square design
Cognitive Domain: Analysis
Difficulty Level: Easy
3. Why would it be difficult to run a one-way chi-square on condom use for education level?
(a) Not enough information is provided. (b) Graduate students cannot be compared to undergraduate students. (c) Not enough power to detect a medium effect. (d) The expected frequency for graduate students would be less than five.
Learning Objective: Chi-square design
Cognitive Domain: Evaluation
Difficulty Level: Hard
Purpose: The purpose of this study was to examine the relationship between stage of change for smoking cessation and stage of change for (1) fruit and vegetable consumption and (2) physical activity.
Design: The data come from a cross-sectional telephone survey administered to a stratified random sample of health plan members (n = 9675).
Setting: This study was conducted at a mixed-model health plan with approximately 1 million adult members.
Subjects: Respondents were adults aged 18 and older, who were randomly selected from five health plan product groups: commercial fully insured, commercial self-insured, two publicly subsidized plans, and Medicare supplemental insurance. Response rates ranged from 74.7% to 90.1% across these groups.
Measures: The assessment included demographics and stage of change for smoking cessation, physical activity, and fruit and vegetable intake. Bivariate relationships among variables were analyzed with the use of contingency tables. Ordered logistic regression was used to examine the effects of stage of change for fruit and vegetable consumption and physical activity on stage of change for smoking while controlling for other factors.
Results: Stage of change for smoking is more clearly related to stage of change for fruit and vegetable consumption (χ2 = 161.3, p < 0.001; Cramer’s V = 0.11, p < 0.001) than to stage of change for physical activity (χ2 = 89.7, p < 0.001; Cramer’s V = 0.08, p < 0.001). However, stage of change for fruit and vegetable consumption and physical activity are not strong predictors of stage of change for smoking.
Conclusions: This study indicates that stage of change for both fruit and vegetable consumption and physical activity are independent constructs from stage of change for smoking cessation.
Questions to Consider
1. Interpret the chi-square and Cramer’s V for comparing stage of smoking to stage of physical activity and state of fruit and vegetable consumption found in Table 4. What do these statistics mean? Which effect is larger?
Learning Objective: Design and effect size
Cognitive Domain: Analysis
Difficulty Level: Medium
2. With a two-way chi-square test with 16 degrees of freedom, which of the following could be the experimental design being tested? (a) 5 × 5, (b) 4 × 4, (c) 8 × 2, (d) 16 × 1.
Learning Objective: Design
Cognitive Domain: Comprehension
Difficulty Level: Medium
3. The authors report a Cramer’s V of 0.11 for the relationship between smoking stage and fruit and vegetable consumption phase. How would you characterize the size of this effect? (a) Large. (b) Medium. (c) Small. (d) Undeterminable.
Learning Objective: Effect size
Cognitive Domain: Comprehension
Difficulty Level: Easy