SAGE Journal Articles

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Alin, A., & Kurt, S. (2006). Testing non-additivity (interaction) in two-way ANOVA tables with no replication. Statistical Methods in Medical Research, 15(1), 63–85. doi:10.1191/0962280206sm426oa

Testing for any significant interaction between two variables depends on the number of replicates in each cell of the two-way table and structure of the interaction. If there is interaction between two factors model of observations include interaction term and is called “non-additive model” which makes interaction and non-additivity equivalent in terms of meaning. When there are several observations taken at each level combination of two variables, testing non-additivity can easily be done by usual two-way ANOVA method which cannot be used when there is only one observation per cell. For the cases with only one observation per cell, some methods have been developed starting with Tukey’s one-degree-of-freedom test in which interaction is supposed to be the product of two factor’s effects. There are other methods which are used for different structures of interaction when there is only one observation. In this paper, we review some of these tests. After presenting general methodology for the two-factor linear model with interaction effect and the general two-way ANOVA method when there are n> 1 observations per cell, we present some methods for testing non-additivity when there is only one observation per cell. Finally, we illustrate these methods on examples.

Questions to Consider

1. The statistical term used for heterogeneity of effect is “interaction.” Summarize what this means.

Cognitive Domain: Comprehension, Knowledge

Difficulty Level: Medium–Hard

 

2. Discuss and define the term “non-additive model.”

Cognitive Domain: Comprehension, Knowledge

Difficulty Level: Medium–Hard

 

3. Explain the reason for using the Tukey post-hoc test. What is this test and how is it derived?

Cognitive Domain: Knowledge, Comprehension

Difficulty Level: Hard

 

Jan, S., & Shieh, G. (2014). Determining sample sizes for precise contrast analysis with heterogeneous variances. Journal of Educational and Behavioral Statistics, 39(2), 91–116. doi:10.3102/1076998614523069.

The ANOVA is one of the most frequently used statistical analyses in practical applications. Accordingly, the single and multiple comparison procedures are frequently applied to assess the differences among mean effects. However, the underlying assumption of homogeneous variances may not always be tenable. This study examines the sample size procedures for precise interval estimation of linear contrasts within the context of one-way heteroscedastic ANOVA models. The desired precision of both individual and simultaneous confidence intervals is evaluated with respect to the control of expected half width and to the tolerance probability of interval half width within a designated value. Supplementary computer programs are developed to aid the usefulness and implementation of the proposed techniques. The suggested sample size procedures improve upon the existing approaches and extend the methodology development in the statistical literature.

Questions to Consider

1. Why do the authors claim that the underlying assumption of homogeneous variances may not always be tenable?

Cognitive Domain: Comprehension

Difficulty Level: Medium

 

2. Explain the example the authors give regarding the simplest case of a linear contrast.

Cognitive Domain: Comprehension

Difficulty Level: Medium

 

3. What is the Monte Carlo simulation and how was this performed to demonstrate the precision behavior for the recommended sample size formulas? Briefly summarize.

Cognitive Domain: Comprehension, Analysis

Difficulty Level: Medium

 

Finch, W. H., & French, B. F. (2012). A comparison of methods for estimating confidence intervals for omega-squared effect size. Educational and Psychological Measurement, 72(1), 68–77. doi:10.1177/0013164411406533.

Effect size use has been increasing in the past decade in many research areas. Confidence intervals associated with effect sizes are encouraged to be reported. Prior work has investigated the performance of confidence interval estimation with Cohen’s d. This study extends this line of work to the ANOVA case with more than two groups. Confidence interval estimation for the omega-squared (ω2) effect size measure was evaluated under a variety of simulated conditions with three methods where the primary interest was in the comparative performance of the three confidence interval calculation methods (i.e., parametric, percentile bootstrap, and bootstrap bias-corrected and accelerated confidence interval [BCA]) across a variety of real-life data situations. Results suggest that sample size and magnitude of the effect influence coverage rates and interval width. The percentile bootstrap method produced the widest intervals and had higher coverage rates in the smaller effect size conditions compared with the parametric and BCA approaches.

Questions to Consider

1. What do you believe is the reason that effect size use has been increasing in the past decade in many research areas?

Cognitive Domain: Comprehension

Difficulty Level: Easy–Medium

 

2. Why is it important that confidence intervals associated with effect sizes be reported?

Cognitive Domain: Comprehension, Knowledge

Difficulty Level: Medium

 

3. Beyond being reported in journals, where else might effect size prove important? Give an example and explain why it is important.

Cognitive Domain: Comprehension, Application

Difficulty Level: Medium

 

Knott, K. B., & Natalle, E. J. (1997). Sex differences, organizational level, and superiors’ evaluation of managerial leadership. Management Communication Quarterly, 10(4), 523–540.

Sex differences and leadership research literature includes many findings concerning subordinate evaluations of managers’ performance, but little is known about superiors’ perceptions of male and female managers. This study explored superiors’ evaluations of the leadership skills of their managers to determine if sex differences exist. A sample of 400 male and female managers, representing middle and upper organizational levels, were rated on Benchmarks, a multirater feedback instrument developed at the Center for Creative Leadership. A 2 × 2 MANOVA detected no interaction effect between sex of the manager and organization level. Main effect analyses revealed one difference: female managers were rated higher on 1 of 16 scales, putting people at ease. Upper level managers were evaluated higher than middle level managers by their superiors on eight scales. Results indicate that sex differences are not salient in distinguishing managerial leadership ability once the manager has crossed a threshold of organizational experience.

Questions to Consider

1. After failing to find an interaction between sex and organization level, how did the authors proceed to analyze the data?

Learning Objective: Interaction

Cognitive Domain: Application

Difficulty Level: Medium

 

2. How many groups were the authors originally comparing? (a) 1. (b) 2. (c) 4. (d) 16.

Learning Objective: Two variables with independent samples

Cognitive Domain: Analysis

Difficulty Level: Easy

 

3. Is there a significant difference between “setting a developmental climate” between male and female managers? (a) Yes, p = 0.057. (b) No, p = 0.057. (c) Unsure, p = 0.057. (d) Not a significance test.

Learning Objective: Significance testing

Cognitive Domain: Comprehension

Difficulty Level: Easy

 

Lee, H. E., Park, H. S., Imai, T., & Dolan, D. (2012). Cultural differences between Japan and the United States in use of “Apology” and “Thank You” in favor asking messages. Journal of Language and Social Psychology, 31(3), 263–289.

Three studies investigated whether apologies and thanks are used differently when asking favors in the United States and Japan and examined whether their use makes a favor asking message less face-threatening. In Study 1, participants (N = 152) composed an email message for a favor asking situation. Next, participants in Study 2 (N = 634) and Study 3 (N = 417) completed one of four versions of a questionnaire regarding a prototype of an email message. Results showed that (a) more Japanese included apologies in their messages while more Americans used thanks and (b) Japanese considered apologies to reduce some face threats while Americans did not consider thanks to reduce face threats. Implications and future research directions are discussed.

Questions to Consider

1. In Study 2, there was an interaction between culture and speech act for H’s positive face threat. Describe what an interaction means in general terms and then describe the interaction found in this study.

Learning Objective: Interaction

Cognitive Domain: Evaluation

Difficulty Level: Hard

 

2. In Study 2, the authors only focus on cultural differences in H’s negative face threat. Why?

(a) They were only interested in culture and not in speech. (b) Without an interaction you can just interpret main effects. (c) Speech did not have a main effect. (d) Both b and c.

Learning Objective: Significance testing

Cognitive Domain: Evaluation

Difficulty Level: Medium

 

3. How many groups were tested in Study 2? (a) 2. (b) 4. (c) 6. (d) 8.

Learning Objective: Two variables with independent samples

Cognitive Domain: Knowledge

Difficulty Level: Easy