Introduction
The current paper examines the results of a repeated-measures ANOVA provided in an article by Raffaelli et al. (2013). The brief information about the article is provided; the assumptions for the test are articulated, and it is assessed whether they were checked in the article; the research questions and hypotheses for the repeated measures ANOVA are articulated; and the results of the repeated measures ANOVA are reported. The paper is concluded by analyzing the strengths and limitations of the analyzed statistical test given by Raffaelli et al. (2013).
Study Description
The article by Raffaelli et al. (2013) reports a study conducted in Mexico and aimed at assessing whether social support can be viewed as serving as a moderator between the levels of stress and the symptoms of depression. The authors conducted a number of tests on the data they collected; one of these tests was the repeated measures ANOVA, the goal of which was to compare the amount of social support that the respondents were able to get from a variety of social relationships (Raffaelli et al., 2013). The repeated-measures ANOVA was run using perceived “support as the dependent variable, relationship (family, friends, and significant other) as the within-subject repeated variable, and gender and age as between-subject factors” (Raffaelli et al., 2013, p. 285).
The support was assessed using the Multidimensional Scale of Perceived Social Support (Zimet, Dahlem, Zimet, & Farley, 1988); the authors averaged the scores on all the completed items from the questionnaire in order to produce a score for a participant (Raffaelli et al., 2013). The within-subjects factor was categorical and consisted of three groups: friends, family, and significant others. The first between-subject factor, gender, was categorical (0=male, 1=female); the second between-subject factor, age, was also categorical, and was measured in years. The sample comprised 16-21-year-old applicants to a public university, N=6,715, 55.0% of whom were female (Raffaelli et al., 2013, p. 285). This article is relevant to the specialization of general psychology due to the fact that depression is a rather widespread phenomenon nowadays, has a profound effect on the lives of a large number of people and is often studied by specialists in the general psychology field.
Testing Assumptions
The assumptions for a one-way repeated measures analysis of variance are as follows (Field, 2013; Warner, 2013):
- Each independent variable (within-subjects factor) needs to consist of at least two groups that are related (consist of the same participants);
- Each independent variable (between-subjects factor) need to consist of at least two independent groups that are not related;
- The dependent variable has to be quantitative;
- The dependent variable needs to have an approximately normal multivariate distribution;
- There should be no extreme outliers;
- Sphericity: the variances of the differences between the subjects’ scores in each pair of the related groups should be approximately equal.
From the article by Raffaelli et al. (2013), it is evident that the first assumption was met; as was noted, the within-subject factor consisted of 3 groups (friends, family, significant others). The second assumption was also met: gender and age were measured on categorical scales (Raffaelli et al., 2013). The scores on the dependent variable were obtained by averaging the scores on questions from a Likert-scale questionnaire (Raffaelli et al., 2013), which means that the scores are not strictly interval/ratio; but such scores, nevertheless, are often treated as quantitative variables by researchers (Warner, 2013), so it might be considered that the third assumption is met. Raffaelli et al. (2013) do not report testing the assumptions 4-6. It might be possible to hypothesize that the distributions were approximately normal for the dependent variable across most groups due to the relatively large sample size N=6,715 (assumption 4). However, since no information on extreme outliers or sphericity is provided, the absence of this information might be considered a limitation of the article by Raffaelli et al. (2013).
Research Question, Hypothesis, and Alpha Level
The goal of the repeated measures ANOVA was to “compare levels of social support Mexican youth receive from different social relationships” (Raffaelli et al., 2013, p. 284). Therefore, the respective research questions can be formulated as follows: “Do the levels of social support that the Mexican youth obtain from various social relationships differ? Are these levels different among various gender and age groups?” The null hypothesis for the overall ANOVA can be stated as follows: “The levels of social support that the Mexican youth obtain from various social relationships do not differ significantly.” The null hypotheses for the between-subjects factors may be worded in the following way: “The levels of social support that the Mexican youth obtain from various social relationships do not differ significantly across gender and age groups.” Consequently, the alternative hypothesis for the overall ANOVA should be as follows: “The levels of social support that the Mexican youth obtain from various social relationships differ significantly,” whereas the alternative hypothesis for the between-subjects factors ought to be: “The levels of social support that the Mexican youth obtain from various social relationships differ significantly across gender or age groups.” The alpha level is not specified in the article by Raffaelli et al. (2013).
Interpretation
The results of the overall repeated measures ANOVA were statistically significant: F(2; 6702)=24.57, p<.001, partial η2=.007 (Raffaelli et al., 2013, p. 286). The effect size is not interpreted verbally, but it is small (Warner, 2013). Participants obtained the greatest support from family (mean=5.80, SD=1.31); the support from the significant other (mean=5.70, SD=1.40), and from friends (mean=5.71, SD=1.32) did not differ significantly (Raffaelli et al., 2013). However, these results allow for rejecting the overall null hypothesis and accepting the alternative hypothesis.
As for the results for the between-subjects factors, it is only stated that significant two-way interactions between the gender and age were revealed, but the results are not reported. It is also stressed that family provided larger support than friends or significant others to participants of all ages, as well as for male participants; female respondents received comparable support from all the three types of relationships; however, the exact results of the test are also not reported, but means are provided in a table (Raffaelli et al., 2013). According to the authors, significant differences were found; consequently, it is possible to reject the null hypothesis for the between-subjects factors, and state that evidence has been found to support the alternative hypothesis.
Conclusion
Thus, the repeated measures ANOVA conducted by Raffaelli et al. (2013) allows for accepting the research hypothesis stating that Mexican youth receive different levels of social support from such sources as family, friends, and significant others; family provided the greatest social support, whereas the other two sources supplied comparable levels of social support. The limitations of the study conducted by Raffaelli et al. (2013) related to the repeated measures ANOVA are that the authors did not check the assumptions of this statistical test, and did not report the exact results of the test for the between-subjects factors. Also, the authors used convenience sampling, which is a limitation of almost any research. One of the strengths of the study is that the authors utilized a large sample, which allowed for detecting even such a small difference that its effect size was.007 as measured by partial η2.
References
Field, A. (2013). Discovering statistics using IBM SPSS Statistics (4th ed.). Thousand Oaks, CA: SAGE Publications.
Raffaelli, M., Andrade, F. D., Wiley, A. R., Sanchez-Armass, O., Edwards, L. L., & Aradillas-Garcia, C. (2013). Stress, social support, and depression: A test of the stress-buffering hypothesis in a Mexican sample. Journal of Research on Adolescence (Wiley-Blackwell), 23(2), 283-289. Web.
Warner, R. M. (2013). Applied statistics: From bivariate through multivariate techniques (2nd ed.). Thousand Oaks, CA: SAGE Publications.
Zimet, G. D., Dahlem, N. W., Zimet, S. G., & Farley, G. K. (1988). The multidimensional scale of perceived social support. Journal of Personality Assessment, 52(1), 30-41. Web.