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Journal Article Link 14.1: Franke, T. M., Ho, T., & Christie, C. A. (2011). The Chi-Square Test: Often Used and More Often Misinterpreted. American Journal of Evaluation, 33(3), 448-458.

The examination of cross-classified category data is common in evaluation and research, with Karl Pearson’s family of chi-square tests representing one of the most utilized statistical analyses for answering questions about the association or difference between categorical variables. Unfortunately, these tests are also among the more commonly misinterpreted statistical tests in the field. The problem is not that researchers and evaluators misapply the results of chi-square tests, but rather they tend to over interpret or incorrectly interpret the results, leading to statements that may have limited or no statistical support based on the analyses preformed. This paper attempts to clarify any confusion about the uses and interpretations of the family of chi-square tests developed by Pearson, focusing primarily on the chi-square tests of independence and homogeneity of variance (identity of distributions). A brief survey of the recent evaluation literature is presented to illustrate the prevalence of the chi-square test and to offer examples of how these tests are misinterpreted. While the omnibus form of all three tests in the Karl Pearson family of chi-square tests—independence, homogeneity, and goodness-of-fit,—use essentially the same formula, each of these three tests is, in fact, distinct with specific hypotheses, sampling approaches, interpretations, and options following rejection of the null hypothesis. Finally, a little known option, the use and interpretation of post hoc comparisons based on Goodman’s procedure (Goodman, 1963) following the rejection of the chi-square test of homogeneity, is described in detail.

1. What Chi-Square tests are described in the article?
2. How are Chi-Square tests misinterpreted?
3. What implications does this have?

Journal Article Link 14.2: Hebron, J., & Humphrey, N. (2013). Exposure to bullying among students with autism spectrum conditions: A multi-informant analysis of risk and protective factors. Autism, 18(6), 618-630.

Research has consistently shown that children and young people with autism spectrum conditions are more likely to be bullied than those with other or no special educational needs. The aim of this study was to examine risk and protective factors that could help to explain variation in exposure to bullying within this group. A sample of 722 teachers and 119 parents reported on their child’s experience of being bullied. This response variable was regressed onto a range of explanatory variables representing individual and contextual factors. The teacher- and parent-rated regression models were statistically significant, explaining large proportions of variance in exposure to bullying. Behaviour difficulties and increased age were associated with bullying in both models. Positive relationships and attending a special school were associated with a decrease in bullying in the teacher model, with use of public/school transport predicting an increase. In the parent model, special educational needs provision at School Action Plus (as opposed to having a Statement of Special Educational Needs) was a significant risk factor, and higher levels of parental engagement and confidence were associated with reductions in bullying. These findings are discussed in relation to the autism spectrum conditions literature, and opportunities for intervention are considered.

1. What is the study’s null hypothesis?
2. Were parametric or non-parametric tests used?
3. What specific analyses were conducted?
4. What were the results of the study?
5. Did the researchers reject or retain the null hypothesis?