Introduction
What is the best way to determine if an intervention had an effect? While there is always a possibility to come to a conclusion through observation, statistics provide a more efficient way to assess the outcomes. One of the ways to evaluate an intervention is to use a chi-square test. According to Tanner (2016), the test identifies whether a difference in frequencies between the expected and observed data occurred by chance or as a result of actions. The present paper provides an example of how the chi-square test can be used for research in behavioral and social sciences.
Problem and Dataset
A counselor working with people with developmental disabilities decided to carry out research to find out if different types of reinforcement had a statistically significant effect on the number of problem-solving tasks completed correctly in an hour. After three weeks of verbal praise, the participants could complete 17 tasks, and after three weeks of tangible rewards, the participants could complete 27 tasks. The observations tell that there is a difference in the outcomes depending on the type of reward; however, these differences may have occurred by chance. Therefore, a chi-square test needs to be conducted to identify if the changes in frequencies are statistically significant. In order to perform the calculations, the information was organized in the form of a table suitable for chi-square analysis (see Table 1). Note that the expected data was calculated by dividing the total by the number of categories.
Table 1. Dataset
Utilized Test
In order to answer the research question, the goodness of fit chi-square test was used, as it is the only appropriate method for the problem. Microsoft Excel was utilized to calculate the chi-square statistics. The Excel file is attached to the present paper. The calculations were arranged following recommendations provided by Tanner (2016). The null hypothesis for the test was that there was no significant difference between the frequencies before and after the intervention. The alternative hypothesis was that there was a significant difference between the frequencies before and after the intervention.
The results revealed that the chi-square value is 2.273, which is below the critical value for alpha = 0.05. According to the chi-square table, the critical value for df = 1 is 3.841. The p-value was calculated in Excel, CHISQ.TEST function was used. The p-value was 0.132. The results of the chi-square test are presented in Table 2 below. In summary, the results of the test were insignificant as the p-value is higher than the significance level, and the chi-square value is below the critical value. Hence, there is no evidence to reject the null hypothesis in favor of the alternative hypothesis.
Table 2. Chi-Square Test Results
Discussion
Statistical analysis revealed that there is no evidence to suppose that the changes in the number of problem-solving tasks completed correctly in an hour were a result of the intervention. In light of the situation, a piece of candy as a reinforcement does not increase the number of successfully completed problem-solving tasks by people with developmental disabilities. However, the results of the test do not reject the hypothesis that the type of reinforcement influences the number of successfully completed tasks as the research design has several limitations.
First, the results of the present research may be statistically insignificant if the sample size was large enough. The generalizability of the results improves with an increase in the sample size. Second, the researcher compared only two types of reward: verbal praise and a piece of candy. The results revealed only that one piece of candy was not a good enough alternative for verbal praise. It is possible that two pieces of candy or a dollar are better alternatives. Finally, the research does not include any information about the preferences of people under study and the type of candy used. The researcher could have used different candies for different people, and some people may not live the candy they received. Considering all the limitations, the research overviewed in the present paper is a good pilot study; however, the design should be enhanced for the results to be significant.
Conclusion
Chi-square test is an excellent method to understand if differences in frequencies occur by chance or as a result of an intervention. Microsoft Excel is an adequate instrument to perform a chi-square analysis. The present paper demonstrates how the conclusions drawn from the initial observations may be different from the results of statistical tests. However, it is vital to read the research results correctly and make adequate judgments, as the results of statistical tests are greatly influenced by the research design limitations.
Reference
Tanner, D. (2016). Statistics for the Behavioral & social sciences (2nd ed.). Bridgepoint Education.