Null and Alternative Hypothesis
The null hypothesis for this study is that there will be no association between gender and blue and brown colors. Any gender will thus, be free and comfortable to associate with any color of their choice. On the other hand, the alternative hypothesis will be that there is a significant association between gender and either blue or brown colors. In this case, the analysis will show that men will be inclined to either a blue or brown color. Similarly, women will mostly prefer another particular color between blue and brown.
Why the Chi-square Test is Appropriate
Chi-square is ideal since two categorical variables are being simultaneously analyzed. For instance, the gender aspect comprises the males and females, and the association of both genders and the particular color is being assessed. The Chi-square is also appropriate since it is possible to conduct the cross-tabulation of variables (Johnson et al., 2015). The two categorical variables can be presented simultaneously in the table cells. The pattern of responses would then be compared to the expectation of variables being independent of each other. The test of independence, which means the association between the two categorical variables and color, will then be ascertained (McHugh, 2013).
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Why Other Tests are not suitable
Other tests such as ANOVA and t-test assume a continuous dependent variable. However, the dependent variable, in this case, color preferences, is not continuous. Thus, these tests are not suitable for data analysis. Also, for other tests to apply, the dependent variable is supposed to be a ratio designed to compare means of continuous distributions in categorical variables (Skaik, 2015). Furthermore, dummy columns are needed in other tests such as ANOVA and t-tests (Kim & Cribble, 2017). Conversion of the data into dummy variables would consume time and can be tiresome. Therefore, the other tests are not suitable for data analysis in question.
References
Johnson, W. D., Burton, J. H., Beyl, R. A., & Romer, J. E. (2015). A Simple Chi-Square Statistic for Testing Homogeneity of Zero-Inflated Distributions. Open journal of statistics , 5 (6), 483–493. Retrieved from https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4664523/pdf/nihms739084.pdf
Kim, Y. J. & Cribbie, R. A. (2017). ANOVA and the variance homogeneity assumption: Exploring a better gatekeeper. British Journal of Mathematical and Statistical Psychology, 71(1), 1–12. Retrieved from https://sci-hub.tw/https://onlinelibrary.wiley.com/doi/full/10.1111/bmsp.12103
McHugh M. L. (2013). The chi-square test of independence. Biochemia Medica , 23 (2), 143–149. Retrieved from https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3900058/pdf/biochem_med-23-2-143-3.pdf
Skaik Y. (2015). The bread and butter of statistical analysis "t-test": Uses and misuses. Pakistan journal of medical sciences , 31 (6), 1558–1559. Retrieved from https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4744321/pdf/PJMS-31-1558.pdf
