The chi-square test examines whether two variables from two different categories are independent of the effect of the test statistic. The test is valid when the test statistic is distributed under the null hypothesis (Sharpe, 2015). In this discussion, I will apply the chi-square test to my research question.
Null and Alternative Hypothesis
In the context of chi-square analysis, the null hypothesis typically states that there is no significant association between two categorical variables, while the alternative hypothesis suggests a significant association.
- Null hypothesis: There is no statistically significant relationship between the two variables.
- Alternative hypothesis: There is a statistically significant relationship between the two variables.
To test these hypotheses, we can use the chi-square test for independence, which evaluates whether the observed frequencies for each category in the contingency table differ significantly from the expected under the assumption of independence between variables (Franke, Ho & Christie, 2012).
Applying to the research question:
- Research question: Is there a significant correlation between the level of construction pollution and the proximity of construction sites to residential areas?
- Null hypothesis: There is no statistically significant relationship between the level of construction pollution and the proximity of construction sites to residential areas.
- Alternative hypothesis: There is a significant correlation between the level of construction pollution and the proximity of construction sites to residential areas.
To test these hypotheses using chi-square analysis, we would collect data on the level of construction pollution (e.g., measured in terms of air quality or noise levels) and the distance of construction sites from residential areas (e.g., measured in miles). We can then create a contingency table showing the number of observations in each variable.
The appropriateness of using Chi-square as an analytical procedure:
According to Ji et al. (2020), the levels of measurement of variables affect the suitability of chi-square use as an analytical measure in several ways. First, the chi-square test is only relevant for categorical variables: both variables must be fixed categories such as gender and blood group. If one of the variables is continuous, such as age or weight, we cannot use a chi-square test. Second, the chi-square test is more robust when the categories are evenly distributed. This means that each category should have approximately the same number of notes. If the categories are not evenly distributed, the chi-square test may not be robust.
In the context of construction pollution, variables of interest may include the level of pollution (measured, for example, by air quality or noise levels) and the proximity of construction sites to residential areas (measured in terms of distance). These variables are continuous and have an interval or ratio measurement level. Therefore, chi-square analysis is not an appropriate analytical procedure to study these variables' relationships. Alternatively, other analytical techniques, such as correlation or regression analysis, may be more appropriate.
Conclusion
Chi-square makes it possible to analyze the relationship between variables, providing valuable information for decision-making. The importance of chi-square depends on its ability to analyze data quickly and easily and to find statistical relationships. The chi-square test is appropriate for testing the relationship between gender and party affiliation, blood type and disease, or the relationship between customer satisfaction and product type. On the other hand, there are cases in which the chi-square test is not appropriate, such as testing the relationship between age and party affiliation, the relationship between weight and disease, and the relationship between customer satisfaction and price (Alavi et al., 2020).
References
Alavi, M., Visentin, D. C., Thapa, D. K., Hunt, G. E., Watson, R., & Cleary, M. L. (2020). Chi-square for model fit in
confirmatory factor analysis.
Franke, T. M., Ho, T., & Christie, C. A. (2012). The chi-square test: Often used and more often misinterpreted. American
journal of evaluation, 33(3), 448-458.
Ji, X., Gu, W., Qian, X., Wei, H., & Zhang, C. (2020). Combined Neyman–Pearson chi-square: An improved approximation to
the Poisson-likelihood chi-square. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 961, 163677.
Sharpe, D. (2015). Chi-square test is statistically significant: Now what?. Practical Assessment, Research, and Evaluation,
20(1), 8.