![]() ![]() The company sent a nurse to every employee who contracted pneumonia to provide home health care and to take a sputum sample for culture to determine the causative agent. In effect, there are two groups employees who received the vaccine and employees who did not receive the vaccine. Due to a production problem at the company that produces the vaccine, there is only enough vaccine for half the employees. There is a vaccine for pneumococcal pneumonia, and the owner believes that it is important to get as many employees vaccinated as possible. Many employees have contracted pneumonia leading to productivity problems due to sick leave from the disease. The owner of a laboratory wants to keep sick leave as low as possible by keeping employees healthy through disease prevention programs. To illustrate the calculation and interpretation of the χ 2 statistic, the following case example will be used: Non-parametric tests should be used when any one of the following conditions pertains to the data: The Chi-square test is a non-parametric statistic, also called a distribution free test. Additionally, the χ 2 is a significance test, and should always be coupled with an appropriate test of strength. ![]() As with any statistic, there are requirements for its appropriate use, which are called “assumptions” of the statistic. Thus, the amount and detail of information this statistic can provide renders it one of the most useful tools in the researcher’s array of available analysis tools. Unlike most statistics, the Chi-square (χ 2) can provide information not only on the significance of any observed differences, but also provides detailed information on exactly which categories account for any differences found. The Chi-square test of independence (also known as the Pearson Chi-square test, or simply the Chi-square) is one of the most useful statistics for testing hypotheses when the variables are nominal, as often happens in clinical research. Limitations include its sample size requirements, difficulty of interpretation when there are large numbers of categories (20 or more) in the independent or dependent variables, and tendency of the Cramer’s V to produce relative low correlation measures, even for highly significant results. Advantages of the Chi-square include its robustness with respect to distribution of the data, its ease of computation, the detailed information that can be derived from the test, its use in studies for which parametric assumptions cannot be met, and its flexibility in handling data from both two group and multiple group studies. The Cramer’s V is the most common strength test used to test the data when a significant Chi-square result has been obtained. ![]() The Chi-square is a significance statistic, and should be followed with a strength statistic. This richness of detail allows the researcher to understand the results and thus to derive more detailed information from this statistic than from many others. Unlike many other non-parametric and some parametric statistics, the calculations needed to compute the Chi-square provide considerable information about how each of the groups performed in the study. It permits evaluation of both dichotomous independent variables, and of multiple group studies. Specifically, it does not require equality of variances among the study groups or homoscedasticity in the data. Like all non-parametric statistics, the Chi-square is robust with respect to the distribution of the data. The Chi-square statistic is a non-parametric (distribution free) tool designed to analyze group differences when the dependent variable is measured at a nominal level. ![]()
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