Chi-Square Analysis of Data

Chi-Square Analysis of Data

What type of data is used in chi-square analyses?

Chi-square analyses are statistical tests that are commonly used to analyze categorical data, which is data that can be classified or sorted into groups. Such information is frequently presented as frequency counts or percentages, and it can take several forms, including nominal (i.e., unordered categories), ordinal (i.e., ordered categories), or dichotomous (i.e., two options) (i.e., binary categories) (Turhan, 2020). Chi-square tests compare observed frequencies in a dataset to expected frequencies if there is no relationship between the categories being analyzed. The end result is a chi-square statistic that quantifies the degree of difference between observed and expected frequencies. This statistic can then be used to determine whether there is a significant relationship between the categories under consideration. Chi-square analyses are widely used to gain insights into patterns and relationships in categorical data in fields such as social sciences, public health, and market research.

Provide two examples.

Example 1

A researcher wants to examine the relationship between gender and political affiliation among a sample of voters. The researcher collected data on 500 voters’ gender and political affiliation and used chi-square analysis to see if there was a significant relationship between the two variables. The following data are presented in a contingency table:

The chi-square analysis results show a significant relationship between gender and political affiliation, X2 (2, N = 500) = 19.8, p.001. A post-hoc analysis reveals that females are more likely than males to identify as Democrats, while males are more likely to identify as Republicans.

Example 2

A study is being conducted to see if there is a correlation between smoking status and lung cancer diagnosis in a group of patients. The researcher collects data on 1,000 patients’ smoking status (current smoker, former smoker, non-smoker) and lung cancer diagnosis (yes, no) and uses chi-square analysis to see if there is a significant relationship between the two variables. The table shows the data that was collected:

The chi-square analysis results show a significant relationship between smoking status and lung cancer diagnosis, X2 (2, N = 1000) = 102.4, p.001. A post-hoc analysis reveals that current smokers are more likely than former smokers or nonsmokers to be diagnosed with lung cancer.

Compare and contrast chi-square goodness of fit and test for independence. Under which conditions are they used?

Chi-square goodness of fit and test for independence are two different kinds of chi-square analysis. The Chi-square goodness of fit test determines whether observed data follows an expected distribution (Turhan, 2020). The expected distribution can be based on a theoretical distribution or a previous study’s distribution. Conversely, the test for independence determines whether or not two categorical variables have a relationship (Turhan, 2020). The primary distinction between the two types of chi-square analysis is that goodness of fit is used when comparing observed data to an expected distribution, whereas the test for independence is used when comparing two variables. Furthermore, the goodness of fit is applied to one categorical variable, while the test for independence is applied to two categorical variables.

Chi-square goodness of fit is used when data is expected to fit a specific distribution, and the researcher wants to see if the observed data fits that distribution. When researchers want to see if two variables are related, they will use the test for independence (Turhan, 2020). A market researcher, for example, might use a test for independence to determine whether there is a link between gender and brand preference.

Identify the pros and cons associated with Chi-square analyses.

The ease of use and ability to analyze categorical data are two advantages of chi-square analysis. Chi-square analysis can be applied to a wide range of research questions and can assist researchers in identifying relationships between categorical variables. The disadvantages of chi-square analysis include its assumption of observational independence, which may not always be met in real-world situations (Pavlov et al., 2020). Furthermore, chi-square analysis may be less effective than other statistical tests at detecting minor differences between groups. Finally, chi-square analysis does not reveal the strength or direction of the relationship between variables, only whether it is statistically significant.

References

Pavlov, G., Shi, D., & Maydeu-Olivares, A. (2020). Chi-square Difference Tests for Comparing Nested Models: An Evaluation with Non-normal Data. Structural Equation Modeling: A Multidisciplinary Journal, 27(6), 908–917. https://doi.org/10.1080/10705511.2020.1717957

Turhan, N. S. (2020). Karl Pearson’s Chi-Square Tests. Educational Research and Reviews, 16(9), 575–580. https://eric.ed.gov/?id=

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What type of data is used in chi-square analyses?

Provide two examples.

Compare and contrast chi-square goodness of fit and test for independence. Under which conditions are they used?

Chi-Square Analysis of Data

Identify the pros and cons associated with Chi-square analyses.

Complete it in APA format using JASP ASAP.