Comparing Statistical Tests: ANOVA vs. Chi-Square

 

What is ANOVA?

ANOVA (Analysis of Variance) is a statistical method that help us to compare the means of two or more groups and check if there are any significant differences. It does so by examining differences within and between groups to see if random variation or actual group inequalities are the root cause of these differences.

When to use ANOVA?

ANOVA is used when there's a continuous dependent variable and one or more categorical independent variables with more than one level. The test contrasts mean within groups and produces an F-statistic and p-value that are used to determine the level of statistical significance.

ANOVA tests come in various forms such as single-way, two-way, and factorial ANOVA which have their own assumptions and requirements.

 

What is Chi-Squere Test?

The Chi-Square test, however, is used to determine the relationship or independence between two categorical variables. The Chi-Square test simply takes observed and expected frequencies and compares them under the assumption of independence in order to measure the strength of relationship.

Chi-Square tests are the most common in the social sciences, biology, market research, and quality control, whereby categorical data are used to help identify any relationships between variables.

Different Chi-Square tests exist, such as the Chi-Square test of independence and the Chi-Square test of goodness of fit which each has unique analytical applications.

 

What is the difference between ANOVA and the Chi-Square test?

In general, ANOVA looks at the mean across groups with continuous dependent variables and categorical independent variables, whereas Chi-square is used to examine the relationship or independence between categorical variables. Whether ANOVA or Chi-Square is better to use is dependent on variable type and the research question.

For ANOVA, the appropriate approach is to use a continuous dependent variable and one or more categorical independent ones when your goal is to compare mean values across groups or test their statistical significance.

Contrasting to it, the Chi-Square is used in case the categorical variables are analyzed in order to test associations or their independence, determining if observed frequencies significantly differ from expected, or to examine relationships between categorical variables.

 

Example of ANOVA and Chi-square test application

For instance, we should evaluate the effectiveness of different teaching approaches on student results. For example, let us assume we are researching the efficacy of three teaching methods (Method A, Method B, and Method C) and their effect on student achievement. We randomly divide 150 students into two groups and measure their results after the semester. For ANOVA, we first check if there is a significant difference in average test scores among the three teaching methods, where test scores are the dependent variable and the teaching method is the independent variable.

By using the ANOVA and getting significant results, we can go further to evaluate if a link does exist between the method of teaching and student preferences or not, utilizing a Chi-Square test. This determines whether there’s a significant relationship between the method of teaching and the choice of the students. To summarize, ANOVA is used to identify the significance of differences in mean across groups and Chi-Square tests the level of association or independence of categorical variables.

WATCH MORE