Test Your Understanding of Chi-Square Tests

Chi-Square Tests: Goodness of Fit and Test of Independence

• Parametric tests make assumptions about population parameters, while non-parametric tests do not.
• Parametric tests require interval or ratio scale data, while non-parametric tests can use data at nominal level.
• Non-parametric tests are not as powerful as parametric tests and can fail to detect differences.
• The Chi-Square test for goodness of fit (GF) is used to answer questions about the proportions of a popular distribution, such as gender bias in a department.
• The GF compares the sample proportions to population proportions as specified by the null hypothesis.
• The observed frequencies are compared to the frequencies predicted by the null hypothesis (expected frequencies).
• The expected frequencies change according to what the null hypothesis is.
• The bigger the gap between observed and expected frequencies, the bigger the Chi-Squared score.
• The Chi-Square test of independence (TI) is used to determine whether two variables are independent or associated.
• The TI uses data in the form of frequencies in different categories, which is compared to expected frequencies predicted from the null hypothesis.
• The H0 for the TI states that the two variables being measured are completely independent from each other.
• The H1 for the TI either states that there is a relationship between the variables or that the proportions are different for each variable.