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Chi-Square Test
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Definition of Chi-Square Test
A statistical hypothesis test that measures how well observed data fits with the expected distribution of the data, assuming the null hypothesis is true.
When to use Chi-Square Test for Goodness of Fit
It is used to determine whether sample data is consistent with a population with a specific distribution.
When to use Chi-Square Test for Independence
It is used to determine whether there is a significant association between two categorical variables.
Formula for Chi-Square Statistic
The formula is
Degrees of Freedom in Chi-Square Test
Degrees of freedom for the Chi-Square test is the number of categories minus one for goodness of fit, or (rows - 1) * (columns - 1) for a test of independence.
Expected Frequency Calculation
Expected frequencies are calculated based on the null hypothesis and the distribution of the sample data.
Null Hypothesis in Chi-Square Tests
In chi-square tests, the null hypothesis asserts that there is no difference between the observed and expected frequencies, or no association between variables.
Chi-Square Test P-value
The p-value assesses the evidence against the null hypothesis, with values less than the significance level indicating a rejection of the null hypothesis.
Limitations of Chi-Square Test
It requires a large enough sample size for accuracy, cannot be used for small expected frequencies, and is not suitable for ordinal or continuous data without categorization.
Assumptions of the Chi-Square Test
Data must be randomly sampled, observations should be independent of each other, and expected frequencies should be at least 5.
Chi-Square Distribution
The distribution of the chi-square statistic under the null hypothesis, which is dependent on degrees of freedom.
Contingency Table
A data table that displays frequencies for two categorical variables and is used in chi-square tests of independence.
Post-hoc Analyses in Chi-Square Tests
Used to explore which specific categories or cells contribute to the significance in the chi-square test, in the case of a significant overall result.
Effect Size in Chi-Square Tests
Measures the strength of association or the practical significance of findings, not just the probability of results occurring by chance.
Reporting Chi-Square Test Results
Results are reported with the chi-square statistic value, degrees of freedom, p-value, and possibly an effect size measure, alongside a conclusion regarding the null hypothesis.
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