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chi squared test

The Chi-Squared test is a statistical method used to determine if there is a significant association between categorical variables. It is commonly applied in two main contexts: the Chi-Squared Goodness of Fit Test and the Chi-Squared Test of Independence.

The Chi-Squared Goodness of Fit Test assesses whether the observed frequencies of a categorical variable match the expected frequencies based on a specific hypothesis. This test is useful for determining if a sample distribution fits a population distribution 2.

On the other hand, the Chi-Squared Test of Independence evaluates whether two categorical variables are independent of each other. It compares the observed frequencies in a contingency table to the frequencies expected if the variables were independent. A significant result indicates that the variables are related 35.

To perform a Chi-Squared test, you calculate the Chi-Squared statistic using the formula: χ² = Σ((O - E)² / E), where O represents the observed frequency and E represents the expected frequency. The resulting statistic is then compared to a critical value from the Chi-Squared distribution to determine significance 4.

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