Calculating Degrees of Freedom for Chi-Square Test

When conducting a test to determine if observed frequencies significantly differ from expected frequencies using the critical value approach, it is essential to calculate the degrees of freedom (df) for the chi-square test statistic. The df represents the number of independent pieces of information in the data that are used to estimate the population parameters.

In the case where you don't want to reject the null hypothesis, if the calculated chi-square value is smaller than the critical value, then the observed frequencies fit the model, and you fail to reject the null hypothesis. On the other hand, if the calculated chi-square value is larger than the critical value, then the observed frequencies do not fit the model, which means you have to reject the null hypothesis.

To calculate the degrees of freedom for a chi-square test, follow these steps:

1. Identify the number of rows in your table (k) minus one. This will give you the degrees of freedom (df) for your test.

2. Use the calculated df to look up the critical value of the chi-square test statistic, also known as the chi-square-crit, in a chi-square table.

The chi-square table provides probabilities for the chi-square distribution with degrees of freedom (df) k-1. Once you know the degrees of freedom, you can find the critical value in this table.

For example, if your table has 5 rows, then the df would be 4 (k-1). You would look up the critical value for a chi-square test with 4 degrees of freedom in the chi-square table to determine the significance level.

In summary, calculating the degrees of freedom for a chi-square test is crucial when using the critical value approach. By following these steps and consulting a chi-square table, you can determine whether your observed frequencies significantly differ from expected frequencies and make informed decisions about rejecting or failing to reject the null hypothesis.

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