Step 1: State the problem and hypothesisClearly define the research question: Identify the two categorical variables to be analyzed for goodness of fit.
Formulate the null and alternative hypothesis:1. Null Hypothesis (H0): The observed frequencies are consistent with the expected frequencies under a specific distribution (e.g. uniform, normal).
2. Alternative Hypothesis (H1): The observed frequencies are not consistent with the expected frequencies.Step 2: Use appropriate test statistic
Choose the appropriate test statistic: Select the Chi-Square Test of Goodness of fit as the test statistic.
Check for Assumptions.Step 3: Calculate the test statistic
Create a table: Organize the data into a table to display the observed frequency (O) and expected frequencies (E) for each category.Step 4: Decide the H0:
Compute the Degrees of freedom (df): Calculate df = k - 1, where k is the number of categories.Look-up for the critical values: Use the Chi-Square distribution table to find the critical value for the calculated df and chosen significance level (usually 0.05). And calculate the p-value using software or a calculator.Make a decision.1. Reject the null hypothesis.
If the x² value is greater than the critical value then the data allows us to reject the null hypothesis that the variables are unrelated and provides support for the alternative hypothesis that the variables are related.2. Fail to reject the null hypothesis.
If the x² value is less than the critical value then the null hypothesis will not be rejected, that means the variables are unrelated and doesn’t provide support for the alternative hypothesis that the variables are related.Step 5: State the conclusion.1. Interpret the result: Explain the implications of rejecting or failing to reject the null hypothesis.
2. State the conclusion: Clearly state whether the populations have the same distribution of categorical variables or not.