REQUIREMENTS FOR USE
To use the Chi-Square test for Homogeneity, the following requirements must be met:- The data must be categorical.
- The observed data must consist of two or more samples and one variable.
- The expected frequencies must be at least five.
FORMULA
x² = Σ[(O-E)²/E]
Where:
x² = Chi-square Test Statistic
Σ = Summation
O = Observed Frequency
E = Expected Frequency
To calculate the expected frequencies:E = (RT)(CT)/NWhere:
E = Expected Frequency
RT = Row Total
CT = Column Total
N = Grand Total
To calculate the degrees of freedom:df = (R-1)(C-1)Where:
R = Number of Rows
C = Number of Columns
STEPWISE CALCULATION
TEST FOR HOMOGENEITY
Step 1: State the problem and hypothesisClearly define the research question: Identify the categorical variables to be compared across different populations or groups.Formulate the null and alternative hypothesis:1. Null Hypothesis (H0): The populations have the same distribution of categorical variables.
2. Alternative Hypothesis (H1): The population does not have the same distribution of categorical variables.Step 2: Select appropriate test statistic and check assumptionsChoose the appropriate test statistic: Select the Chi-Square Test of Homogeneity as the test statistic.Check for AssumptionsStep 3: Calculate the test statisticCalculate the expected frequencies. Use the formula; E = (RT)(CT)/N
Calculate the Chi-Square statistic: Use the formula; x² = Σ[(O-E)²/E]Step 4: Decide the H0:Compute the Degrees of freedom (df): Calculate df = (R-1)(C-1)Find the Critical value: Use the Chi-Square distribution table to find the critical value for the calculated df and chosen significance level (usually 0.05).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.
2. Fail to reject the null hypothesis. If the x² value is less than the critical value then we fail to reject the null hypothesis.Step 5: State your 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.