REQUIREMENTS FOR USE
To use the Chi-Square test for Independence, the
following requirements must be met:• The data must be categorical.
• The observed data must consist of one sample and two variables.
• The expected frequencies must be at least five.
FORMULA
X² = ∑(O −E)²/Ewhere:
X² is the chi-square statistic
∑ is the summation
O is the observed frequency
E is the 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 INDEPENDENCE
Step 1: State the problem and hypothesisClearly define the research question: Identify the two categorical variables to be analyzed for independence.Formulate the null and alternative hypothesis:
1. Null Hypothesis (H0): There is no significant relationship between the two variables.
2. Alternative Hypothesis (H1): There is a significant relationship between the two variables.Step 2: Select appropriate test statistic and check assumptionsChoose the appropriate test statistic: Select the Chi-Square Test of Independence as the test statistic.
Check for AssumptionsStep 3: Calculate the test statisticCreate a contingency table: Organize the data into a contingency table to display the frequency distribution of two variables.Step 4: Decide the H0:
Compute the Degrees of freedomLook-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).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 your conclusion.
Interpret the result: Explain the implications of rejecting or failing to reject the null hypothesis.State the conclusion: Clearly state whether the populations have the same distribution of categorical variables or not.