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S12.2 - Tests for Independence
Tests for Independence and the Homogeneity of Proportions
14
Mathematics
Graduate
11/11/2013

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Term
Chi-square test for independence
Definition
Used to to determine whether there is an association between a row variable and a column variable in the contingency table constructed from sample data
Term
If two events E and F are independent, then P(E and F) =
Definition
P(E) x P(F)
Term
Expected frequency =
Definition
(row total)(column total)/table total
Term
Test statistic for the test of independence, X^2 =
Definition
Summation[(Oi-Ei)^2/Ei]
where Oi = observed number of counts
Ei = expected number of counts
Term
2 assumptions for test statistic for the test of independence
Definition
1. All expected frequencies are greater than or equal to 1
2. No more than 20% of the expected frequencies are less than 5
Term
All hypothesis tests for chi-square tests for independence are
Definition
Right-tailed tests
Term
Right-tailed test, chi-square test for independence
H0:
H1:
Definition
H0: The row variable and the column variable are independent
H1: The row variable and the column variable are dependent
Term
Chi-square test for independence, classical approach
X0^2 > Xalpha^2
Definition
Reject the null
Term
Chi-square test for independence, classical approach
X0^2 < Xalpha^2
Definition
Fail to reject the null
Term
Chi-square test for independence, p-value approach
P-value < alpha
Definition
Reject the null
Term
Chi-square test for independence, p-value approach
P-value > alpha
Definition
Fail to reject the null
Term
Chi-square test for homogeneity of proportions
Definition
Testing whether different populations have the same proportion of individuals with some characteristic
Term
Chi-square test for homogeneity of proportions is identical to
Definition
The chi-square test for independence
Term
Right-tailed test, chi-square test for homogeneity of proportions
H0:
H1:
Definition
H0: p1=p2=p3
H1: At least one of the population proportions is different from the others
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