Please enable JavaScript.
Coggle requires JavaScript to display documents.
Chi-Squared Tests (Chi-Squared Goodness of Fit Test – used to determine if…
Chi-Squared Tests
Chi-Squared Goodness of Fit Test – used to determine if data fits a given distribution. One set of categorical variables.
-
Assumptions – Random, independent, categorical data (based on counts), and all expected counts are at least
-
Test statistic: the larger values indicate observed not close to expected 
-
Decision Rule – If Calculated Test Statistic is past the critical value, you reject Ho.
-
-
The x2 distribution is skewed to the right. But, as df increases, it becomes less skewed. You would look at the greater than region to determine the p-value from a test statistic, or obtain the critical value from degrees of freedom and significance level.
Standardized Residuals – (observed-expected)/ Expected
• Positive means more in the category than expected.
• Negative means less in the category than expected.
.
x2 calc < x2 crit or p > a
FTR Ho
There is sufficient evidence to believe variables are associate/dependent
x2 calc ≥ x2 crit or p < a
reject Ho
There is sufficient evidence to believe variables are associate/dependent
-
Chi Squared Test for Homogeneity – tests a single categorical variable over two populations to determine if
they have the same distribution or not. The procedure is the same as the test for independence.
H0: The two populations have the same distribution.
HA: The two populations do not have the same distribution.
Graph – Mosaic plot
Assumptions – Random, independent, categorical data (based on counts), and all expected counts are at least 5.
test statistic= sigma ((observed - expected) ^2) /Expected
where expected = (row total * column total)/grand total
-