AP Statistics CH 12 The Analysis of Categorical Data and Goodness-of-Fit Tests

Chi-Squared Test

* used for categorical variables
* used to test 3 or more category proportions
* X² is always positive
* a chi-squared distribution is skewed right, becoming more normal as df increases

Chi-Squared Test for Goodness of Fit

1 population & 1 variable

Conditions:


1. Random Sampling
2. All expected counts ≥ 5

E = (sample size)(hypothesized proportions)

k = number of categories

df = k - 1

\
H0: p= (list the given proportions)

Ha: At least one of these category proportions is not the same.

Chi-Squared Test for Homogeneity

2 populations & 1 variable

Conditions:


1. Independent Samples
2. Random Sampling
3. All expected counts ≥ 5

E = (row total)(column total) / (grand total)

df = (# of rows - 1)(# of columns - 1)

\
H0: p= The category proportions are the same for

_ and _.

Ha: The category proportions are not the same for

_ and _.

Chi-Squared Test for Independence

1 population & 2 variables

Conditions:


1. Random Sampling
2. All expected counts ≥ 5

E = (row total)(column total) / (grand total)

df = (# of rows - 1)(# of columns - 1)

\
H0: There is no association between _ and _.

Ha: There is an association between _ and _.