X 2 Testof Independence/

Homogeneity

still Ch. 26 - AP Statistics

Three TYPES of X2 tests:

1. X2 goodness of fit test ○ ONE row or column of observed counts ○ Only looking at one variable

2. X2 test of homogeneity○ Two (or more) samples○ Multiple rows and columns of observed counts

3. X2 test of independence○ ONE sample (with multiple variables)○ Multiple rows and columns of observed counts

From last time’s notes...

Conditions for X2 test of ...

Homogeneity:● randomization (SEPARATE random

samples, and/or random assignment to

treatments)

● Expected counts ≥ 5

Independence:● Randomization (ONE random sample)

● Expected counts ≥ 5

And of course, make sure that we have COUNTS of CATEGORICAL data!

So, the big question…

How do I know if it’s a test of homogeneity or a test of independence??

Firstly, know that it’s essentially the same test, and the only change comes in the wording of your hypotheses/conclusion.

HOMOGENEITY: SEPARATE samples are taken, and we’re

comparing the two samples to each other.

“Is there evidence of a DIFFERENCE between…”

INDEPENDENCE:ONE sample is taken, and we’re looking for

dependence between multiple variables.

“Is there evidence of an ASSOCIATION between…”

Examples:

Homogeneity2 different samples taken,

one in 1980 and one in 2000

IndependenceMost likely one sample

taken, where each subject was asked their gender &

fav. TV show

Hypothesis Statements for X2 test of ...

Homogeneity:Ho: the distributions of proportions are the

SAME for all the groups

Ha: the distributions of proportions are

DIFFERENT for all the groups

Independence:Ho: there is NO association between the two

variables (or, the two variables are

independent)

Ha: there IS an association between the two

variables (or, the two variables are

dependent)

As always, make sure you write your hypotheses IN CONTEXT!!