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X 2 Testof Independence/
Homogeneity
still Ch. 26 - AP Statistics
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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...
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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!
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So, the big question…
How do I know if it’s a test of homogeneity or a test of independence??
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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…”
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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
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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!!
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