Ch 22 - Chi square test for two-way tables Flashcards
An experiment has a two-way, or block, design if
two categorical factors are studied with several levels of each factor.
Two-way tables organize data about
two categorical variables with any number of levels/treatments obtained from a two-way, or block, design
The marginal distributions
(in the “margins” of the table) summarize each factor independently.
The conditional distributions
The cells of the two-way table represent the intersection of a given level of one factor with a given level of the other factor. They represent the conditional distributions.
A two-way table has r rows and c columns. H0 states
that there is no association between the row and column variables in the table.
he expected count in any cell of a two-way table when H0 is true is:
We will compare actual counts from the sample data with expected counts given the null hypothesis of no relationship.
Observed vs Expected
The chi-square test for two-way tables looks for evidence of association between
2 categorical variables (factors) in sample data.
The samples for the chi-square test for two-way tables can be drawn by
We can safely use the chi-square test when:
1) no more than 20% of expected counts are less than 5 (< 5)
2) all individual expected counts are 1 or more (≥1)
The chi-square test for two-way tables The __ statistic is summed over all r x c cells in the table
χ2
When H0 is true, the χ2 statistic follows
~ χ2 distribution WITH (r-1)(c-1) degrees of freedom.
When the χ2 test is statistically significant The_____ indicate which condition(s) are most different from H0.
largest components
You can also compare the observed and expected counts, or compare the computed proportions in a graph.
An association that holds for all of several groups can reverse direction when
the data are combined to form a single group.
This reversal is called Simpson’s paradox.
