Slides 8: Chi Square Tests

What kind of variables do you use chi square for?

categorical

What do chi square tests use for test statistics and compare?

use z and t to compare sample means to hypothesized population mean

the further t gets from 0…

the less likely you get your data if the null is true

X² measures…

the difference between the frequency distribution in thr sample and the frequency you would expect if null is true

Describe chi square distribution

follows a known distribution

What depends on df?

width of the distribution

What kind of X² values are more likely to be under the null if the null is true?

small values

If you have a single categorical value, what is X² called?

goodness-of-fit test

X² equation and variable meanings

X² = ∑((E-O)²)/E

X² - chi square

∑ - sum of

E - expected frequencies

O - observed frequencies

You reject the null if…

X² test statistic > X² critical value, and p < 0.05

Goodness-of-fit test assumptions

representative of population, independent individual observations, large enough so all expected values greater than 1, 80% expected values 5 or greater

What frequencies and study types can you use for goodness-of-fit tests?

use absolute frequencies, can be experimental or observational

X² test of association

for questions about relationship between two categorical variables

What is the null hypothesis for a X² test of association?

X and Y are unrelated/frequency distribution of X same for all Y values and vice versa

Give an example of a X² test of association

biology major students admitted as freshman or as transfer students, null is academic standing is not associated with admission