Chi-Squared Tests

What are other names for the Chi-squared test?

• x² test

• Chi-squared test of independence

• contingency table test

The chi-squared test was publushed in 1900 by who?

Karl Pearson—father of mathematical statistics

The chi-squared test is an _________ statistic

inferential

The chi-squared test tests if…?

two categorical variables are related

Chi-squared test is used to determine if there is a significant difference between the ________ ________ and the ________ ________ in one or more categorical variable.

expected frequency; observed frequencies

non-parametric test

“distribution free test”

• data doesnt have to be normally distributed

Non-parametric tests are commonly used with ________ data.

skewed/irregular

non-parametric tests overall make ____ assumptions than parametric tests.

less

Chi-square assumptions

Data must be:

 Random

 Mutually exclusive

 Drawn from independent variables

 Large sample

 Nominal and categorical data

The chi-square test of independence assesses..?

whether an association exists between the two variables

• if not, variables are independent

chi-square test also assesses goodness of fit from…?

from an observed distribution and theoretical distribution

If there are no differences between two groups, you would expect them to have ______ ________ of your categorical variable

similar frequencies

If there are significant differences in the frequencies of your categorical variable between the two groups, there must be ____ ________ between those groups

some difference

Example of when you would run a chi-squared test

“Is there an association between relationship status and education level?”

___________ presents the distribution of two categorical variables simultaneously.

crosstabulation/contingency table

Calculating the Chi-Square statistic and comparing it against a value from the Chi-Square distribution allows you to assess whether the observed cell counts are _______ ______ from the expected cell counts

significantly different

Similar to a T-test, the significance of a Chi-squared test is based on:

The χ2 value

The degrees of freedom

Comparing the p-value to the alpha level of your test

If the p-value is less than or equal to alpha, the variables are ________.

associated

i.e., Differences are statistically significant

If the p-value is greater than the alpha,

the variables are _________

not associated

i.e., Differences are NOT statistically significant