Chi-Squared Tests + Correlation Tests

simpsons paradox

the association between two variables changes when data are separated into groups defined by a third variable (potentially even reversing direction)

chi-squared statistic idea

measures the strength of the association between two categorical variables

compare observed contingency table to some theoretical contingency table that would be expected if there was no relationship (i.e. compare observed counts v expected counts)

chi-squared formula

(observed-expected)²/expected

chi-squared for independence

tests the independence of two categorical variables using counts in a contingency table

chi-squared statistic is a test statistic

chi-test for indpendece hypotheses

Ho= two variables are independent

Ha = two variables are not independent

degrees of freedom (df) for x² of independence

(r-1)(c-1)

df based on size of contingency table

r=number of rows

c= number of columns

sampling distribution

sampling distribution of the chi-squared statistic if the null hypothesis is true

right skewed

assigns probabilities to positive values

identified by degrees of freedom

approaches normal distribution as df increases

goodness of fit test

a test of the distribution of a single categorical variable

testing for randomness

correlation

a standard measure of the strength of the linear association between two numeric variables

sign shows direction, magnitude shows strength

covariance

a measure that quantifies the linear association between x + y

corr (x,y)

cov(x,y)/SxSy