Chi square

Chi square goodness of fit

tests if a distribution of one variable matches expected distribution

Null hypothesis for chi square goodness of fit

the observed distribution matches what is expected

alternate hypothesis for chi square goodness of fit

the observed distribution does not match what is expected

degrees of freedom of chi square goodness of fit

(number of categories)-1

Assumptions for chi square goodness of fit

-all expected counts are over 5
-random sampling
-independent observations

formula

(observed-expected)^2/expected

contingency tables

look at the bivariable relationship between 2 categorical variables

marginal distriubtion

looks at the probability of events happening for only one of the variables ignoring the other one
-always sums to 100%

conditional probabilities

focus on the probability of randomly selecting someone with certain characteristics from their group

Chi-square test of independence

are two categorical variables independent of one another

bivariate relationship

when there are 2 categorical variables we can make a bar chart or a pie chart to compare the conditional distributions to see if they differ

assumptions of chi square test of independence

-random sampling
-independent observations
-expected counts are over 5

null hypothesis for chi square test of independence

x is independent of y

alternate hypothesis for chi square test of independence

x is not independent of y

first step to analyze chi square of independence

fill in contingency table with observed values

second step to analyze chi square of independence

determine expected count (this is equal to marginal distribution)

third step to analyze chi square of independence

calculate chi square statistic

degrees of freedom for chi square test of independence

(rows-1)(columns-1)
-this excludes the total column

to calculate marginal distribution

((row total)(column total))/grand total

probability notatoin

p(x|reference group)