TOPIC #11: Tests for relationship

Module 4 DATA1001

Chi-squared test (x²)

Assesses goodness of fit and independence

In terms of the chi squared test, what is goodness of fit?

assesses whether the observed frequency distribution of a categorical variable matches an expected theoretical distribution.

in terms of the chi squared test, what is independence?

examines whether there is a significant association between the two qualitative variables

difference between goodness of fit and independence?

goodness of fit examines 1 qualitative variable, whereas independence examines 2 qualitative variables. moreover, the goodness of fit compares observed data to theoretical distribution whereas independence examines relationship between variables in the same population.

test statistic for x²test for goodness of fit

x² = sum of [(observed frequency - expected frequency)²/ expected frequency]

why do we square the differences between observed frequency and expected frequency?

squaring the differences between observed and expected frequencies ensures that both positive and negative differences contribute to the test statistic

what are the differences between chi squared goodness of fit and independence?

hypotheses and the way the degrees of freedom are calculated