analysing categorical data

Question 1

how can you analyse categorical data?

Answer 1

create a contingency table

perform a chi-square test (do people fall into a category more often than we expect them too?)

Question 2

what are contingency tables?

Answer 2

a table for frequencies for how often an observation occurs in a category

Question 3

what must categories be in a contingency table?

Answer 3

mutually exclusive

exhaustive

Question 4

what is a chi-square test?

Answer 4

devised by Karl Pearson in 1900, also known as Pearson’s chi-square

calculates how often a particular observation falls into a category based on how many were expected by chance

Question 5

what is the null hypothesis in a chi-square test?

Answer 5

the frequencies observed were expected by chance

Question 6

what is the alternative hypothesis in a chi-square test?

Answer 6

the frequencies observed reflect real differences in categories

Question 7

what are the assumptions in a chi-square test?

Answer 7

independence - each person can only contribute to one cell of a contingency table

expected frequencies - all expected counts should be greater than 1 and no more than 20% of expected counts should be less than 5 - if violated, power reduced

Question 8

what are the options if expected frequencies assumption violated?

Answer 8

use an “exact” test instead (e.g. Fisher’s or MLR)

collapse/remove data across one variable

collapse levels of one variable

collect more data

accept the loss of power

Question 9

what are the steps of chi-square by hand with one IV?

Answer 9

calculate expected frequencies

calculate chi-square value based on observed and expected frequencies

compared chi-square value against critical values table

to interpret table, need to know degrees of freedom (number of categories - 1) and our desired alpha value

reject H- when X2observed > X2critical

Question 10

how is chi-square with two IVs calculated?

Answer 10

with two IVs, difference will be in calculating the expected values in each case

to calculate expected frequencies for two IVs, need to calculate expected frequencies of specific cells

degrees of freedom = (number of rows - 1) x (number of cells - 1)

Question 11

what is a binomial test?

Answer 11

compares observed and expected frequencies for variable with only two levels