Equality of Proportions (chi squared test) Flashcards
What tests would you used to compare categorical/non-parametric data?
Chi squared tests
What test would you used to see whether the population proportion is equal to a certain value?
One sample χ2 test
What assumptions are needed for the one sample chi-square test?
▪️Observations are randomly and independently drawn
▪️Number of cells (categories) with expected frequencies less than 5 are less than 20%
▪️The minimum expected frequency is at the very least 1
What is the df for a one sample chi-square test?
categories-1
What test would you used to see whether the proportions in the population of one variable change based on another variable (are the proportions different) ?
Person’s chi square test
(Independent samples)
What is the null hypothesis of a person’s chi square test?
There is no association between the two variable (proportions are the same)
What assumptions are needed for Pearson’s chi square test?
▪️Observations are randomly and independently drawn
▪️Number of cells with expected frequencies less than 5 are less than 20%
▪️Minimum expected frequency is at the very least 1
▪️Observations are not paired
When do you check assumptions for chi-square tests?
AFTER the test
Look at bottom of the table
How do you know whether to compare proportions by row or column for a Pearson’s chi square test?
You cannot statistically compare proportions that add up to 100%
If they add by column, compare them by row!
We cannot compare proportions that….
Add up to 100%!!
Why can’t you compare proportions that add up to 100?
▪️Only the descriptive indices of one of the variables
▪️Doesn’t consider the relationship between variables
E.g. 15 of the 30 who died were vaccinated. Reporting it as 50% is just descriptive of those who died, it doesn’t consider the rest of the population who didnt
What is the df for a Pearson’s chi square test?
(c1-1)(c2-1)
For a 2x2 grid this is 1
What test do we use to see whether the proportion of a variable changes based on another matched variable (is proportion in one condition different to that in the same/paired group in another condition?
McNemar χ2 test
What is the null hypothesis of a McNemar chi square test?
There is no association between two (paired) variables
What assumptions are needed for the McNemar chi square test?
▪️Observations are randomly and independently drawn
▪️At least 25 observations in the discordant cells
▪️Data are paired
What are the discordant cells?
Cells that have changed from yes to no or vice versa
What are the concordant cells?
Cells that haven’t changed (still yes or still no)
Which cells do you use for the McNemar chi square test?
Only the discordant cells
What symbol is used for means?
μ
What symbol is used for proportions?
π
