Nominal Data Flashcards
Examples of nominal data
Categories
Yes or no responses
Counts / frequencies
Leads to proportions
E.g
Number of Yes/No responses
Number of Heads or Tails in a coin toss game
Number of left/right-handers in a sample
Number of Votes for and against
What are expected frequencies?
The chance level depends on what we are testing…
Coin Flip
50/50 chance of heads or tails
→ Chance level = 50% or 0.50
What do binomial tests tell us?
A binomial test tells us the probability of finding our observed proportion given the expected proportion (chance).
E.g. If I flip a coin 100 times I would expect to get 50 Heads and 50 Tails
Assumptions for a binomial test
- Single Dichotomy – One variable with 2 mutually exclusive outcomes
- The scores are from a random sample of the population
- Data are independent (participants contribute one data point)
- You know the expected distribution of scores (chance level)
What does a Chi square test of independence tell us?
Are the proportions significantly different between groups?
How to know if Chi squared results are significant
Look at critical values table for 0.05
If chi-squared result is higher than the critical value then it is significant and the results are significantly different
Assumptions of a Chi squared test
- Data are nominal
- There are two dichotomies – e.g. male/female AND yes/no
- The scores are from a random sample of the population
- Data are independent (participants contribute one data point)
- Sample size must be at least 40
- Each category must have an expected N of 5 or above
What is the non parametric alternative for Chi square test?
Fisher’s Exact Test
What does a Chi square goodness of fit test tell us?
How does an observed proportion differ from an expected proportion?
Assumptions for a
Chi square goodness of fit test
Data are nominal
Multiple levels of a single dependent variable
*e.g. Location (Africa, Asia, Australasia, Europe, N.America, S.America)
Scores are from a random sample of the population
Scores are independent
Each category has an expected N of 5 or above
Reporting p values
To 3 decimal places
With no leading zero (.050)
Lowercase and in italics (p)
Report exact values not < .050 or > .050
The only exception is p <.001 (never .000)
How to know if goodness of fit test is significant?
If p is equal to or less than 0.05 then results are significantly different than those expected by chance
What is a problem with a one tailed hypothesis?
May miss an effect on the other tail (direction)
Use one tailed/directional hypothesis!!!
But also report two tailed results
