Lecture 10 - Categorical Data Flashcards
How is x^2 calculated?
The frequency of each mutually exclusive, exhaustive category is recorded and compared to the frequencies expected by chance:
X^2=E((obs f-exp f)^2/exp f)
This test statistic is them compared to critical values in a table using degrees of freedom (no. of categories – 1). We can reject H0 when x^2>=critical.
What is Chi square (x^2)?
A test for categorical data to determine how often observations fall into a particular category. It compares how many observations fall into a category with how many were expected based on a model
Also known as Pearson’s Chi-square
How does Chi-squared change when there is more than one IV?
The expected values are calculated as (row total x column total)/grand total, so that the row and column totals still hold true.
The degrees of freedom is calculated by (rows-1)(columns-1)
How do you carry out a Chi-squared test in SPSS?
For one IV:
Analyse|non-parametric tests|Chi-square
For multiple IVs:
Analyse|descriptive statistics|crosstabs, on next window click statistics and select x^2. In output, first box is about missing entries, 2nd counts per category and IV, 3rd is the useful stuff!
What assumptions does Chi-squared make?
- the data are assumed to be a random sample
- the expected frequencies for each category must be at least one and no more than 20% should be less than 5
- he categories must be exhaustive and mutually exclusive
How can low expected frequencies be dealt with in a Chi-squared test?
- categories can be collapsed
* small categories can be discarded or excluded (‘select cases’ on SPSS), which must then be declared with the results
What is the binomial test?
A statistical test used for data that can only have two values which, like the Chi-square, compares whether the frequency of occurrence for two values has some expected ratio.
Could be used to test heads/tails.
How do you do a binomial test in SPSS?
Analyse|non-parametric tests|binomial test
