Tests Of Nominal Data

Question 1

Examples

Answer 1

Left handedness and creativity.
Gender and criminality.
Gender and course acceptance.

Question 2

Contingency and associations

Answer 2

Contingency- a relationship between two categories.
A is contingent upon b: a depends on b/ b is necessary for a.
Contingent can mean- a is more likely after b; there is some relationship.

Question 3

Contingency

Answer 3

Involves two (or more) nominal variables. 
Works out the percentage of people in one category are associated with the other category. 
Then construct a contingency table.

Question 4

Contingency tables

Answer 4

Enter four counts into 2 X 2 table.

Calculate row totals, column totals and overall total got the table as shown below.

Question 5

Hypothesis testing

Answer 5

H: is an association between the two variables.
We test it as- does the contingency table differ from what we would expect if there was no relationship? Does it differ significantly from what we would expect to see if the null hypotheses were true?

Question 6

Null hypothesis

Answer 6

We must calculate a contingency for when the null hypothesis is true- we calculate an expected value for each cell of the contingency table.
Expected=(Row total X column total)/overall total.

Work out what numbers would look like in a world there was no association between variable.

Question 7

Chi square

Answer 7

Chi square (X^2) test of associations. 
Degrees of freedom= (Nrows-1) X (Ncolumns-1). 
Look up chi square value and compare to critical value.

Question 8

Types of statistic

Answer 8

Pearson- standardised test.
Likelihood ratio.
Fisher’s exact test- used when the sample size is too low.

Question 9

Assumptions of chi square

Answer 9

You must have at least 5 counts in each cell.

If not, use fisher’s exact test.

Question 10

Goodness-of-fit

Answer 10

When to use-
Looking for how well a set of numbers fit a pattern.
When looking for an odd value from a single population.
When you have nominal data.

Logic is that we compare data obtained with an expected value.
Hypotheses: Ho- data are consistent with a specified distribution.
Ha- data are not consistent with a specified distribution.

Question 11

Assumption of the goodness-of-fit test:

Answer 11

Sampling method is simple random sampling.
Variable understudy is categorical.
Expected value of the number of sample observations in each level of the variable is at least 5.