inferential statistics

Question 1

What is the Chi-Square test used for?

Answer 1

To test for a difference between observed and expected frequencies in categorical (nominal) data.

Question 2

When is Chi-Square appropriate?

Answer 2

Nominal data
Independent groups design
Test of difference

Question 3

Strengths and weaknesses of Chi-Square?

Answer 3

Simple to use with categorical data
Widely applicable
− Requires expected frequencies
− Less powerful than parametric tests

Question 4

What is the Mann-Whitney U test used for?

Answer 4

To test for a difference between two independent groups using ordinal data.

Question 5

When is it appropriate?

Answer 5

Independent groups design
Ordinal data or non-normal interval data

Question 6

strengths and weaknesses of the mann-whitney u test?

Answer 6

Good alternative to independent t-test
Works with small samples
− Less sensitive than parametric tests
− Uses ranks → loss of detail

Question 7

What is the Sign Test used for?

Answer 7

To test for a difference in repeated measures designs using nominal data (direction of change).

Question 8

When is it appropriate?

Answer 8

Repeated measures design
Nominal data (e.g. + / − changes)

Question 9

Strengths and weaknesses of the sign text?

Answer 9

Very simple to calculate
Minimal assumptions
− Very low sensitivity
− Ignores magnitude of change

Question 10

What is Spearman’s rank used for?

Answer 10

To test for a correlation between two co-variables.

Question 11

When is it appropriate?

Answer 11

Correlational design
Ordinal data (or non-parametric interval data)

Question 12

Strengths and weaknesses of the spearman’s rank test?

Answer 12

Identifies strength and direction of relationship
Works with ranked data
− Cannot show causation
− Affected by outliers

Question 13

What is the Wilcoxon test used for?

Answer 13

To test for a difference in repeated measures or matched pairs designs using ordinal data.

Question 14

When is it appropriate?

Answer 14

Repeated measures or matched pairs
Ordinal data

Question 15

Strengths and weaknesses of the Wilcoxon test?

Answer 15

More sensitive than Sign Test
Considers magnitude of differences
− More complex to calculate
− Still less powerful than parametric tests

Question 16

What is a probability value (p-value)?

Answer 16

The probability that the results occurred by chance.

Question 17

How are p-values interpreted?

Answer 17

p ≤ 0.05 → significant (reject null hypothesis)
p > 0.05 → not significant (accept null hypothesis)

Question 18

What is a significance level?

Answer 18

The threshold used to decide if results are statistically significant (usually 0.05).

Question 19

Why is 0.05 commonly used?

Answer 19

It means there is only a 5% probability results are due to chance.

Question 20

What is an observed value?

Answer 20

The test statistic calculated from the data

Question 21

What is a critical value?

Answer 21

The value taken from a statistical table to compare against the observed value.

Question 22

How do you decide whether results are significant?

Answer 22

If observed value ≥ critical value → significant → reject null
If observed value < critical value → not significant → accept null

Question 23

What do the symbols mean in inferential statistics?

Answer 23

= equal to
< less than
> greater than
≤ less than or equal to
≥ greater than or equal to

Question 24

How do you choose the correct statistical test?

Answer 24

1. Identify difference or correlation
2. Identify type of data (nominal/ordinal/interval)
   Identify experimental design
3. → Then match to the correct test (e.g. Mann-Whitney = independent + ordinal)