2.3.4 Inferential Testing

What is inferential testing in psychology?

A set of statistical tests used to determine whether findings are due to chance or are statistically significant.

What does “statistically significant” mean?

The probability that results are due to chance is low (usually p ≤ 0.05).

What is the purpose of inferential testing?

To decide whether to accept or reject the null hypothesis.

What is the sign test used for?

To analyse differences between paired data (repeated measures or matched pairs) using nominal data.

When is the sign test appropriate?

When data is nominal (categories), and you are comparing two related conditions.

What does the sign test measure?

The number of + and – differences between paired scores.

What is the null hypothesis in a sign test?

There is no difference between conditions; any difference is due to chance.

What is the formula for the sign test?

S = number of less frequent sign (ignore ties).

How do you calculate the sign test?

1. Ignore ties
2. Count + and – differences
3. Take smaller value as S
4. Compare with critical value
5. If S ≤ critical value, results are significant.

What is probability in inferential testing?

The likelihood that results occurred by chance.

What is a p-value?

The probability of obtaining results at least as extreme as those observed, assuming the null hypothesis is true.

What is a critical value?

The value from statistical tables that results are compared against to determine significance.

What does p ≤ 0.05 mean?

There is a 5% or less probability that results are due to chance.

What is a Type I error?

Incorrectly rejecting the null hypothesis (false positive).

What is a Type II error?

Failing to reject the null hypothesis when it is false (false negative).

What increases the risk of a Type I error?

Using a lenient significance level (e.g. p ≤ 0.10).

What increases the risk of a Type II error?

Using a very strict significance level (e.g. p ≤ 0.01).

What are the key factors in choosing a statistical test?

Level of measurement and experimental design.

What is nominal data?

Data in categories (e.g. yes/no, male/female).

What is ordinal data?

Data ranked in order but with unequal intervals.

What is interval data?

Data with equal intervals between values (e.g. test scores).

When is Spearman’s rho used?

To test for a correlation between two variables using ordinal or non-parametric data.

When is Pearson’s r used?

To test for a correlation between two variables using interval/ratio data that is normally distributed.

Difference between Spearman’s rho and Pearson’s r?

Spearman’s uses ordinal/non-parametric data; Pearson’s uses interval/ratio and assumes normal distribution.

When is the Wilcoxon test used?

To test differences in related data (repeated measures or matched pairs) using ordinal data.

When is the Mann-Whitney test used?

To test differences between two independent groups using ordinal data.

Difference between Wilcoxon and Mann-Whitney?

Wilcoxon is for related groups; Mann-Whitney is for unrelated groups.

When is the related t-test used?

To compare means in related samples using interval data.

When is the unrelated t-test used?

To compare means between independent groups using interval data.

Difference between parametric and non-parametric tests?

Parametric tests use interval data and assume normal distribution; non-parametric tests use ordinal/nominal data or non-normal distributions.

When is the Chi-Squared test used?

To test for an association between two categorical (nominal) variables.

What does Chi-Squared measure?

The difference between observed and expected frequencies.

What type of data is used in Chi-Squared?

Nominal data.

What is the null hypothesis in Chi-Squared?

There is no association between variables.

When is Chi-Squared significant?

When the calculated value is greater than or equal to the critical value.

When is a related t-test or Wilcoxon used in design terms?

Repeated measures or matched pairs design.

When is an unrelated t-test or Mann-Whitney used in design terms?

Independent groups design.

When are correlation tests used in design terms?

When looking at relationships between variables, not differences.

What is the main difference between parametric and non-parametric tests?

Parametric tests use interval data and assume normal distribution; non-parametric tests do not.

What is the main purpose of all inferential tests?

To determine whether results are statistically significant or due to chance.