statistical tests

Spearman’s Rho

Purpose:

To test for a relationship (correlation) between two variables.
It tells you whether, as one variable increases, the other increases or decreases.

Type of Hypothesis:

• Correlation hypothesis (e.g. “There will be a positive relationship between stress and illness.”)

Design:

• Not about groups, just two continuous or ranked variables measured in the same participants.

Level of Measurement:

• Ordinal (ranked data) or interval (if not normally distributed).

pearsons r

Purpose:

To test for a linear relationship (correlation) between two continuous variables.

Type of Hypothesis:

• Correlation hypothesis (e.g. “There will be a positive correlation between revision time and test score.”)

Design:

• Not about groups, same participants measured on both variables.

Level of Measurement:

• Interval or ratio data

• Data must be normally distributed

Wilcoxon Signed-Rank Test

Purpose:

To test for a difference between two related conditions.

Type of Hypothesis:

• Difference hypothesis (e.g. “There will be a difference in anxiety before and after therapy.”)

Design:

• Related design → same or matched participants (repeated measures / matched pairs).

Level of Measurement:

• Ordinal data (ranked scores).

Mann–Whitney U Test

Purpose:

To test for a difference between two independent groups.

Type of Hypothesis:

• Difference hypothesis (e.g. “There will be a difference in stress levels between males and females.”)

Design:

• Unrelated design → different participants in each condition (independent groups).

Level of Measurement:

• Ordinal data (ranked scores).

Related t-test

Purpose:

To test for a difference between two related conditions when data are numerical.

Type of Hypothesis:

• Difference hypothesis (e.g. “There will be a difference in memory scores before and after caffeine.”)

Design:

• Related design (repeated measures or matched pairs).

Level of Measurement:

• Interval or ratio data

• Must be normally distributed (parametric test).

Unrelated t-test

Purpose:

To test for a difference between two independent groups when data are numerical.

Type of Hypothesis:

• Difference hypothesis (e.g. “There will be a difference in test performance between sleep-deprived and non-sleep-deprived groups.”)

Design:

• Unrelated design (independent groups).

Level of Measurement:

• Interval or ratio data

• Data must be normally distributed (parametric test).

Chi-Squared Test (χ²)

Purpose:

To test for an association (or difference) between categorical variables.

Type of Hypothesis:

• Difference or association hypothesis (e.g. “There will be a difference between males and females in preference for therapy type.”)

Design:

• Unrelated design → independent groups.

Level of Measurement:

• Nominal data (categories like yes/no, male/female, etc.)