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Null Hypothesis Significance Testing (NHST)

Decides whether observed patterns in data reflect a real effect or simply random sampling variation

Reject Null Hypoth

p value LESS THAN <0.05

• means there is a meaningful effect or difference, and the observed results are highly unlikely to have happened by random chance alone

Retain Null Hypoth

p value GREATER THAN >0.05

• the null hypothesis means there is not enough evidence to show a difference, meaning any observed patterns could easily be due to random variation.

Single sample tests

One sample vs a reference value

One sample z-test

Used to determine whether the mean of one sample is significantly different from a known population mean.

• When SD is known

One sample t-test

Used to determine whether the mean of one sample is significantly different from a known or hypothesised population mean.

• When SD is UNknown

Two sample tests

Two distinct independent groups or repeated measures

Paired samples t-test

compares the means of two related sets of scores to determine whether there is a significant difference between them.

• repeated measures design

• pre or post test score comparison

Independent samples t-test

compares the means of two separate, unrelated groups to determine whether there is a significant difference between them

• two different groups of participants

• continuous, normal distrubution

Pearson correlation

measure the strength and direction of the relationship between two continuous variables

• Produces a correlation coefficient (r) between -1 and +1.

• Positive = both variables increase together.

• Negative = one increases while the other decreases

Cohen’s d

Cohen's d tells us how large or meaningful the difference is between two means.

• 0.2 small, 0.5 medium, 0.8 large

• one sample t-test, paired samples t test, independent samples t test

• requires normally distrubuted data, continous interval or ratio scale data

Degrees of freedom (df)

Number of independent values that can vary in a statistical analysis.

• Used to help calculate statistical significance (p-values).

• Larger sample size → more degrees of freedom

One-sample t-test = n − 1

Paired-samples t-test = n − 1

Independent-samples t-test = n₁ + n₂ − 2

Absolute r for correlations

How strong the relationship is between two variables.

Absolute r value	Strength
0.00–0.19	Very weak
0.20–0.39	Weak
0.40–0.59	Moderate
0.60–0.79	Strong
0.80–1.00	Very strong

Parametric tests vs non parametric tests

P = Assume data follows a normal distribution (bell-shaped curve).

• Usually used with continuous data

NP = Do not require data to follow a normal distribution.

• Often used with ordinal, ranked or non-normally distributed data.

Assessing normality

Q-Q plot: points match on diagonal line indicate normality

Shapiro wilk: non-significant p values indicate normality

• A non-significant p-value (p > 0.05) suggests normality, while a significant p-value (p < 0.05) suggests non-normality.

Spearman correlation

Measures the strength and direction of the relationship between two variables using ranked data.

• alternative to pearsons correlation

• converts raw continuous data to ranks then computing correlation

Wilcoxon rank-sum test

Used to compare two independent groups to see whether their scores differ.

• independent t-test alternative

• adds all scores, assigns overall rank and sums ranks per grouo

Wilcoxon signed rank test

Used to compare two related sets of scores to see whether there is a significant difference.

• paired t-test alternative

• Usually involves the same participants measured twice (e.g. before and after).

• Uses the size and direction of the differences between paired scores, ranks them, and determines whether there is a significant change.