- Quantitative data
- Data consisting of numbers — frequencies, scores, measurements, ratings — that can be analysed statistically. Enables objective comparison across groups, hypothesis testing, and generalisation via inferential statistics. Generated by closed questionnaire items, reaction time tasks, physiological measures, structured observations with frequency counts, and standardised tests.
- Qualitative data
- Data consisting of non-numerical information — words, descriptions, themes, narratives — typically analysed through thematic analysis, content analysis, grounded theory, or interpretative phenomenological analysis (IPA). Provides depth, nuance, and insight into meaning and experience that quantitative data cannot capture. Generated by open-ended interviews, open survey questions, case studies, and naturalistic observations.
- Correlation
- A statistical relationship between two variables: as one changes, the other tends to change in a consistent direction. Positive correlation: both increase together. Negative correlation: as one increases, the other decreases. Zero correlation: no systematic linear relationship. Correlations describe associations but do not establish cause — the direction of influence is unknown, and both variables may be driven by a third.
- Correlation coefficient (r)
- A standardised measure of the strength and direction of a linear relationship between two variables, ranging from −1.00 to +1.00. The sign indicates direction; the absolute value indicates strength (closer to 1 = stronger, scores cluster tightly around the trend line; closer to 0 = weaker, scores scatter widely). Cohen's benchmarks: |r| ≈ 0.1 small, |r| ≈ 0.3 medium, |r| ≈ 0.5 large.
- Correlation ≠ causation
- Three reasons prevent a correlation from establishing causation. Reverse causation: the direction of influence is unknown (does A cause B, or B cause A?). Third-variable problem: a confounding variable C may cause both A and B, producing an association with no direct causal link between them. No manipulation: in a correlational study, the researcher does not change any variable — only true experiments (with IV manipulation and random allocation) establish causal direction.
- Statistical significance and p-values
- A p-value answers: given that the null hypothesis is true, how probable is it that we would observe results at least as extreme as these? A p < .05 threshold means researchers accept a 5% risk of falsely rejecting the null when it is actually true (Type I error rate). Statistical significance does not mean the effect is large, important, or replicable — only that it is unlikely to be due to chance at the chosen alpha level.
- Type I error (false positive)
- Rejecting the null hypothesis when it is actually true — concluding there is an effect when there is none. The probability of a Type I error is set by the alpha level (typically .05). Reducing alpha (e.g. to .01) decreases Type I errors but increases Type II errors. Multiple comparisons inflate Type I error rates — testing 20 hypotheses at p < .05 produces on average one false positive by chance.
- Type II error (false negative)
- Failing to reject the null hypothesis when it is actually false — missing a real effect. The probability of a Type II error is β; statistical power = 1 − β (the probability of detecting a real effect). Power increases with: larger sample sizes, larger true effect sizes, more sensitive measurement, and higher alpha (at the cost of Type I errors). Most psychology studies conducted before the 2010s were substantially underpowered (Cohen, 1962).
- Effect size and Cohen's d
- Effect size quantifies how large a difference or relationship is, independent of sample size. Cohen's d is the standardised difference between two group means: d = (M₁ − M₂) / SD_pooled. Benchmarks: d ≈ 0.2 small, d ≈ 0.5 medium, d ≈ 0.8 large. A study can be statistically significant (unlikely due to chance) but have a trivially small effect size — common in large-sample studies. Effect sizes are comparable across studies using different scales and are the basis of meta-analysis.