Educational Research and Statistics
Expect two kinds of question: conceptual (which design, which variable, which sampling technique) and computational (a simple mean, standard deviation, z, t or chi-square). Know the logic behind each formula, because distractors are usually built from one wrong step.
Research concepts
Variables: independent, dependent, intervening, control; operational definition. Hypotheses: null and alternative, directional and non-directional. Scales of measurement: nominal, ordinal, interval, ratio - they determine which statistic is legitimate. Sampling: probability (simple random, systematic, stratified, cluster, multi-stage) and non-probability (convenience, purposive, quota, snowball). Designs: survey, correlational, causal-comparative (ex post facto), experimental with randomisation, quasi-experimental (intact groups, pre-test/post-test), single-subject, case study, ethnographic, historical, and action research (practitioner, cyclical: plan, act, observe, reflect). Validity threats: history, maturation, testing, instrumentation, selection, mortality, regression to the mean. Ethics: consent, anonymity, confidentiality, no harm, honest reporting, no plagiarism. Triangulation strengthens credibility. Report structure follows standard conventions: problem, objectives, hypotheses, methodology, analysis, discussion, conclusion, references.
Statistics
Measures of central tendency: mean, median, mode. Dispersion: range, quartile deviation, mean deviation, variance, standard deviation, coefficient of variation. Normal curve: about 68-95-99.7 per cent within one, two and three standard deviations. Correlation: Pearson r for interval data, Spearman rho for ordinal; correlation is not causation. Inferential tests: t-test for two means, ANOVA for three or more (F ratio), chi-square for association of categorical data. Know standard error, degrees of freedom, significance level, Type I error (rejecting a true null) and Type II error, and one- versus two-tailed tests.
Traps
- Using parametric tests on nominal data.
- Reading p less than 0.05 as proof the effect is large.
- Confusing standard deviation with standard error.
Worked example
Scores 4, 6, 8, 10, 12: mean = 8; deviations -4, -2, 0, 2, 4; squared 16, 4, 0, 4, 16 = 40; variance = 40/5 = 8; SD = 2.83. A pupil scoring 12 has z = (12 - 8)/2.83 = 1.41, above about 92 per cent of the group.