Research Methodology · Short notes

Biostatistics: Short Notes & Cheat Sheet

Types of data, averages and spread, the normal distribution, hypothesis testing and errors, choosing a statistical test, and risk measures such as NNT.

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Short notes

Read these before you attempt the topic's MCQs.

Picking a statistical test

Ask two questions: what type of data is it, and are the groups independent or paired?

Describing data

Data types: nominal (blood group), ordinal (pain scores), interval (temperature in °C) and ratio (weight, with a true zero).
Mean is affected by outliers; median suits skewed data; mode is the most frequent value.
Spread: range, interquartile range, variance and standard deviation. Standard error = SD ÷ √n describes the precision of a mean.
Normal distribution: mean = median = mode, and about 68%, 95% and 99.7% of values lie within 1, 2 and 3 SD of the mean.
In a positively (right) skewed distribution, mean > median > mode.

Hypothesis testing

The null hypothesis states there is no difference. The p-value is the probability of results at least this extreme if the null hypothesis is true.
A type I error (α, usually 0.05) is a false positive: rejecting a true null hypothesis. A type II error (β) is a false negative.
Power = 1 − β, usually set at 80% or more. Larger samples, bigger effects and less variability increase power.
A 95% confidence interval that excludes the 'no effect' value (0 for differences, 1 for ratios) is statistically significant at p < 0.05.

Choosing tests and measuring effect

Two means: t-test (paired for the same subjects). Three or more means: ANOVA.
Non-parametric versions: Mann–Whitney U (two independent groups), Wilcoxon signed-rank (paired), Kruskal–Wallis (three or more groups).
Categorical data: chi-square test, or Fisher's exact test when expected counts are small (under 5).
Correlation: Pearson (linear, normal data) or Spearman (ranks); r runs from −1 to +1. Regression predicts one variable from others.
Relative risk comes from cohort studies; odds ratio from case-control studies.
Absolute risk reduction (ARR) = control event rate − treatment event rate; number needed to treat (NNT) = 1 ÷ ARR.

Cheat sheet

High-yield facts in one place. Cover the right-hand column and test yourself.

Which test?

Question	Test
2 means, independent groups	Unpaired t-test
2 means, same subjects	Paired t-test
≥ 3 means	ANOVA
2 groups, non-normal	Mann–Whitney U
Paired, non-normal	Wilcoxon signed-rank
≥ 3 groups, non-normal	Kruskal–Wallis
Proportions / categories	Chi-square (Fisher's if small)
Linear relationship	Pearson correlation
Survival over time	Kaplan–Meier, log-rank, Cox

Errors and risk

Term	Meaning
Type I error (α)	False positive
Type II error (β)	False negative
Power	1 − β
ARR	CER − EER
NNT	1 ÷ ARR
Relative risk	Cohort studies
Odds ratio	Case-control studies

Memory aids

Type I = I see something that isn't there: A type I error is a false positive; type II misses a real effect.

Exam traps

A p-value is not the probability that the null hypothesis is true.
Standard error is not the same as standard deviation; SE shrinks as sample size grows.
A confidence interval for a ratio is significant only if it excludes 1, not 0.
Correlation does not prove causation.

Revised? Now test yourself.

Attempt the Biostatistics MCQs while the notes are fresh. Anything you get wrong is saved to your incorrect list for the next revision round.