Biostatistics Basics
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Direct answer
Data type decides the statistical test — that single sentence organises the whole chapter. Qualitative data (nominal and ordinal) is summarised by proportions and compared with the chi-square test; quantitative data is summarised by mean and standard deviation and compared with t-tests or ANOVA, switching to non-parametric tests when the distribution is skewed. Around this sit the normal distribution's 68-95-99.7 rule, standard error and confidence intervals, the null hypothesis with type I and type II errors, and power. FMGE asks tests, definitions and one-step calculations rather than derivations.
What you must remember
- Mean is distorted by outliers; median suits skewed data (income, hospital stay); mode is the most frequent value — all three coincide in a symmetric distribution.
- The normal curve fixes 68.3% of values within ±1 SD, 95% within ±2 SD (precisely 1.96) and 99.7% within ±3 SD.
- Standard error of the mean = SD/√n; the 95% confidence interval is mean ± 1.96 SE, meaning 95 of 100 such intervals would contain the true population mean.
- The null hypothesis states no difference; p < 0.05 means a difference this large would arise by chance less than 5% of the time if the null were true.
- Type I (alpha) error rejects a true null — a false positive, conventionally 5%; type II (beta) error accepts a false null — a false negative, conventionally 20%.
- Power = 1 − beta, set at 80% or more; it rises with sample size, effect size and measurement precision — the reason sample size calculation precedes every trial.
- Parametric tests: chi-square for proportions, unpaired t-test for two independent means, paired t-test for before-after values, ANOVA for three or more means.
- Non-parametric equivalents: Mann-Whitney U, Wilcoxon signed-rank and Kruskal-Wallis; Spearman's rank correlation replaces Pearson's for skewed or ordinal data.
Picking the right test: four worked scenarios
First: does a new antihypertensive lower systolic pressure more than the old one? Two independent groups, continuous outcome — unpaired t-test on the mean fall. Second: the same 30 patients measured before and after yoga — paired t-test, because values are paired within persons. Third: comparing HbA1c across three diets — ANOVA, because multiple pairwise t-tests inflate the type I error. Fourth: is smoking status associated with a positive treadmill test? Two categorical variables, so a chi-square on the counts. Now the twist examiners add: C-reactive protein is heavily right-skewed, so comparing CRP between groups calls for Mann-Whitney U, or log transformation before a t-test. Every choice is two questions in sequence — what type of data, and how many groups or pairings — and answering them in order selects the test.
The SD versus SE confusion
The most persistent viva error is swapping standard deviation and standard error. Standard deviation describes variability of individual observations around the mean — patients differ from each other. Standard error describes variability of the sample mean itself across repeated samples — it shrinks as √n grows, which is why big studies have tight confidence intervals. A related trap is reading the p-value as the probability that the null hypothesis is true; it is the probability of the observed data, or data more extreme, given that the null is true. Remember also the asymmetry of the two errors: a type I error wrongly declares a drug effective (licensing a useless drug), a type II error misses an effective one; regulators fear the first more, hence alpha at a stricter 5% than beta at 20%.
Frequently asked questions
What is the difference between standard deviation and standard error?
Standard deviation measures scatter of individual observations around the sample mean; standard error measures how much the sample mean itself would vary across samples and equals SD divided by the square root of n.
Which test compares two proportions, and which compares two means?
Proportions (smoking rates in two cities) are compared with the chi-square test; means of a continuous variable in two independent groups are compared with the unpaired t-test.
How do type I and type II errors differ?
Type I error (alpha) rejects a true null — concluding a drug works when it does not; type II error (beta) fails to reject a false null — declaring an effective drug useless. Alpha is conventionally 5%, beta 20%.
What is the power of a study and how can it be increased?
Power is 1 − beta, the ability to detect a real difference as significant, conventionally 80%; it increases with larger sample size, larger true effect size and reduced measurement variability.
What does a 95% confidence interval of 4 to 8 mmHg for a blood-pressure difference mean?
If the study were repeated many times, 95% of such intervals would contain the true mean difference; since the interval excludes zero, the difference is significant at the 5% level.
Which non-parametric tests replace the t-test and ANOVA?
Mann-Whitney U replaces the unpaired t-test, Wilcoxon signed-rank replaces the paired t-test, and Kruskal-Wallis replaces one-way ANOVA when data is skewed or ordinal.