Choosing the right statistical test for your hypothesis
A practical table linking the type of hypothesis and variables to the appropriate test, with each test's assumptions before applying it.
One of the most common questions researchers face: how many people do I need? The answer depends on the population size, the confidence level, the margin of error you accept, and the type of statistical analysis you'll run.
Types of samples
- Simple random: every individual has an equal chance of being selected.
- Stratified: divides the population into groups (such as governorates or departments) and samples from each group in proportion.
- Cluster: selects whole groups such as schools or branches; useful for geographically dispersed populations.
- Convenience: whoever is easy to reach; it's non-probability and hard to generalize from.
- Purposive: deliberately selecting those with the required expertise; common in qualitative studies.
Cochran's formula
For a large or infinite population the formula used is:
n₀ = z² × p × (1 − p) / e²
where z is the standard score for the confidence level (1.96 at 95%), p is the expected proportion (0.5 when unknown since it gives the largest sample), and e is the margin of error (usually 0.05). With these values the sample is about 385.
And if the population is finite and known with size N, the result is corrected:
n = n₀ / (1 + (n₀ − 1) / N)
Sample size calculator (Cochran's formula)
Minimum sample385
Number of questionnaires to distribute428
Assuming a proportion of 0.5 (the most conservative).
Additional rules
- In structural equation modeling (SEM) the sample should preferably be at least 200, or 10 individuals per measurement item according to some references.
- Add a buffer of 10% to 20% to compensate for incomplete or unreturned questionnaires.
- In experimental studies the size is calculated with a power analysis using software such as G*Power.
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