A power analysis is the calculation that tells you how large a sample size your study needs to reliably detect the effect you care about. It links four quantities, your target power, your significance level, the effect size you expect, and the sample size, so that fixing any three solves for the fourth. For a dissertation, it is the principled way to justify how many participants you will recruit.
Why a justified sample size strengthens your thesis
Picking a sample size by guesswork or convenience is one of the weaknesses your committee looks for first. An a priori power analysis replaces that guess with a defensible number, run before any data is collected. It protects you on two fronts: too small a sample risks an underpowered study that misses a real effect, while a needlessly large one wastes time and resources. Stating the calculation in your methods chapter shows that your dissertation was designed to answer its research questions, not merely to fill a spreadsheet. The underlying idea of detecting a true effect is set out in what statistical power is.
The four inputs every power analysis needs
To run a calculation you must supply, or deliberately decide, four things. The first is the significance level, the threshold for your p-value, conventionally 0.05. The second is your target power, usually 0.80 or 0.90. The third is the expected effect size, the hardest input, which you justify from prior studies, a pilot, or a smallest effect that would matter in practice, as explained in effect size explained. The fourth is the statistical test you plan to run, because the formula differs for a t-test, an ANOVA, a correlation, or a regression; matching the test to your design is covered in choosing a statistical test. Get these four right and the required sample size follows directly.
A priori vs post hoc power analysis
The timing of the calculation changes everything. An a priori power analysis runs before data collection: you fix your target power, significance level, and expected effect size, then solve for the sample size you need. This is the version your committee wants, because it justifies recruitment in advance and protects against an underpowered study. It is forward-looking and design-led, which is exactly the framing set out in what statistical power is.
A post hoc power analysis, by contrast, plugs the effect size you actually observed back into the formula after the study is done. It feels reassuring but is widely criticised, because observed power is a one-to-one function of your p-value and therefore tells you nothing new: a non-significant result will always look underpowered by this measure. If you must comment on a null finding, report the smallest effect your sample could have reliably detected, or the confidence interval around the estimate, rather than a circular post hoc figure.
Calculating sample size with G*Power
G*Power is the free, widely cited tool most students use for a defensible calculation, and committees recognise it. The workflow is consistent across designs: choose the test family (for example t tests, F tests, or exact tests), pick the specific test that matches your design, then set the analysis type to a priori so it solves for sample size. You then enter your chosen effect size, an alpha of 0.05, and a target power of 0.80 or 0.90, and it returns the total sample and the critical value.
The one step people get wrong is the effect size convention, since G*Power uses its own metrics such as f for ANOVA rather than eta squared, so convert carefully before you type a number in. Record every input you used, because the screenshot or the listed parameters are what make the calculation reproducible in your methods chapter. If you would rather not install software, the sample size calculator runs the same logic in your browser, and choosing the matching test first is covered in selecting the right statistical test.
How effect size drives required sample size
Of all four inputs, the effect size moves the required sample size the most, and it moves it non-linearly. Halving the effect you expect to detect roughly quadruples the number of participants you need, because power depends on the effect scaled by the standard error, and that error only shrinks with the square root of the sample. This is why an honest, slightly conservative effect estimate matters so much: an optimistic guess produces a comfortably small sample on paper and an underpowered study in reality.
The safest practice is to plan around the smallest effect size of interest, the smallest difference that would actually change a decision or a theory, rather than the largest effect you hope to see. Justify that figure from prior studies or a pilot, using the benchmarks in the guide to effect size, and you can pressure-test it by converting raw means into a standardised value with the effect size calculator before it ever enters the power calculation.
Can you do it by hand, and rules of thumb
For a simple design you can calculate sample size with a formula and a table of critical values, but most researchers use dedicated software because it handles the awkward distributions behind an ANOVA or a multiple regression cleanly. Quick rules of thumb exist, such as requiring roughly ten cases per predictor in a regression, and they are useful for a sanity check, but they are no substitute for a calculation tied to your real effect size and target power. Treat a rule of thumb as a rough floor and the formal power analysis as the number you actually report. To run the calculation now, the sample size calculator solves for the n you need from the exact distributions.
Sizing a sample from a finite population
When you are sampling from a known, finite group, such as the students on one programme or the staff at one hospital, the question shifts slightly. Here you often want a sample large enough to estimate a proportion within a chosen margin of error and confidence level, and a finite population correction reduces the required number when the population itself is small. The practical takeaway is that sample size does not grow without limit as the population grows: beyond a certain point, a few hundred well-chosen cases estimate a proportion almost as precisely for a population of one hundred thousand as for one million. Whichever route fits your dissertation, the distinction between describing your sample and generalising to the population is worth keeping clear, as set out in descriptive versus inferential statistics. State your assumptions, show the calculation, and your sample size becomes a strength of the thesis rather than a question mark.