How to justify your sample size (and answer "why 384?")

Almost every quantitative thesis in India contains the number 384, and almost none of them explain it. Examiners have noticed. If you are using it, you should know exactly what it means and be able to derive it.

Where 384 comes from

It is Cochran's formula for an infinite population at a 95% confidence level, 5% margin of error and maximum variability (p = 0.5):

n₀ = Z²pq / e²   =   (1.96)² × 0.5 × 0.5 / (0.05)²   =   384.16

Round up and you get 385, or 384 depending on convention. That is the entire derivation. If your population is finite and known, you should be applying the finite population correction, which will give you a smaller number:

n = n₀ / (1 + (n₀ − 1)/N)

With a population of 1,000, that correction brings 384 down to about 278. Reporting 384 for a population of 1,000 tells your examiner you copied the number rather than calculated it.

When Cochran is the wrong tool entirely

Cochran's formula estimates a proportion. If your study tests relationships — regression, SEM, ANOVA — you need a power analysis, not a proportion formula. The inputs are different:

• Effect size you expect, ideally taken from published studies in your field
• Statistical power, conventionally 0.80
• Alpha, conventionally 0.05
• Number of predictors in your largest regression

G*Power will do this for you in about a minute, and the output is exactly what belongs in Chapter 3. Screenshot it, cite the effect size source, and the question is answered before it is asked.

SEM has its own rules

For covariance-based SEM, common guidance is a minimum of 200 cases, or 10 to 20 cases per estimated parameter. For PLS-SEM, the older "ten times rule" is widely criticised; a power analysis based on the most complex regression in your model is more defensible. Whichever you use, cite the source you took the rule from.

What actually goes in your methods chapter

1. Which approach you used and why it suits your design
2. The inputs — effect size, power, alpha, population — and where each came from
3. The calculated minimum
4. Your achieved sample, and the response rate
5. What you did about non-response bias

Five sentences. That is the difference between a question you dread and a question you welcome.