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Sample Size

Sample Size for a Master's Thesis — Step-by-Step Guide

How to calculate the minimum sample size for a two-group comparison study. Covers Cohen's d, z-values, attrition buffer, and APA-7 a priori power analysis statement.

📊 n = 63/group (N = 126) — recruit 75 with 15% buffer

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📐 20 · Sample Size for a Master's Thesis

How Many Participants Do I Need? — Two-Group Comparison

Sample Size

Research Question: A master's student compares blended vs. traditional teaching (two groups). What is the minimum sample size to detect a medium effect (d = 0.5) with 80% power at α = .05?

Parameter	Value	Why
Effect size d	0.5	Medium — Cohen (1988) convention
α	0.05	Standard significance level
Power (1−β)	0.80	80% — minimum recommended

Formula — n per group

n = \frac{2 (z_{α / 2} + z_{β})^{2}}{d^{2}}

1

Find z-values:
$z_{α / 2} = z_{0.025} = 1.96 z_{β} = z_{0.20} = 0.842$
2

Calculate n per group:
$n = \frac{2 (1.96 + 0.842)^{2}}{(0.5)^{2}} = \frac{2 \times 7.857}{0.25} = \frac{15.713}{0.25} \approx 63$
3

Add 15% attrition buffer (recommended):
$n_{a d j} = \frac{63}{1 - 0.15} = \frac{63}{0.85} \approx 75 per group$
4

Total sample to recruit:
$N_{t o t a l} = 75 \times 2 = 150 participants$

Min. per group

Recruit per group

150

Total N

80%

Power

APA-7

An a priori power analysis (Cohen, 1988) indicated that 63 participants per group (total N = 126) were required to detect d = 0.50 with 80% power (α = .05, two-tailed). To account for attrition, 75 participants per group (total N = 150) were recruited.

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Sample Size for a Master's Thesis — Step-by-Step Guide

📐 20 · Sample Size for a Master's Thesis

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