Post-Hoc Power Analysis for Underpowered Study

POST-HOC POWER ANALYSIS

Your Study:

• Control: n=25, M=72, SD=8
• Treatment: n=23, M=75, SD=9
• P-value: 0.08 (not statistically significant)
• Effect size: Cohen’s d = 0.35 (small-to-medium)

RESULT: Your study was SEVERELY UNDERPOWERED

Achieved Power: 22.1%

• You had only a 22% chance of detecting this effect
• Standard threshold is 80%
• With 48 total participants, you were underpowered by nearly 6x

Required for 80% power: 130 per group (260 total)

What This Means:

Your p=0.08 result is inconclusive. The 3-point difference between groups (75 vs 72) represents a small-to-medium effect that would require 130 participants per condition to reliably detect. With only ~24 per group, you had less than 1-in-4 odds of finding a significant result even if the true effect exists.

RECOMMENDATIONS:

1. Report as pilot study - Frame this as preliminary/exploratory research with promising but inconclusive findings
2. Design properly powered follow-up - Recruit 130+ per group for definitive test
3. DO NOT p-hack - Resist temptation to add a few more participants hoping to cross p<0.05
4. Focus on effect size - Report the confidence interval around the 3-point difference rather than fixating on p-value

The Bottom Line: Yes, this study was underpowered. The marginally non-significant result (p=0.08) combined with low power (22%) means you cannot draw meaningful conclusions about whether the treatment works.