Post Hoc Statistical Power is the probability that leads to the rejection of the null hypothesis and it indicates the power of a statistical test.
P =2 x ( 1 - Φ(z) )
z = x̄ / σ√N
P = Post HOC Statistical Power z = z-score x̄ = Mean σ = Standard Deviation N = Number of samples
The weekly salaries of six employees at McDonalds are $140, $220, $90, $180, $140, $200. Perform the power analysis
Number of samples = 6, sample values = 140,220,90,180,140,200
Post HOC Statistical Power
Let us first calculate the value of z-score (z),
| Mean (x̄) | = 140+220+90+180+140+200 / 6 |
| = 970 / 6 | |
| = 161.6667 | |
| Standard deviation (σ) | = (((140-161.6667)2 + (220-161.6667)2 + (90-161.6667)2 + (180-161.6667)2 + (140-161.6667)2 + (200-161.6667)2)/6)1/2 |
| = (((-21.6667)2 + (58.3333)2 + (-71.6667)2 + (18.3333)2 + (-21.6667)2 + (38.3333)2)/6)1/2 | |
| = ((469.4459 + 3402.7739 + 5136.1159 + 336.1099 + 469.4459 + 1469.4419)/6)1/2 | |
| = (11283.3334/6)1/2 | |
| = (1880.555)1/2 | |
| = 43.365 | |
| z | = x̄ / σ√N |
| = 161.6667 / ( 43.365 x √6 ) | |
| = 1.52 |
Substitute the values in the Post Statistical Power (P) formula,
| p | = 2 x ( 1 - Φ(z) ) |
| = 2 x ( 1 - Φ(1.52) ) | |
| = 2 x ( 1 - 0.9357 ) | |
| = 0.1286 |
Learn how to calculate the post hoc statistical power analysis in this tutorial, given with the definition, formula and example.
