# Learn how to calculate Multiple Regression Post Hoc Statistical Power - Tutorial

## How to calculate Multiple Regression Post Hoc Statistical Power - Definition, Formula, and Example

##### Definition:

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.

#### Formula:

x̄ = Sum of X values / N(Number of values) P =2 x ( 1 - Φ(z) ) z = x̄ / σ√N
###### where,

P = Post HOC Statistical Power z = z-score x̄ = Mean σ = Standard Deviation N = Number of samples

##### Example :

The weekly salaries of six employees at McDonalds are \$140, \$220, \$90, \$180, \$140, \$200. Perform the power analysis

##### Given,

Number of samples = 6, sample values = 140,220,90,180,140,200

##### To Find,

Post HOC Statistical Power

##### Solution
###### Step 1:

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
###### Step 2:

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

#### Related Calculator:

Learn how to calculate the post hoc statistical power analysis in this tutorial, given with the definition, formula and example.