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) standard-deviation 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

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

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