+34 616 71 29 85 carsten@dataz4s.com
Select Page

# Statistical power calculation

The statistical power calculation is the calculation of the probability that we reject a false null hypothesis. So, this calculation returns a numbered probability. Statistical power is also known via the term Power of Test.

If we test a H0 for µ ≥ 60 in a world where the true mean is 53 and our statistical power calculation = 0.70, we can say that there is approximately a 70% probability that we will reject H0, in case the true mean is 53.

## The procedure

The statistical power calculation, or calculation of Power of Test, can be done by following these three steps:

## Statistical power calculation example

Let’s run through an example where we have a one sample and one-tailed z-test around a mean. The same procedure goes for other tests.

Say we are going to test the following hypotheses:

H0: µ ≥ 60

Ha: µ < 60

Significance level (α) = 0.10

We are about to run a simple random sample of 38 and assume that our population is normally distributed with a known standard deviation (σ) = 24 and with an unknown mean (µ).

### Step 1: Critical value for z

The critical z for an alpha level of 0.10 is -1.28. This can be looked up in the normal distribution table and is also embedded in statistical software.

### Step 2: Critical value for the sample mean (x̄):

We apply the z-statistic formula plugging in our existing values in order to calculate the critical value: So, our critical value for x̄ is 55.01 meaning that we will reject for any sample mean equal to or less than 55.01.

### Step 3: The statistical power calculation

What is the statistical power in case the true H0 is 53? We can calculate this via the z formula finding first the Type II Error: The probability of z > 0.52 is looked up in the normal distribution table and returns a value of 0.30. This is our Type II Error (β). The power calculation is 1-β, so we get a Power of Test, or a statistical power, of 0.70 in case the true mean should be 53.

As also described in Statistical power, we can see the relation between alpha, beta and power in a power curve and in the bell curves:  ## Statistical power calculation in Excel

Statistical power calculation in Excel can be calculated with the help of the =NORM.S.INV and the =NORM.DIST functions:

Left tailed and right tailed examples:  ## Learning statistics

Some of my preferred materials for learnings on statistical power calculation: #### Carsten Grube

Freelance Data Analyst

p
p
p
##### ANOVA & the F-distribution +34 616 71 29 85

Call me Spain: Ctra. 404, km 2, 29100 Coín, Malaga

...........

Denmark: c/o Musvitvej 4, 3660 Stenløse

Drop me a line

What are you working on just now? Can I help you, and can you help me?