Wemedoo Sample Size and Power Calculator

TEST FOR ONE MEAN

Purpose: Tests for the difference between the mean of a sample and a user specified value.

Example: A researcher is planning a study with individuals who have been smokers for 20 or more years. Average FEV1 (maximal amount of air the person can forcefully exhale in one second) in the general population is 4.0 liters. The assumption of the researcher is that smokers’ average FEV1 is 3.5 liters with a standard deviation (SD) of 1.2 liters. Alpha (the significance level) is set to 0.05. In statistical testing, this is probability of obtaining a false positive result.

SAMPLE SIZE CALCULATION

How many subjects need to be tested in order to achieve an 80% probability to detect a significant difference between the average of the general population (4 liters) and that of smokers’ (3.5±1.2 liters). Power is set to 0.80 (80%).

Design:
Alpha (α) = 0.05
Power = 0.80
Mean 1 = 4
Mean 2 = 3.5
Standard Deviation = 1.2

Result: A sample size of 46 subjects is required to achieve 80% power to detect a significant difference between the mean results for the null and alternative hypotheses.

POWER CALCULATION

What power achieves a sample size of 72 subjects if smokers have and average FEV1 of 3.5 liters with a standard deviation 1.2 liters?

Design:
Alpha (α) = 0.05
Sample Size (N) = 72
Mean 1 = 3.5
Mean 2 = 4
Standard Deviation = 1.2

Result: A sample size of 72 subjects achieves 94% power to detect a significant difference between the mean FEV1s of the null and alternative hypotheses.