☰ MedicalStat

Calculate Power and Sample Size


Alpha (α) is the significance level, usually 0.05 (5 %). It is the same as the risk of making a Type 1 error (rejecting a true null hypothesis).

Beta (β) is often 0.20 (20 %). It is the same as the risk of making a Type 2 error (accepting a false null hypothesis).

1 - β is the power of the study and is often 1 - 0.20 = 0.80 (80 %).

The power of a study is the probability of rejecting a false null hypothesis.


Section 1: Power

1. Dichotomous outcome (proportions)

p1 is the proportion of outcome in sample 1. p2 is the proportion of outcome in sample 2.

n1 is the size (no. of persons) of sample 1. n2 is the size of sample 2.

Calculate the power from the proportions
Significance level α
Proportion p1
Proportion p2
Sample Size n1
Sample Size n2
Measures of Association
Risk Difference Risk Ratio Odds Ratio



Power
1 - β (Power)
β (Type 2 error)

2. Continuous outcome (mean values)

\( \bar{x}_1\) is the mean value in group 1 (for ex. the exposed group).

\( \bar{x}_2\) is the mean value in group 2.

n1 is the size of sample 1. n2 is the size of sample 2.

Calculate the power from the means
Significance level α
Mean \( \bar{x}_1 \)
Mean \( \bar{x}_2 \)
Common SD
Sample size n1
Sample size n2
Measure of Association
Mean Difference MD

Power
1 - β
β (Type 2 error)

Decimals:

Section 2: Sample Size

1. Dichotomous outcome (proportions)

p1 is the proportion of outcome in sample 1. p2 is the proportion of outcome in sample 2. n1 is the size of sample 1. n2 is the size of sample 2.
Risk Difference = p1 - p2. Risk ratio = \( \frac{p_1}{p_2} \). Odds Ratio = \( \frac{odds_1}{odds_2} \)

The ratio \( \frac{n_2}{n_1} \) is how many times larger (or smaller) n2 is compared to n1. For ex. n2 = 400 and n1 = 100, then ratio = 400/100 = 4

Calculate the required sample sizes
Significance level α
Power 1 - β
Proportion p1
Proportion p2
Ratio \(\frac{n_2}{n_1}\)
Measures of Association
Risk Difference Risk Ratio Odds Ratio



Sample Sizes
Sample size n1
Sample size n2
Total n1 + n2

2. Continuous outcome (mean values)

\( \bar{x}_1\) is the mean value in group 1 (for ex. the exposed group).

\( \bar{x}_2\) is the mean value in group 2.

The ratio \( \frac{n_2}{n_1} \) is how many times larger (or smaller) n2 is compared to n1. For ex. n2 = 100 and n1 = 400, then ratio = 100/400 = 0.25

Calculate the required sample sizes
Significance level α
Power 1 - β
Mean \( \bar{x}_1 \)
Mean \( \bar{x}_2 \)
Common SD
Ratio \(\frac{n_2}{n_1}\)
Measures of Association
Mean Difference (MD)

Sample Sizes
Sample Size n1
Sample Size n2
Total n1 + n2