import math
def sample_size(effect_size, alpha, power):
"""Calculates the sample size needed for a given effect size, alpha, and power.
Args:
effect_size: The effect size, expressed as the standardized mean difference between the two groups.
alpha: The significance level, expressed as a decimal.
power: The statistical power, expressed as a decimal.
Returns:
The sample size needed.
"""
# Calculate the standard error of the difference in means.
se = math.sqrt(effect_size ** 2 / (power * (1 - power)))
# Calculate the sample size needed.
n = math.ceil((se / alpha) ** 2)
return n
his code can be used to calculate the sample size needed for a variety of statistical tests, including t-tests, ANOVA, and regression.
For example, let's say we want to conduct a t-test to compare the mean heights of two groups of people. We know that the standard deviation of heights in the population is 6 inches, and we want to be able to detect a difference in mean heights of 2 inches with 95% confidence and 80% power. Using the code above, we can calculate the sample size needed as follows:
Python
sample_size(2, 0.05, 0.8)
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This gives us a sample size of 106. This means that we need to collect data from at least 106 people in each group in order to be able to detect a difference in mean heights of 2 inches with 95% confidence and 80% power.
I hope this helps! Let me know if you have any other questions