Power Analysis for a Two-Sample t-Test

​
effect size
0.4
sample size
30
p-value
0.05
power: 32%
A
t
-test examines a statistical hypothesis following a Student
t
distribution under the null hypothesis. The object is to estimate the mean of a normal distribution for small sample size and unknown standard deviation. The
t
-test can be used to determine if two sets of data are significantly different from one other. This Demonstration provides a visual representation for calculating power in a two-sample
t
-test. Use the sliders to manipulate effect size, sample size and the
p
-value to see how they affect the power in hypothesis testing. The area of the blue shaded region represents the power.

Details

This Demonstration provides a visualization of power analysis for a two-tailed, two-sample
t
-test. A two-sample
t
-test is a hypothesis test to check for statistical significance between two samples. The red curve is the
t
distribution of the null hypothesis. In a two-sample test, this is normally the control sample. The blue curve is the noncentral
t
distribution of the alternative hypothesis. This is normally the experimental sample. The effect size and the sample size determine the noncentrality parameter
δ
. This value appears above the alternative hypothesis distribution. The two vertical lines represent the critical
t
values. The area outside these values represents statistical significance for the given
p
-value. Any part of the noncentral distribution outside the given
t
values represents experiments that would be considered statistically significant. This total area is referred to as the power.

Permanent Citation

Philip Bontrager
​
​"Power Analysis for a Two-Sample t-Test"​
​http://demonstrations.wolfram.com/PowerAnalysisForATwoSampleTTest/​
​Wolfram Demonstrations Project​
​Published: March 2, 2017