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Power & Sample Size Calculator

*using the 2-Sample T-test method

Use this test method to:

  • Determine whether the means of two independent groups (populations) differ.
  • Calculate a range of values that is likely to include the difference between the population means.

Calculations are based on formulas for the 2-Sample T-test. To perform a 2-Sample T-test, the two populations must be independent; in other words, the observations from the first sample must not have any bearing on the observations from the second sample. If you have questions or problems you can contact Statistical Solutions via E-mail by clicking the following link. Contact Us

2-Sample T-test calculates a confidence interval and does a hypothesis test of the difference between two population means when standard deviations are unknown and samples are drawn independently from each other. This procedure is based on the t-distribution, and for small samples it works best if the data were drawn from distributions that are normal or close to normal. You can have increasing confidence in the results as the sample sizes increase.

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Calculate Sample Size

Choose which calculation you desire, either to determine a power or a sample size. See more for the power of the test below.

Calculate Power

Enter a value for mu(1)

This should be the "known" mean value for population 1.

Enter a value for mu(2)

This should be the "known" mean value for population 2

Enter a value for sigma

This should be the common sigma (standard deviation) for the population.


One-sided test

Choose whether your test is based on one-sided or two-sided criteria. A single specification limit or pass/fail is one-sided, alternately an upper and lower specification is two-sided.

Two-sided test

Enter a value for alpha (a)

(default is .05)

The outcome of the test depends on whether the null hypothesis (H0) is true or false and whether you reject or fail to reject it. When H0 is true and you reject it, you make a Type I error. The probability (p) of making a Type I error is called alpha (a), or the level of significance of the test. When H0 is false and you fail to reject it, you make a Type II error. The probability (p) of making a Type II error is called beta (b). See more on the Type I and Type II errors below.

Power of the test

(default is .80)

The power of a test is the probability of correctly rejecting H0 when it is false. In other words, power is the likelihood that you will identify a significant effect when one exists. If you are solving for power, leave this field blank. If you are solving for sample size, it is recomended to leave this field at the default value of .80 and the associated sample size will be generated when you click the calculate button.

Sample size for the test

*sample size is for each group

If you are solving for sample size, leave this field blank. If you are solving for power, enter your desired sample size and the associated power will be generated when you click the calculate button..

 

Null Hypothesis (H0)
Decision H0 is True H0 is False
Fail to reject H0

Correct decision

p = 1 - a

Type II error

p = b

Reject H0

Type I error

p = a

Correct decision

p = 1 - b

 

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