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Power & Sample Size Calculator

*using the 1-Sample Z-test method

Use the form below to perform power & sample size calculations. A hypothesis test of the mean, the mu(0) value on the form, when the population standard deviation (sigma) is known. Calculations are based on formulas for the 1-Sample Z-test. If you have questions or problems you can contact Statistical Solutions via E-mail by clicking the following link. Contact Us

Use the 1-Sample Z-test to estimate the mean of a population and compare it to a target or reference value when you know the standard deviation of the population. This method is based on the normal distribution. For small samples, this procedure works best if your data were drawn from a normal distribution or one that is close to normal. You can use this procedure if you have a large sample, substituting the sample standard deviation for the population sigma (σ). Usually, you can consider samples of size 30 or higher to be large samples.

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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(0)

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

Enter a value for mu(1)

This should be the "expected" mean value from your sample. The delta between mu(0) and mu(1) is what you should consider a significant difference for the test.

Enter a value for sigma

This should be the known 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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