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Publication date: 11/10/2021

One Sample Mean Calculator Fields

Specify the following quantities:


The probability of a type I error, which is the probability of rejecting the null hypothesis when it is true. It is commonly referred to as the significance level of the test. The default alpha level is 0.05.

Tip: For a one-sided test, use α = α *2. For a one sided test with α = 0.05, use the two-sided calculator with α = 0.10. The resulting values are those needed for a one-sided test with α = 0.05.

Std Dev

The assumed standard deviation. An estimate of the error standard deviation could be the root mean square error (RMSE) from a previous model fit.

Tip: Use a standard deviation of 1 to estimate the sample size needed to detect differences measured in standard deviation units.

Extra Parameters

The number of parameters other than μ in the hypothesis test. This option can be used for multi-factor designs. Leave the default zero in this field for simple cases.

In a multi-factor design where effects are orthogonal, you can specify the number of additional model parameters here. For example, in a three-factor, two-level design with all three two-factor interactions, the number of additional parameters is five: two parameters for the other main effects, and three parameters for the interactions.

Specify two of the following values to calculate the third value, or specify one value to obtain a plot of the relationship between the other two:

Difference to Detect

The smallest difference between the true mean and the hypothesized or reference mean you want to be able to declare statistically significant.

Sample Size

The total number of observations (runs, experimental units, or samples) in your experiment.


The probability of rejecting the null hypothesis when it is false. With all other parameters fixed, power increases as sample size increases.

Calculator Buttons


Evaluates the missing value when two parameters are specified, or launches a plot comparing two missing parameters if only one parameter is specified.


Returns to the previous Sample Size and Power launch window.

Animation Script

Launches an interactive plot to illustrate and explore the relationship between power and the difference to detect. See Example of an Animation Script.

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