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# Power for Regression

When planning a regression study, it can be useful to know how likely a response is to be detected. This probability of detection, known as the power of the study with respect to the response of interest, helps to determine whether the study is sufficiently large or accurate to achieve its purpose. Use this to calculate the power either for the assessment of the whole model (as represented by the regression sum of squares), or the assessment of individual parameters in the regression model.

This dialog is opened from the Linear Regression dialog after running an analysis, clicking the Further output button then clicking Power calculations. ## Significance level (alpha)%

Significance level as a percentage (0-100) at which the response is required to be detected; default 5%.

## Residual sum of squares

Specifies the anticipated residual sum of squares. If this field is left blank the residual sum of squares from the current regression model will be used.

## Type of test

Specifies the type of test. You can select to assess the individual parameters using a one -sided or two-sided t-test. You can also test individual parameters for equivalence or for non-inferiority. With equivalence, the size to be detected defines a threshold below which the parameter can be assumed to be equivalent to no response. If the future estimate of the parameter is b and the threshold is blim, the null hypothesis for equivalence is that either

b ≤ -blim or b ≥ -blim

with the alternative hypothesis that they are equivalent, i.e.

-blim < b < blim

With non-inferiority, the null hypothesis becomes

b ≥ -blim

which represents a simple one-sided t-test. You can also set F-ratio, to assess the power of the F test for the regression in the summary analysis of variance; this is an overall test for the whole regression model.

## Display

Specifies which items of output are to be displayed in the Output window.

 Power Display the probability of detection (power)

## Action buttons

 OK On clicking OK the power is calculated and a small dialog displaying the result is opened. Clicking OK on this dialog closes both the Result and Power dialogs returning to the Further output dialog. Clicking the Change button returns you to the Power dialog where you can recalculate the power using different settings. Cancel Close this dialog.