Getting started...

Overview

The program Power on X provides a method to determine the statistical power of a data set, or to determine the sample size required to produce a particular power.

This is not the appropriate place to discuss power calculations, however, a brief discussion and overview is provided.

Starting Power on X

Double click the icon!

Performing a calculation

At present Power on X will perform power calculations based on one and two-tailed t-Tests of means or correlations. Calculations can be a priori (performed on data derived from a pilot or previous studies) or post hoc where the data has already been derived.

A priori calculation

  1. Select the 'Pre' tab on the 'Power on X' window.
  2. Select the 'tailing' of the calculation (either one-tailed or two-tailed).
  3. Select the test type (t-Test means or t-Test correlation).
  4. Enter alpha value (significance level; typically 0.05, but must be between 0 and 1).

For t-Test of means

  1. Enter the effect size (d). This value can be calculated (see below) and is greater than 0. (Cohen (see reference section below) suggests an effect size of 0.8 should be considered as 'large', 0.5 as 'medium' and 0.2 as 'small'.)

For t-Test of correlations

  1. Enter the effect size (r). This value can be calculated (see below) and is greater than 0 and less than or equal to 1. In general r = 0.5 is considered a large effect, r = 0.3 is considered as medium and r = 0.1 a small effect.

Finally (for all tests)

  1. Enter desired power. (Value is between 0 and 1)
  2. Click the 'Calculate' button.

Post hoc calculation

  1. Select the 'Post' tab on the 'Power on X' window.
  2. Select the 'tailing' of the calculation (either one-tailed or two-tailed).
  3. Select the test type (t-Test means or t-Test correlation).
  4. Enter alpha value (significance level; typically 0.05, but must be between 0 and 1).

For t-Test of means

  1. Enter the effect size (d). This value can be calculated (see below) and is greater than 0. (Cohen (see reference section below) suggests an effect size of 0.8 should be considered as 'large', 0.5 as 'medium' and 0.2 as 'small'.)

For t-Test of correlations

  1. Enter the effect size (r). This value can be calculated (see below) and is greater than 0 and less than or equal to 1. In general r = 0.5 is considered a large effect, r = 0.3 is considered as medium and r = 0.1 a small effect.

Finally (for all tests)

  1. Enter the sample size. (This may be entered as either sizes for samples 1 and size for sample 2, or by taking the full sample size and dividing between the two.)
  2. Click the 'Calculate' button.

The results

The a priori calculation will return the sample size for the experiment. It should be noted that this is TOTAL sample size, and NOT per group.

The post hoc analysis will return the power of the statistical test.

In addition, both power calculations will return:

Effect size calculation

Three methods available for calculating the effect size for a t-Test of means:

1 SD - Calculates the effect size using two means and a standard deviation (SD; see equations for formula used).

2 SD - Calculates the effect size using two means and two standard deviations (SD 1 and SD 2). This method also requires the sample sizes (n 1 and n 2) associated with the two standard deviations to allow a pooled value to be calculated (see equations for formula used).

SEM - Calculates the effect size using two means and two standard error of means (SEM 1 and SEM 2). This method also requires the sample sizes (n 1 and n 2) associated with the two standard error of means to allow the standard deviations to be back calculated and final a pooled value to be calculated (see equations for formula used).

For the calculation of the effect size r in t-Test correlations only one calculation is available and that is teh conversion of r-squared to r.

Power and sample size table generation (only available in paid mode)

Power tables can be calculated for any given alpha (significance) values and a range of sample sizes and effect sizes. In addition, the table generator will also produce a sample size table for any given alpha (significance) value and a range of powers and effect sizes. These calculations can be performed one or two sided tests and for t-Test means or correlation,

  1. Start the table calculator from the new section of the file menu.

Calculation of power tables

  1. Select 'Power' in the pull down 'Table type:' menu.
  2. Enter the alpha value.
  3. Select tail type ('Two' or 'One') in the 'Tail type:' menu.
  4. Select the test type (mean or correlation).
  5. Click on the 'Run' button.

Calculation of sample size tables

Note: The size returned is per sample set.

  1. Select 'n =' in the pull down 'Table type:' menu.
  2. Enter the alpha value.
  3. Select tail type ('Two' or 'One') in the 'Tail type:' menu.
  4. Select the test type (mean or correlation).
  5. Click on the 'Run' button.

References

See: http://www.mmisoftware.co.uk/pages/library/

Cohen J. Statistical Power Analysis fro Behavioral Sciences. New York: Academic Press, 1969, 1977, 1988

Minimum, E.W, Roberts, R.C., Coladarci, T. Elements of Statistical Reasoning. Wiley, 1999

Pagano, R.P. Understanding Statistics in the Behavioral Sciences. Brooks/Cole, 1998