Power Analysis of One-Sample T Test

This feature requires IBM® SPSS® Statistics Base Edition.

Power analysis plays a pivotal role in a study plan, design, and conduction. The calculation of power is usually before any sample data have been collected, except possibly from a small pilot study. The precise estimation of the power may tell investigators how likely it is that a statistically significant difference will be detected based on a finite sample size under a true alternative hypothesis. If the power is too low, there is little chance of detecting a significant difference, and non-significant results are likely even if real differences truly exist.

In one-sample analysis, the observed data are collected as a single random sample. It is assumed that the sample data independently and identically follow a normal distribution with a fixed mean and variance, and draws statistical inference about the mean parameter.

  1. From the menus choose:

    Analyze > Power Analysis > Means > One-Sample T Test

  2. Select a test assumption Estimate setting (Sample size or Power).

  3. When Sample size is selected, enter either a Single power value for sample size estimation value (the value must be a single value between 0 and 1), or select Grid power values and then click Grid to view projected sample sizes for a range of specific Power values.

    For more information, see Power Analysis: Grid Values.

  4. When Power is selected as the test assumption Estimate method, enter an appropriate Sample size for power estimation value. The value must be an integer greater than 1.
  5. Optionally, select an option from the Specify field.
    Hypothesized Values
    The default setting provides the Population mean and Null value settings.
    Population mean
    Enter a value that specifies the population mean under testing. The value must be a single numeric.
    Null value
    Optionally, enter a value that specifies the null hypothesis value to be tested. The value must be a single numeric.
    Effect Size
    Cohen's f is used to estimate the effect size as an input to the estimation of the power or sample size. The defined effect size Value is passed to the intermediate step in the procedure and calculates the desired power or sample size.
  6. Enter a Population standard deviation value. The value must be a single numeric greater than 0.
  7. Select whether the test is one or two-sided.
    Nondirectional (two-sided) analysis
    When selected, a two-sided test is used. This is the default setting.
    Directional (one-sided) analysis
    When selected, power is computed for a one-sided test.
  8. Optionally, specify the significance level of the Type I error rate for the test in the Significance level field. The value must be a single double value between 0 and 1. The default value is 0.05.
  9. You can optionally click Plot to specify Power Analysis of One-Sample T Test: Plot settings (chart output, two-dimensional plot settings, and three-dimensional plot settings).
    Note: Plot is available only when Power is selected as the test assumption.
  10. Optionally, click Precision to estimate the sample size based on confidence intervals by specifying the values of the confidence interval half-widths. For more information, see Power Analysis: Precision.
Note: Precision is available only when Sample size is selected as the test assumption Estimate method, Hypothesized Values is selected from the Specify list, and Non-directional (two-sided) analysis is selected as the Test Direction.

This procedure pastes POWER MEANS ONESAMPLE command syntax.