Power Analysis of Paired-Samples 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 paired-samples analysis, the observed data contain two paired and correlated samples, and each case has two measurements. It is assumed that the data in each sample independently and identically follow a normal distribution with a fixed mean and variance, and draws statistical inference about the difference of the two means.

  1. From the menus choose:

    Analyze > Power Analysis > Means > Paired-Samples 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 the appropriate Sample size value. The value must be a positive integer greater than, or equal to, 2.
  5. Optionally, select an option from the Specify field.
    Hypothesized Values
    The default setting provides the Mean and Standard Deviation settings.
    Population mean difference
    When a single population mean is required, enter a Population mean difference value. When single value is specified, it denotes the population mean difference μd.
    Note: The value cannot be 0 when Sample size is selected.
    Population mean for group 1 and group 2
    When multiple population means are required for the specified group pairs, enter values for Population mean for group 1 and Population mean for group 2. When multiple values are specified, they denote the population mean difference μ1 and μ2.
    Note: The two values cannot be the same when Sample size is selected.
    Population standard deviation for mean difference
    When a single population mean is specified, enter the population standard deviation for mean difference value. When a single value is specified, it denotes the population standard deviation of the group difference σd. The value must be a single numeric greater than 0.
    Population standard deviation for group 1 and group 2
    When multiple population means are specified, enter the population standard deviation for group 1 and group 2 values. When multiple values are specified, they denote the population standard deviation of the group difference σ1 and σ2. The values must be a single numerics greater than 0.
    Pearson product-moment correlation coefficient
    Optionally, enter a value that specifies the Pearson product-moment correlation coefficient ρ. The value must be a single numeric value between -1 and 1. The value cannot be 0.
    Note: When a single Population standard deviation for mean difference value is specified, this setting is ignored. Otherwise, the values for Population standard deviation for group 1 and group 2 are used to compute σd.
    Effect Size
    Estimates 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. 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.
  7. 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.
  8. Optionally, click Plot to specify Power Analysis of Paired-Samples T Test: Plot settings (chart output, two-dimensional plot settings, three-dimensional plot settings, and tooltips).
    Note: Plot is available only when Power is selected as the test assumption.
  9. 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 and Hypothesized Values is selected from the Specify list.

This procedure pastes POWER MEANS RELATED command syntax.