Power Analysis of Independent-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 independent-samples analysis, the observed data contain two independent samples. 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 > Independent-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.

    Enter a Group size ratio value for specifying the ratio of the sample sizes (the value must be a single value between 0.01 and 100.

  4. When Power is selected as the test assumption Estimate method, enter values to specify the sample size for Sample size for group 1 and group 2 for comparison. The values must be an integers greater than 1.
  5. Optionally, select an option from the Specify field.
    Hypothesized Values
    The default setting provides the Population mean and Population standard deviations settings.
    Population mean difference
    When a single population mean is specified, enter the population mean difference value. When a single value is specified, it denotes the population of the group mean difference σd. The value must be a single numeric greater than 0.
    Population mean for group 1 and group 2
    When multiple population means are specified, enter the population mean for group 1 and group 2 values. When multiple values are specified, they denote the population mean of the group difference σ1 and σ2. The values must be a single numerics greater than 0.
    Population standard deviations are
    Specify whether the population standard deviations are Equal for two groups or Not equal for two groups.
    • When the population standard deviations are equal for two groups, enter a value for Pooled standard deviation that denotes σ, and assumes that the two group variances are equal, or σ1 = σ2 = σ.
    • When the population standard deviations are not equal for two groups, enter values for Standard deviation for group 1 and group 2 that denote σ1 and σ2.
      Note: When the values for Standard deviation for group 1 and group 2 are identical, they are treated as a single value.
    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 Independent-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, 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 INDEPENDENT command syntax.