Power Analysis of Independent-Sample Binomial 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.

The binomial distribution is based on a sequence of Bernoulli trials. It can be used to model those experiments including a fixed number of total trials that are assumed to be independent of each other. Each trial leads to a dichotomous result, with the same probability for a "successful" outcome. The independent-sample binomial test compares two independent proportion parameters.

  1. From the menus choose:

    Analyze > Power Analysis > Proportions > Independent-Samples Binomial 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.

    Optionally, specify a Group size ratio value. The default value is 1.

  4. When Power is selected as the test assumption Estimate setting, enter values to specify the Total number of trials for group 1 and group 2. The values must be an integers greater than 1.
  5. Specify the proportion parameters for the two groups. Both values must be in the range 0 - 1.
    Note: The two values cannot be the same when a Power value is specified.
  6. 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.
  7. Select the desired test method:
    Chi-squared test
    Estimates the power based on Pearson's chi-squared test. This is the default setting.
    Standard deviation is pooled
    This optional setting controls whether the estimation of the standard deviation is pooled or unpooled. The setting is enabled by default.
    Apply continuity correction
    This optional setting controls whether or not the continuity correction is used. The setting is disabled by default.
    T-test
    Estimates the power based on Student's t-test.
    Standard deviation is pooled
    This optional setting controls whether the estimation of the standard deviation is pooled or unpooled. The setting is enabled by default.
    Likelihood ratio test
    Estimates the power based on the likelihood ratio test.
    Fisher's exact test
    Estimates the power based on Fisher's exact test.
    Notes:
    • In some cases, Fisher's exact test may take an extended amount of time to complete.
    • All plots are blocked when Fisher's exact test is selected.
  8. Select a method for estimating the power.
    Normal approximation
    Enables normal approximation. This is the default setting.
    Binomial enumeration
    Enables the binomial enumeration method. Optionally, use the Time limit field to specify the maximum number of minutes allowed to estimate the sample size. When the time limit is reached, the analysis is terminated and a warning message is displayed. When specified, the value must be a single positive integer to denote the number of minutes. The default setting is 5 minutes.
  9. 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.
  10. You can optionally click Plot to specify Power Analysis of Independent-Samples Binomial 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 Estimate and Binomial enumeration is not selected.
  11. 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 Non-directional (two-sided) analysis is selected as the Test Direction.

This procedure pastes POWER PROPORTIONS INDEPENDENT command syntax.