Power Analysis of One-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.
Binomial distribution is based on a sequence of Bernoulli trials. It can be used to model experiments, including a fixed number of total trials, which are assumed to be independent of each other. Each trial leads to a dichotomous result, with the same probability for a successful outcome.
The one-sample binomial test makes statistical inference about the proportion parameter by comparing it with a hypothesized value. The methods for estimating the power for such a test are either the normal approximation or the binomial enumeration.
- From the menus choose:
- Select a test assumption Estimate setting (Sample size or Power).
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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.
- When Power is selected as the test assumption Estimate setting, enter the appropriate Total number of trials value. The value must be an integer greater than, or equal to, 1.
- Enter a value that specifies the alternative hypothesis value of the proportion parameter in the
Population proportion field. The value must be a single numeric.Note: When a Power value is specified, the Population proportion value cannot be equal to the Null value.
- Optionally, enter a value that specifies the null hypothesis value of the proportion parameter to be tested in the Null value field. The value must be a single numeric in the range 0 - 1. The default value is 0.50.
- Select a method for estimating the power.
- Normal approximation
- Enables normal approximation. This is the default setting.
- Apply continuity correction
- Control whether or not the continuity correction is used for the normal approximation method.
- 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.
Note: The selected power estimation assumption has no effect when the Total number of trials value exceeds 500. - 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.
- 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.
- Optionally, click Plot to specify Power Analysis of One-Sample Binomial: 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.
- 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.
This procedure pastes POWER PROPORTIONS ONESAMPLE command syntax.