# Power Analysis of One-Way ANOVA

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.

Analysis of variance (ANOVA) is a statistical method of estimating the means of several populations which are often assumed to be normally distributed. The One-way ANOVA, a common type of ANOVA, is an extension of the two-sample t-test. The procedure provides approaches for estimating the power for two types of hypothesis to compare the multiple group means, the overall test, and the test with specified contrasts. The over test focuses on the null hypothesis that all group means are equal. The test with specified contrasts breaks down the overall ANOVA hypotheses into smaller but more describable and useful pieces of the means.

Analyze > Power Analysis > Means > One-way ANOVA

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.

4. Optionally, select an option from the Specify field.
Hypothesized Values
The default setting provides the Pooled population standard deviation setting. Enter a single numeric value greater than 0. The default value is 1.
Effect Size: Cohen's f
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.
Effect Size: Eta-squared
Eta-squared (η2) 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.
5. When Power is selected as the test assumption Estimate setting, specify the Group sizes and Group means values. At least two group size values must be specified, and each of the group size values must be greater than or equal to 2 (but cannot exceed 2,147, 483, 647). At least two group mean values must also be specified (the number of specified values must equal the group size values).
When Sample size is selected as the test assumption Estimate setting, specify the Group weights (optional) and Group means values. Group weights assign the group size weights when Power is selected.
Note: The Group weights settings are ignored when Group sizes values are specified.

Click Add to include more Group sizes, Group weights, and Group means values. Click Delete to remove existing values.

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. Optionally, click Contrast to specify Power Analysis of One-way ANOVA: Contrast settings (contrast test, pairwise differences, effect sizes, and estimate the sample size based on confidence intervals).
8. Optionally, click Plot to specify Power Analysis of One-way ANOVA: Plot settings (chart output, two-dimensional plot settings, three-dimensional plot settings, and tooltips).
Note: Plot is available only when Group sizes values are specified and Power is selected as the Estimate setting.
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.

This procedure pastes POWER ONEWAY ANOVA command syntax.