# Power Analysis of One-Sample Pearson Correlation 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.

Pearson's product-moment correlation coefficient measures the strength of linear association between two scale random variables that are assumed to follow a bivariate normal distribution. By convention, it is a dimensionless quantity and obtained by standardizing the covariance between two continuous variables, thereby ranging between -1 and 1.

The test uses Fisher's asymptotic method to estimate the power for the one-sample Pearson correlation.

Analyze > Power Analysis > Correlations > Pearson Product-Moment

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. When Power is selected as the test assumption Estimate setting, enter the appropriate Sample size in pairs value. The value must be a single integer greater than 3.
5. Enter a value that specifies the alternative hypothesis value of the correlation parameter in the Pearson correlation parameter field. The value must be a single numeric between -1 and 1.
Note: When Power is specified, the Pearson correlation parameter value cannot be -1 or 1 and cannot be equal to the Null value.
6. Optionally, enter a value that specifies the null hypothesis value of the correlation parameter to be tested in the Null value field. The value must be a single numeric between -1 and 1. The default value is 0.
Note: When Power is specified, Null value cannot be -1 or 1.
7. Optionally, select Use bias-correction formiula in the power estimation to specify whether the bias adjustment is involved or ignored. The setting is enabled by default, which includes the bias adjustment term in the power estimation. When the setting is not selected, the bias adjustment term is ignored.
8. 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.
9. 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.
10. You can optionally click Plot to specify Power Analysis of One-Sample Pearson Correlation: 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.
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 PEARSON ONESAMPLE command syntax.