Power Analysis of One-Sample Spearman 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.
Spearman rank-order correlation coefficient is a rank-based nonparametric statistic to measure the monotonic relationship between two variables that are usually censored and not normally distributed. The Spearman rank-order correlation is equal to the Pearson correlation between the rank values of the two variables, thereby also ranging between -1 and 1. Detecting the power of the Spearman rank correlation test is an important topic in the analysis of hydrological time series data.
The test uses Fisher's asymptotic method to estimate the power for the one-sample Spearman rank-order correlation.
- From the menus choose:
- Select a test assumption Estimate setting (Sample size or Power).
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 Sample size in pairs value. The value must be a single integer greater than 3.
- Enter a value that specifies the alternative hypothesis value of the correlation parameter in
the Spearman correlation parameter field. The value must be a single numeric
between -1 and 1.Note: When Power is specified, the Spearman correlation parameter value cannot be -1 or 1 and cannot be equal to the Null value.
- 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.
- Optionally, select an option that determines how the asymptotic variance is
estimated for the power analysis.
- Bonett and Wright
- Estimates the variance suggested by Bonett and Wright. This is the default setting.
- Fieller, Hartley and Pearson
- Estimates the variance suggested by Fieller, Hartley and Pearson.
- Caruso and Cliff
- Estimates the variance suggested by Caruso and Cliff.
- 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 Spearman 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.
- 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 SPEARMAN ONESAMPLE command syntax.