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 nonsignificant results are likely even if real differences truly
exist.
In pairedsamples analysis, the observed data contain two paired and correlated samples, and each
case has two measurements. It is assumed that the data in each sample independently and identically
follow a normal distribution with a fixed mean and variance, and draws statistical inference about
the difference of the two means.
 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 method, enter the appropriate Sample size
value. The value must be a positive integer greater than, or equal to, 2.
 Optionally, select an option from the Specify
field.
 Hypothesized Values
 The default setting provides the Mean and
Standard Deviation settings.
 Population mean difference
 When a single population mean is required, enter a Population
mean difference value. When single value is specified, it denotes the population mean
difference μ_{d}.
Note: The value cannot be 0 when
Sample size is selected.
 Population mean for group 1 and group 2
 When multiple population means are required for the specified group pairs,
enter values for Population mean for group 1 and Population mean
for group 2. When multiple values are specified, they denote the population mean
difference μ_{1} and μ_{2}.
Note: The two values
cannot be the same when Sample size is selected.
 Population standard deviation for mean difference
 When a single population mean is specified, enter the population standard
deviation for mean difference value. When a single value is specified, it denotes the population
standard deviation of the group difference σ_{d}. The value must be a single numeric
greater than 0.
 Population standard deviation for group 1 and group 2
 When multiple population means are specified, enter the population standard
deviation for group 1 and group 2 values. When multiple values are specified, they denote the
population standard deviation of the group difference σ_{1} and σ_{2}.
The values must be a single numerics greater than 0.
 Pearson productmoment correlation coefficient
 Optionally, enter a value that specifies the Pearson productmoment
correlation coefficient ρ. The value must be a single numeric value between 1 and 1. The
value cannot be 0.
Note: When a single Population standard deviation
for mean difference value is specified, this setting is ignored. Otherwise, the values
for Population standard deviation for group 1 and group 2 are used to compute
σ_{d}.
 Effect Size
 Estimates 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.
 Select whether the test is one or twosided.
 Nondirectional (twosided) analysis
 When selected, a twosided test is used. This is the default setting.
 Directional (onesided) analysis
 When selected, power is computed for a onesided 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 PairedSamples T Test: Plot settings (chart output, twodimensional plot settings,
threedimensional plot settings, and tooltips).
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 halfwidths.
For more information, see Power Analysis: Precision.
Note: Precision is available only when
Sample size is selected as the test assumption
Estimate method and Hypothesized Values is selected
from the Specify list.
This procedure pastes POWER MEANS RELATED
command syntax.