# Power Analysis

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.

IBM® SPSS® Statistics provides the following Power Analysis procedures:
One Sample T-Test
In one-sample analysis, the observed data are collected as a single random sample. It is assumed that the sample data independently and identically follow a normal distribution with a fixed mean and variance, and draws statistical inference about the mean parameter.
Paired Sample T-Test
In paired-sample 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.
Independent Sample T-Test
In independent-sample analysis, the observed data contain two independent samples. 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.
One-way ANOVA
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.

Example. The power of a hypothesis test to detect a correct alternative hypothesis is the probability that the test will reject the test hypothesis. Since the probability of a type II error is the probability of accepting the null hypothesis when the alternative hypothesis is true, the power can be expressed as (1-probability of a type II error), which is the probability of rejecting the null hypothesis when the alternative hypothesis is true.

Statistics and plots. One-sided test, two-sided test, significance level, Type I error rate, test assumptions, population standard deviation, population mean under testing, hypothesized value, two-dimensional power by sample size, two-dimensional power by effect size, three-dimensional power by sample size, three-dimensional power by effect size, rotation degrees, group pairs, Pearson product-moment correlation coefficient, mean difference, plot range of the effect size, pooled population standard deviation, contrasts and pairwise differences, contrast coefficients, contrast test, BONFERRONI, SIDAK, LSD, power by total sample size, two-dimensional power by pooled standard deviation, three-dimensional power by total sample, three-dimensional power by total sample size, pooled standard deviation, Student’s t-distribution, non-central t-distribution,

## Power Analysis data considerations

Data
In one-sample analysis, the observed data are collected as a single random sample.
In paired-sample analysis, the observed data contain two paired and correlated samples, and each case has two measurements.
In independent-sample analysis, the observed data contain two independent samples.
Analysis of variance (ANOVA) is a statistical method of estimating the means of several populations which are often assumed to be normally distributed.
Assumptions
In one-sample analysis, it is assumed that the sample data independently and identically follow a normal distribution with a fixed mean and variance, and draws statistical inference about the mean parameter.
In paired-sample analysis, 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.
In independent-sample analysis, 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.
In one-way ANOVA, the statistical method of estimating the means of several populations are often assumed to be normally distributed.

## Obtaining a Power Analysis

This feature requires the Statistics Base option.