# 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.

- 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.
- 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.

## Obtaining a Power Analysis

This feature requires the Statistics Base option.

- From the menus choose:
Paired-Sample T-Test, or Independent-Sample T-Test, or One-way ANOVA

, or - Define the required test assumptions.
- Click OK.