# Interpret all statistics and graphs for Power and Sample Size for 1-Sample Z

Find definitions and interpretation guidance for every statistic and graph that is provided with Power and Sample Size for 1-Sample Z.

## α (alpha)

The significance level (denoted as α or alpha) is the maximum acceptable level of risk for rejecting the null hypothesis when the null hypothesis is true (type I error). Alpha is also interpreted as the power of the test when the null hypothesis (H0) is true. Usually, you choose the significance level before you analyze the data. The default significance level is 0.05.

### Interpretation

Use the significance level to minimize the power value of the test when the null hypothesis (H0) is true. Higher values for the significance level give the test more power, but also increase the chance of making a type I error, which is rejecting the null hypothesis when it is true.

## Assumed standard deviation

The standard deviation is the most common measure of dispersion, or how much the data vary relative to the mean. Variation that is random or natural to a process is often referred to as noise.

### Interpretation

The assumed standard deviation is a planning estimate of the population standard deviation that you enter for the power analysis. Minitab uses the assumed standard deviation to calculate the power of the test. Higher values of the standard deviation indicate that there is more variation in the data, which decreases the statistical power of a test.

## Difference

This value represents the difference between the actual population mean and the hypothesized mean.

### Interpretation

Minitab calculates the minimum difference for which you can achieve the specified level of power for each sample size. Larger sample sizes enable the test to detect smaller differences. You want to detect the smallest difference that has practical consequences for your application.

To more fully investigate the relationship between the sample size and the difference at a given power, use the power curve.

## Sample Size

The sample size is the total number of observations in the sample.

### Interpretation

Use the sample size to estimate how many observations you need to obtain a certain power value for the hypothesis test at a specific difference.

Minitab calculates how large your sample must be for a test with your specified power to detect each specified difference. Because sample sizes are whole numbers, the actual power of the test might be slightly greater than the power value that you specify.

If you increase the sample size, the power of the test also increases. You want enough observations in your sample to achieve adequate power. But you don't want a sample size so large that you waste time and money on unnecessary sampling or detect unimportant differences to be statistically significant.

To more fully investigate the relationship between the sample size and the difference at a given power, use the power curve.

## Power

The power of a hypothesis test is the probability that the test correctly rejects the null hypothesis. The power of a hypothesis test is affected by the sample size, the difference, the variability of the data, and the significance level of the test.

### Interpretation

Minitab calculates the power of the test based on the specified difference and sample size. A power value of 0.9 is usually considered adequate. A value of 0.9 indicates that you have a 90% chance of detecting a difference between the population mean and the target when a difference actually exists. If a test has low power, you might fail to detect a difference and mistakenly conclude that none exists. Usually, when the sample size is smaller or the difference is smaller, the test has less power to detect a difference.

If you enter a difference and a power value for the test, then Minitab calculates how large your sample must be. Minitab also calculates the actual power of the test for that sample size. Because sample sizes are whole numbers, the actual power of the test might be slightly greater than the power value that you specify.

## Power curve

The power curve plots the power of the test versus the difference between the mean and the target.

### Interpretation

Use the power curve to assess the appropriate sample size or power for your test.

The power curve represents every combination of power and difference for each sample size when the significance level and the standard deviation are held constant. Each symbol on the power curve represents a calculated value based on the values that you enter. For example, if you enter a sample size and a power value, Minitab calculates the corresponding difference and displays the calculated value on the graph.

Examine the values on the curve to determine the difference between the mean and the target that can be detected at a certain power value and sample size. A power value of 0.9 is usually considered adequate. However, some practitioners consider a power value of 0.8 to be adequate. If a hypothesis test has low power, you might fail to detect a difference that is practically significant. If you increase the sample size, the power of the test also increases. You want enough observations in your sample to achieve adequate power. But you don't want a sample size so large that you waste time and money on unnecessary sampling or detect unimportant differences to be statistically significant. If you decrease the size of the difference that you want to detect, the power also decreases.

In this graph, the power curve for a sample size of 32 shows that the test has a power of 0.9 for a difference of 1.5. As the difference approaches 0, the power of the test decreases and approaches α (also called the significance level), which is 0.05 for this analysis.

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