# Minitab 15 Tutorial: Using Power and Sample Size Tools with Power Curves

For any job, you need a tool that offers the right amount of power. You don’t use a telescope to examine a stamp collection or a handheld magnifying glass to search for new galaxies because neither provide you with meaningful observations. To complicate matters, the cost of achieving the necessary power might be more than you can afford.

Anyone who uses statistical tests faces the same issues. You must consider the precision that you need to meet your goals (should your test detect subtle effects or massive shifts?) and balance it against the cost of sampling your population (are you testing toothpicks or jet engines?). You also want the confidence in your results that’s appropriate for your situation (tests for seat belts demand a greater degree of certainty than tests for shampoo require). We can measure this certainty using statistical power—the probability that your test will detect an effect that truly exists.

Minitab’s Power and Sample Size tools, with Power Curves, help you to balance these issues that may compete for your limited resources. Here are three examples of how a quick Power and Sample Size test can help you to save time and money, while still providing results that you can trust.

## Don’t leave success to chance

A paper clip manufacturer wants to detect significant changes in clip length. The manufacturer samples thousands of clips because it is cheap and quick to do. But this huge sample makes the test too sensitive: the red line shows that the test warns of a change even if the average length differs by a trivial amount (0.05).

This Power Curve shows that the manufacturer is wasting resources on excessive precision. A sample size of just 100 will detect meaningful differences (0.25) without generating a false alarm at every negligible change.

An aerospace company is designing an experiment to test a new rocket. Each rocket is very expensive, so it is critical to test no more than necessary.

This Power Curve confirms an experiment with 6 replicates will give researchers the power that they need without spending more than they must.

“We’ve always done it this way.” That’s why workers at a lumber company sample 10 beams to test whether their strength meets the target.

The Power Curve shows that this sample size is too small for the test to detect important effects. The workers must sample 34 beams for the test to detect meaningful differences (0.50).

## Balancing Priorities

A power analysis helps you to weigh your resources against your demands and quantifies a test’s ability to answer your question. It can expose design problems, like the lumber company’s insufficient sample size. It can also reveal design solutions that you haven’t considered.

Take, for example, the packaging plant of a snack company. Customers complain that the company’s pretzel bags are sealed with glue that’s too strong, so researchers use One-Way ANOVA to compare their current glue with three potential replacements. Differences in seal strength that are less than 10 are undetectable to most people, so the test needs to detect a difference of only 10. A power value of 80% is acceptable, but 90% is ideal. What sample size meets the researchers’ needs?

30 samples of each glue ensure that the test detects a difference of 10 with 90% power.

Or, the researchers could detect the same difference with 23 samples and 80% power. If this represents a considerable savings, the researchers may consider using the smaller sample.

The Power Curve illustrates this information, but it also charts every other combination of power and difference for a given sample size.

The black line indicates that researchers can attain 90% power with just 23 samples if they are willing to seek a difference of 12 instead of 10. This might be the ideal choice.

## How to create Power Curves in Minitab

Performing power analyses with Power Curves couldn’t be simpler. Supply the factors that you know, and Minitab calculates the one that you omit.

Suppose a trainer wants to compare two training courses for forklift operators. She will use a 2-sample t-test to compare the average scores that operators from each course earn on the final exam. She knows that she must be able to detect a difference of 5 between the two courses with 80% power, and historical data suggest a standard deviation of 5. But how many participants must she sample from each course?

1. Choose Stat > Power and Sample Size > 2-Sample t.
2. In Differences, type 5.
3. In Power values, type 0.80.
4. In Standard deviation, type 5.
5. Click OK.

This Power Curve indicates that the trainer must sample 17 participants from each class for her test to detect the difference that she seeks with 80% power.