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With the Assistant, You Won't Have to Stop and Get Directions about Directional Hypotheses

I got lost a lot as a child. I got lost at malls, at museums, Christmas markets, and everywhere else you could think of. Had it been in fashion to tether children to their parents at the time, I'm sure my mother would have. As an adult, I've gotten used to using a GPS device to keep me from getting lost.

The Assistant in Minitab is like your GPS for statistics. The Assistant is there to provide you with directions so that you don't get lost. One particular area where it's easy to get lost is with directional hypotheses.Wait... is my hypothesis the other direction?

What Is a Directional Hypothesis?

When you do a statistical hypothesis test, you have a null hypothesis and an alternative hypothesis. Directional hypotheses refer to two types of alternative hypotheses that you can usually choose. The common alternative hypotheses are these three:

  • The value that you want to test is greater than a target.
  • The value that you want to test is different from a target.
  • The value that you want to test is less than a target.

If you select an alternative hypothesis with "greater than" or "less than" in it, then you've chosen a directional hypothesis. When you choose a directional hypothesis, you get a one-sided test.

What does it look like to choose a one-sided test, and why would you? Let's consider an example.

Choosing Whether to Use a One-sided Test or a Two-sided Test

Suppose new production equipment is installed at a factory that should increase the rate of production for electrical panels. Concern exists that the change could increase the percentage of electrical panels that require rework before shipping. A quality team prepares to conduct a hypothesis test to determine whether statistical evidence supports this concern. The historical rework rate is 1%.

At this point, you would usually choose an alternative hypothesis. Maybe you remember hearing that you should think about whether to use a one-sided test or a two-sided test, or you may not even know how a test can have a side.

To keep from getting lost, you use your GPS. To keep from getting confused about statistics, you can use the Assistant. The Assistant uses clear and simple language. The Assistant doesn't ask you about "directional hypotheses" or "one-sided tests." Instead, the Assistant asks the question, "What do you want to determine?"

Is the % defective of Panels greater than .01? Is the % defective of Panels less than .01? Is the % defective of Panels different from .01?

In this scenario, it's easy to see why the team would want to determine whether the percent is greater than 1. By performing the one-sided test for whether the percentage is greater than 1, the team can determine if there is enough statistical evidence to conclude that the percentage increased. If the percentage increased, then the concern is justified.

In practical terms, you should consider what it means to limit your decision to whether there is evidence for an increase. A one-sided test of whether the percentage increased will never show a statistically significant decrease in the percentage of boards that require rework. Evidence of a decrease in the number of defectives might guide the quality team to investigate the reasons for the unforeseen benefit.

Why Use a One-sided Test?

Given this possible concern about whether a one-sided test excludes important information from the result, why would you ever use one? The best answer is that you use a one-sided test when the one-sided test tells you everything that you need to know.

In the example about the electrical panels, the quality team might feel completely secure in assuming that the new equipment will not result in a decrease in the percentage of panels that require rework. If so, then a test that checks for a decrease is flawed. The team needs only to determine whether to solve a problem with increased defectives or not.

The Assistant Gets Even Better

While a p-value for a one-sided test can be useful, more analysis can help you make better decisions. For example, in the electrical panel example, if the team finds a statistically significant increase, it will be important to know what the percentage increase is. The Assistant produces several reports with your hypothesis tests that help you get as much information as you can from your data. The report card verifies your analysis by providing assumption checks and identifying any concerns that you should be aware of. The diagnostic report helps you further understand your analysis by providing additional detail. The summary report helps you to draw the correct conclusions and explain those conclusions to others. The series of reports includes a variety of other statistics and analyses. That way, you have everything that you need to interpret your results with confidence.

The % defective of Panels is not significantly greater than the target (p > 0.05)

The image of the face in the crowd without the thought bubble is by _Imaji_ and is licensed under this creative commons license.

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