# Hypothesis Testing

## What is a Hypothesis Test?

Hypothesis testing helps identify ways to reduce costs and improve quality. Hypothesis testing asks the question: Are two or more sets of data the same or different, statistically.

In Six Sigma, hypothesis tests help identify differences between machines, formulas, raw materials, etc. and whether the differences are statistically significant or not. Without such testing, teams can run around changing machine settings, formulas and so on causing more variation. These knee-jerk responses can amplify variation and cause more problems than doing nothing at all.

In manufacturing, you might want to compare two or more types of raw materials and determine if they produce the same quality. In other words, do the products have the same or different means and variances? If they are the same, which one is less expensive to produce? If they are different, which one best meets the customer's requirements?

### Three Types of Hypothesis Tests

• Classical Method - comparing a test statistic to a critical value
• p value Method - the probability of a test statistic being contrary to the null hypothesis
• Confidence Interval Method - is the test statistic between or outside of the confidence interval

### Conducting a Hypothesis Test

1. Define the null (H0) and an alternate (Ha) hypothesis.
2. Conduct the test
3. Using data from the test:
• Calculate the test statistic and the critical value (t test, f test, z test, ANOVA, etc.).
• Calculate a p value and compare it to a  significance level (a) or confidence level (1-a)
4. Interpret the results to determine if you can accept or reject the null hypothesis. Which test do I run?
What do these numbers mean?

### QI Macros for Excel Makes Hypothesis Testing as Easy as 1-2-3! 1. Just input your data into an Excel spreadsheet and select it.
2. Click on QI Macros menu, Statistical Tools and the test you want to run (t test, f test, z test, ANOVA, etc.).  If you are not sure which test to run, QI Macros Stat Wizard will analyze your data and run the possible tests for you.
3. QI Macros performs all of the calculations AND interprets the results for you.  Hypothesis Test Compare Result What Does It Mean? Classical Method test statistic > critical value  (i.e. F > F crit) Reject the null hypothesis Means or Variances are Different Classical Method test statistic < critical value  (i.e. F < F crit) Cannot Reject the null hypothesis Means or Variances are the Same p value Method p value < a Reject the null hypothesis Means or Variances are Different p value Method p value > a Cannot Reject the null hypothesis Means or Variances are the Same

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