# Statistical Hypothesis Testing

Skill level: Specialty – expert

#### Description

Statistical hypothesis testing can be performed in many ways, depending on the objective and the data available. The test is designed to verify if there is a statistical difference between various predictor(s) or factor(s) of interest. The test can verify if the means or the variances of two or more groups are equal and if there is a correlation between two or more variables.

#### Benefits

• Provides necessary information for decision making
• Confirms whether improvements or changes in a process are making a difference
• Helps to determine which factor/predictor has more impact on the response (output)
• Easily performed with a specialized statistical software package
• Broad range of applications in various types of businesses and processes

#### How to Use

• Step 1.  Collect data on the factors and output of interest (must be variable data).
• Step 2.  Enter data in a statistical application spreadsheet.
• Step 3.  Run the statistical analysis as needed.
• Step 4.  Interpret results in the table provided by the software.
• Step 5.  Validate results by running additional trials if necessary.

#### Relevant Definitions

Predictor or factor: Variable of a process that has an effect on the outcome. For example, saltiness of water depends on the ratio of water and salt. The higher the amount of salt, the saltier the water will be.

For detailed definitions and applications of the various statistical tests, such as t-test, F-test, ANOVA, regression, and many more, please refer to a statistical book or manual available through the ASQ bookstore.

#### Example

A large retail store considering a major expansion in many different towns is preparing a hiring plan. The human resources manager wants to know what strategy to use, considering that the corporation will require the new stores to become profitable within a few months after opening.

Based on past experience and tribal knowledge, management wants to hire people experienced in sales rather than younger candidates with less experience. Hiring experienced people will require more screening, research, and recruitment time and will increase the payroll.

The management team wants to know if the level of sales really depends on experience, or if this is just an assumption. The entire recruiting strategy depends on this information.

All available data are pulled from the accounting system to determine whether or not experience really matters. The data in the table below (partial data only) have been grouped as follows:

• Between 1 and 5 years as junior
• Between 6 and 10 years as intermediate (inter)
• Above 10 years as senior

Below is a summary of the data showing average sales (in units of \$100) based on years of experience in retail sales. The average number of years of experience comes from more than 1000 employees working the floor at various locations.

The box plot graph illustrates how the data (sales) are distributed among the junior, intermediate, and senior sales people. This clearly indicates much higher average sales by experienced people.

The analysis of variance (ANOVA) table shows the results of the statistical hypothesis test that has been performed with this data set. It confirms that there is a statistical difference (p = 0) between the three different groups, therefore removing any doubt about the outcome. Experienced people land bigger sales.

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