Analysis of variance (ANOVA)

Skill level: Specialty – expert


ANOVA (analysis of variance) is a mathematical test designed to verify if there is a statistical difference between various predictor(s) or factor(s) of interest. In its simplest form, ANOVA provides a statistical test of whether or not the means of several groups are equal.


  • Provides necessary information for decision making through the use of a statistical test
  • Confirms whether some improvements or changes in a process are making a difference
  • Helps to determine which factor or predictor has more impact on the response (output)
  • Easy to perform using a specialized statistical software package
  • Very broad range of applications in various types of businesses and processes

How to Use

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

Relevant Definitions

One-way ANOVA: Only one predictor (factor) of interest with several levels.

Two-way ANOVA: Two predictors (factors) of interest with several levels.

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


The members of the board of education want to know if there is a difference between two teaching methods for children in primary school. They have monitored several schools that are running either the standard teaching method (STD) or the new, progressive method (PROG) during the last three years. Now, they want to decide if they should maintain the status quo or shift to the new method.

The data show the average performance index (API) from the schools in relation to the method used (predictor). The higher the API score, the better. The tables below show the results:


The results from the ANOVA table indicate the students under the new, progressive method (PROG) have higher API scores than the students under the old method (STD), and that there is a statistical difference between the two. Therefore, the board can implement the new method (PROG) in all the schools with confidence that all students will benefit from this method.

*Note: The technical details of the ANOVA tables and the statistical analysis are beyond the objectives of this document. Please refer to statistical books and documentation in order to understand it. This an expert tool for professionals and practitioners of statistics.


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