Analysis of Means

Summary

  

Analysis of Means (ANOM), a graphical analog to ANOVA, tests the equality of population means. You can use ANOM with one or two factors, though two-factor designs must be balanced.

Minitab displays a graph, similar to a control chart, that shows how the mean for each level of a factor compares to the overall mean (also called the grand mean). Minitab flags means that are significantly different from the overall mean. ANOM, therefore, tells you when the level means differ and what those differences are.

As with analysis of variance, you can use ANOM if you can assume that the response approximately follows a normal distribution. In addition, you can use special versions of ANOM when your response consists of proportions (binomial data) and counts (Poisson data). With binomial data, the sample size (n) must be constant.

Note

ANOM uses a normal approximation with both binomial and Poisson data. With binomial data, both np and n(1-p) should be at least 5. With Poisson data, the mean should be at least 5.

Data Description

Analysis of Means uses four data sets:

 

Driving data: data for a two-factor design

A study compared experienced and inexperienced drivers on three types of roads. The two factors are:

·    Driving experience. Eight inexperienced drivers and eight experienced drivers took part in the study. The two levels were coded as experience =1 and inexperience = 0.

·    Road type. Each driver drove on one of three road types. The three levels were coded as first class road = 1, second class road = 2, and dirt road = 3.

A tester recorded the number of steering corrections each driver made on each type of road. The response variable is Corrects.

 

Wine data: data for an unbalanced one-factor design

A study compared wine produced in three different regions. A panel of judges sampled wines from each region – 17 from Region 1, 9 from Region 2, and 12 from Region 3 – and scored each sample on various characteristics.

 

Weld data: data from a binomial distribution

A tester took 11 samples, each consisting of 80 welds. In each sample, he recorded the number of welds that did not meet specifications.

 

Packing data: data from a Poisson distribution

The manager of a food packing company wants to monitor the number of overfilled containers for each of the packing machines. She counts the number of overfilled containers per machine on the same day.

Data: Driving.MTW, Packing.MTW, Weld.MTW, WineTaste.MTW (available in the Sample Data folder).