One-Way ANOVA

 

Overview  |  How to  |  Data  |  Example

 

 

 

Overview

 

The One-Way Analysis of Variance (ANOVA) is like an extension of the two-sample t-test.  It is use to compare the equality of more than two means.

 

Null Hypothesis, H0

Alternate Hypothesis, H1

m1 = m2 = . . . = mi

m1 ¹ m2 ¹ . . . ¹ mi

 

where mi are the means of population i.

 

 

 

 

 

How to

 

1.       Choose ProcessMA > Statistics > ANOVA > One-Way ANOVA.

 

2.       In Data in, choose how your data is stored.

 

·         If your data in stored in a single column:

 

-         In Variable, select the column containing the response.

 

-         In Category, select the column containing subgroup codes.

 

·         If your data in stored in different columns:

 

-         In Variables, select the columns containing the separate responses.

 

3.       Click OK.

 

 

Optional

 

4.       In Confidence level, enter the desired confidence level for the confidence interval.

 

5.       Check Plot confidence interval, if you want to display the confidence intervals for the means.

 

6.       Check Plot boxplot, if you want to display a Boxplot of the data.

 

7.       Check Plot residuals, if you want to display the residual plots for analysis.

 

 

Note       To select a column of data into a textbox, double-click on any of the column names shown in the list on the left of the dialog box while in the textbox.

 

 

 

 

 

Data

 

Variable: Numeric.

 

Category: Text or Numeric; Must have the same number of data points as the Variable; Must and contain at least 2 distinct categories.

 

Variables: Numeric.

 

Confidence level: Numeric; between 0 and 100.

 

 

 

 

 

Example

 

A company makes steel bolts using four different machines.  You want to assess if the dimensions of the steel bolts made are the same for the different machines.  You randomly selected 50 steel bolts made by each machine.

 

1.       Open worksheet ProcessMA > Tools > Data Files > Stat.xls.

 

2.       Choose ProcessMA > Statistics > ANOVA > One-Way ANOVA.

 

3.       In Data in, select different columns.

 

4.       In Variables, select J – Machine1, K – Machine2, L – Machine3, M – Machine4.

 

5.       In Confidence level, enter 95.

 

6.       Check Plot confidence interval.

 

7.       Check Plot boxplot.

 

8.       Check Plot residuals.

 

9.       Click OK.

 

 

 

 

Interpretation

 

For a desired a = 0.05, since p = 0. 3089 > a, we fail to reject H0.  Therefore, we conclude that there is no significant evidence that the dimensions of the steel bolts made by the different machines are different. It can also be observed from the individual confidence intervals that there are significant overlaps.

 

The residual plots show that the residuals are normally distributed, centered about zero and random.  The results should be valid.