Analysis of Variance 

The computations for an analysis-of-variance can be summarized in an anova table. 

The null hypothesis 

is rejected at the -level of significance if the F-Ratio  

The null hypothesis 

is rejected at the -level of significance if the F-Ratio  

The null hypothesis 

is rejected at the -level of significance if the F-Ratio  

• TwoFactorAnova in the calc package performs a two-factor analysis of variance with a multiple observations per cell summarized in an analysis-of-variance table. L is a list of lists of data

Example 3 

An experiment was carried out to test the hardness of an alloy. Three operators made the experiment on the five machines available. Each of the operators carried out the experiment three times for each treatment combination. The data recorded are 

Test the hypotheses 

a) No row effect , b) No column effect , c) No interaction 

Solution 

>	restart:MathMaple:-ini():

 

>	L:=[[[15,6,8,4,6],[16,4,5,6,8],[18,5,9,5,7]],[[25,15,8,14,10],[20,8,9,12,8],[23,17,10,8,9]],[[12,13,4,9,7],[17,14,13,11,9],[22,12,8,12,8]]];

 

The analysis of variance table is 

>	TwoFactorAnova(L,Multiple);

 

a)  The critical -value is  > f[0.05]=ProbTable([FRatio,2,30],p=0.95);     reject (no row effect).

b)  The critical -value is  > f[0.05]=ProbTable([FRatio,4,30],p=0.95);     reject (no column effect).

c) 

The critical -value is 

>	f[0.05]=ProbTable([FRatio,8,30],p=0.95);

 

accept (no interaction).