Question

Three groups are tested in an experiment and the results for the measurements are: Group 1: 5, 7, 5, 3, 5, 3, 3, 9 Group 2: 8, 1, 4, 6, 6, 4, 1, 2 Group 3: 7, 3, 4, 5, 2, 2, 3, 3 Test for the equality of the means at 5% significance.

Answer 1

We have three groups, and we have to test the equality of means, so we use analysis of variance, ANOVA.

If are the means of group 1, group2 and group3, respectively, then our hypothesis is,

i.e. Means are equal among the three groups

Analysis of variance has require following steps:

• For group means,

Group1:

• The estimated overall mean

• The estimated treatment effects are the difference between the estimated treatment mean and the estimated overall mean, i.e.

• Degree of freedom

for column degree of freedom

We have 3 different treatments (groups):

and have 24 different observation i.e

• For column SS (Sum of square):

sum of squares between treatment groups

   # observations

  

• Sum of squares within treatment groups

  

  

• For the column MS (Mean square):

• F- value:

Now tabulated F value for (2,21) degree of freedom at 5% level of significance for two tail test is is 4.419918

Since, calculated F is less than tabulated F i.e.,

Cal F < Tab F, null hypothesis is accepted at 5% significance level.

Therefore, we conclude that means are equal among the three groups.