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# ANOVA:Interpretation of Table, Analysis and Fischer LSD Test

Question1:
The manager of a small company is interested in increasing the French language literacy of his employees. Three different training programmes were investigated, and as a result of these investigations, the manager sent 15 randomly selected employees to each of the three different training programmes (X, Y and Z). At the end of the 6-week sessions, the manger assessed the French language proficiency of each of the employees. The average French language scores for participants in each of the three programmes were as follows:
x (Group 1) = 59.07
y (Group 2) = 66.40
z (Group 3) = 71.73
To test whether or not there were significant differences among the groups, an ANOVA procedure was executed and the ANOVA table was constructed (Please refer to the attachment)

a.From the information given, fill in the missing degrees of freedom (df).
b.What does the ANOVA tell the manager about the differences among the three groups?
c.How many different comparisons between groups can the manager make? What are these comparisons?
d.Use the Fischer LSD procedure to test the hypothesis that the mean of Group 1 (X programme students) is not significantly different from the mean of Group 3 (Z programme students). Use &#945; = .05. What conclusion can you draw from this procedure?

Question 2
Describe the difference between a completely randomized experimental design and a randomized block design. What is the main advantage of using a randomized block design?

#### Solution Summary

The solution provides step by step method for interpretation of ANOVA Table and calculation of Degrees of Freedom, Sum of Squares for Treatment (SST), Sum of Squares for Error (SSE), Mean Square for Treatment (MST), Mean Square for Error (MSE). The solution also provides step by step method of perfoming Fischer LSD Test. Formula for the calculations and interpretations of the results are also included. A detailed discussion involving the difference between a completely randomized experimental design and a randomized block design, and the main advantage of using a randomized block design are also included.

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