Question

1. Part of an ANOVA table involving 8 groups for a study is shown below.

Source of Variation	Sum of Squares	Degrees of Freedom	Mean Square	F
Between Treatments	126	_____?	_____?	_____?
Within Treatments	240	_____?	_____?
(Error)
Total	_____?	67

1. Complete all the missing values in the above table and fill in the blanks.

Use α = 0.05 to determine if there is any significant difference among the means of the eight groups.

Answer 1

Solution:-

Source of Variation	Sum of Squares	Degrees of Freedom	Mean Square	F
Between Treatments	126	7	18	4.5
Within Treatments (Error)	240	60	4
Total	366	67

1) Total sum of square = Sum of treatment square + sum of error square

                                 = 126 + 240 = 366

2) Degree of freedom

Degree of freedom treatment (DFT) = 8-1= 7

    Degree of freedom error = Total DF - DFT = 67-7 = 60

3) Mean square

Mean square treatment (MST) = Treatment sum of square/Treatment degree of freedom

                                             = 126/7 = 18

   Mean square error (MSE) = error sum of square/error degree of freedom

= 240/60= 4

4) The F- test

F = MST/MSE = 18/4 = 4.5

Critical value of F at = 0.05 = 2.17

Since

So, H0 is rejected.

Therefore there is a significant difference among the means of the eight group