One Way Anova

Example B: Raw Score Method You may wish to test the effects of a number of experimental treatments (counselling approaches): group counselling, peer counselling and individual counselling on the self-concepts of students. In this case, the independent variable, counselling approach has three levels. Necessarily there should be three groups randomly selected from the school population which will be exposed to three different counselling approaches. The dependent variable, self-concept, may be measured through a standardized self-concept instrument which yields interval scores for the subjects. In this problem, application of the one-factor ANOVA will test the following hypothesis: There is no significant difference in self-concept among the three groups of students exposed to different counselling approaches.
Step 1 Enter the data in a worksheet table. (See below.)
Step 2 Find the square of each raw score (X2).
Step 3 Compute the sum of N for each group, the total N, the sums of the raw scores and the sums of the squared scores.
N1 = 6; N2 = 6; N3 = 6; Nt = 18
ƩX1 = 366; ƩX2 = 492: ƩX3 = 510: ƩXt = 1368
ƩX21 = 23, 866; ƩX22 = 40, 798; ƩX23 = 43, 652; ƩX2t = 108, 316
WORKSHEET TABLE for the One-Way ANOVA
Counselling Conditions Group (1) Peer (2) Individual (3) X1 X21 X2 X22 X3 X23 78 6084 77 5929 78 6084 46 2116 83 6889 91 8281 41 1681 97 9409 97 9409 50 2500 69 4761 82 6724 69 4761 79 6241 85 7225 82 6724 87 7569 77 5929
SUMS 366 23866 492 40798 510 43652 ƩXt=1368
Means 61 82 85 ƩX2t = 108, 316
N 6 6 6 Nt = 18
Step 4 Compute Sums of Squares.
a. SSt (SS for total variability)
=ƩXt2 – (ƩXt)2 N
SSt = 108,316 – 13682 = 4348 18
b. SSb (SS for between group variability)
= (ƩX1)2 + (ƩX2)2 + (ƩX3)2 – (ƩXt)2 N1 N2 N3 Nt
= 3662 + 4922 + 5102 - 13682 6 6 6 18
= 106,020 – 103,968 = 2052
c. SSw = (SS for within group