Page 273 - DMGT404 RESEARCH_METHODOLOGY

Unit 12: Hypothesis Testing

which are multiplied by the respective number of items or categories in the samples and then by Notes
obtaining their total. Sum of squares(ss) for variance within samples is obtained by taking
deviations of the values of all sample items from corresponding sample means and by squaring
such deviations and then totalling them. For our illustration then
2
ss between = 4(5 – 4) + 4 (4 – 4) + 4 (3 – 4) 2
2
= 4 + 0 + 4 = 8
-
-
-
{(5 5) + (6 5) + (2 5) + (7 - 5) } {(4 4) + (4 4) + (2 - 4) + (6 4) }
-
-
-
2
2
2
2
2
2
2
2
ss within = + 2
S (x - x ) 2 S (x - x )
2i
2
1i
1
-
-
-
{(4 3) + (3 3) + (2 3) + (3 3) }
-
2
2
2
2
+ S (x - x ) 2
3i 3
= (0 + 1 + 9 + 4) + (0 + 0 + 4 + 4) + (1 + 0 + 1 + 0)
= 14 + 8 + 2
= 24
Step 4: ss of total variance which is equal to total of s.s. between and ss within and is denoted by
formula as follows:
S (x - x) 2
ij
where
i = 1.23
j = 1.23
for our example, total ss will thus be:
+
-
-
-
-
[ {(5 4)- 2 + (6 4) + (2 - 4) + (7 - 4) } {(4 4) + (4 4) + (2 - 4) + (6 4) }
2
2
2
2
2
2
2
-
+ {(4 4)- 2 + (3 4) + (2 - 4) + (3 4) }]
-
2
2
2
= {(1 + 4 + 4 + 9) + (0 + 0 + 4 + 4) + (0 + 1 + 4 + 1)}
= 08 + 8 + 6 = 32
We will, however, get the same value if we simply total respective values of ss between and ss
within. For our example, ss between is 8 and ss within is 24, thus ss of total variance is 32 (8+24).
Step 5: Ascertain degrees of freedom and mean square (MS) between and within the samples.
Degrees of freedom (df) for between samples and within samples are computed differently as
follows.
For between samples, df is (k-1), where k' represents number of samples (for us it is 3). For
within samples df is (n-k), where 'n' represents total number of items in all the samples (for us
it is 12).
Mean squares (MS) between and within samples are computed by dividing the ss between and
ss within by respective degrees of freedom. Thus for our example:
ss between 8
(i) MS between = = = 4
-
(k 1) 2
where (K – 1) is the df.
LOVELY PROFESSIONAL UNIVERSITY 267