Research Methodology - Dr. Krishan K. Pandey

Sampling Fundamentals 161
(ii) To test the difference between the means of two samples
where X 1 = Mean of sample one
X 2 = Mean of sample two
X − X
t =
σ
1 2
X − X
1 2
σ X1 − X = Standard error of difference between two sample means worked out as
2
σ X − X =
1 2
2
2
dX1i X1i dX2i X2i
∑ − + ∑ − 1 1
× +
n + n − 2
n n
1 2 1 2
and the d.f. = (n 1 + n 2 – 2).
(iii) To test the significance of the coefficient of simple correlation
t =
r
1−
r
2
× n − 2 or t = r
n − 2
1−
r
where
r = the coefficient of simple correlation
and the d.f. = (n – 2).
(iv) To test the significance of the coefficient of partial correlation
rp
bn − kg
t = × n − k or t = rp
2
2
1−
r
1−
rp
p
where r p is any partial coeficient of correlation
and the d.f. = (n – k), n being the number of pairs of observations and k being the number
of variables involved.
(v) To test the difference in case of paired or correlated samples data (in which case t test is
ofter described as difference test)
t D
n t D
− μD
− 0
=
i.e., =
σ σ
D D
where
Hypothesised mean difference bμDg is taken as zero (0),
D = Mean of the differences of correlated sample items
σ D = Standard deviation of differences worked out as under
σ D
=
Σ Di− D n
n −
2
1
D i = Differences {i.e., D i = (X i – Y i )}
n = number of pairs in two samples and the d.f. = (n – 1).
2
n