Confidence Interval on Difference Between Means, Independent Groups, Standard
Deviation Estimated (2 of 7)
A concrete example should make the procedure for computing the
confidence interval clearer. Assume that an experimenter were
interested in computing the 99% confidence interval on the difference
between the memory spans of seven- and nine-year old children. Four
children at each age level are tested and their memory spans are
shown below:
Age 7 |
Age 9 |
3
3
4
5 |
5
6
6
7
|
The
first step is to compute the means of each group:
M
Age 7 =
3.75 and M
Age 9 = 6.00.
Therefore, M
d = 3.75 -
6.00 = -2.25.
To obtain a value of t, one must first compute the
degrees of freedom (df). The degrees of
freedom is equal to the degrees of freedom for MSE (MSE is used to
estimate σ²). Since MSE is made up of two estimates of σ² (one
for each sample), the df for MSE is the sum of the df for these two
estimates. Therefore, the df for MSE is (n -1) + (n - 1) = 3 + 3 = 6.