2. Significance Test
Used to:
•Objectively compare two sets of
data.
•Determine whether the difference
is not only due to random error.
•Determine the significance of the
difference, if any.
3. t-test- Applications:
Compare a sample mean with a stated mean.
Compare means of two independent samples.
Compare the means of two matched samples.
4. The Bureau of Environmental Protection made a
study of a river community with regard to the
amount of semi treated sewage released to the
river. t-critical is 1.86. The dissolved oxygen
readings in ppm are as follows:
Above
town
4.9 5.2 5.1 4.8 5.6
Below
Town
5.0 4.9 4.8 4.7 4.9
5.
6. t-test: Comparison of means
of matched samples (paired t-
test)
• Test that is based on the difference between the results
obtained for each sample, rather than on the individual values.
• To ascertain whether there is a significant difference in the
results obtained using two methods on a set of different
samples.
7. Platt Tire Company tested the wearing the qualities of two types of
tires (A and B) it manufactures. For comparison, five samples or
tire A and five samples of tire B were randomly assigned and
mounted on each of the rear wheels of five automobiles. The
automobiles were allowed to travel for a specific number of miles.
The amount of wear of each of the tires is recorded. Test for
significance of the difference in the average wear of the two tires.
Use alpha 0.05 the t-critical is +/- 2.776. The following data are
obtained.
Automobile 1 2 3 4 5
Tire A 8.8 12.3 9.8 9.7 10.6
Tire B 8.3 11.8 9.4 9.1 10.2
Editor's Notes
Compare the population mean to sample mean.
Thus, an independent-measures used to test for mean differences between two distinct populations (such as men versus women) or between two different treatment conditions (such as drug versus no-drug).
The distributions of dependent variable are highly corelataed, either because they are distributions of pre and post tests from the same sample.
Tstat is less than tcrit is within the acceptance region. Accept null hupothesis. No significant difference
