Chapter 25

Paired Samples and Blocks

Example

Measure effectiveness of exercise program in lowering blood cholesterol levels.SRS of men from a population.Measure cholesterol before program starts.Go through exercise program for 12 weeks.Measure cholesterol after program ends.

Do cholesterol levels decrease?

Example - Data

Subject 1 2 3 4 5 6 7 8 9 10

Pre 210 236 220 250 209 236 240 236 222 210

Post 204 210 218 200 208 234 246 240 208 220

Example

Two observations from each subject. Post value depends on pre value.Two observations are dependent.

Example

Cannot use inference for ____________Violates independent samples assumption.

A Visual of the Difference

A Visual of the Difference

Example - Data

Still interested in difference of two values. Pre-program minus post-program.

Subject 1 2 3 4 5 6 7 8 9 10

Pre 210 236 220 250 209 236 240 236 222 210

Post 204 210 218 200 208 234 246 240 208 220

Diff.

Inference for μ

μD = ________________________________________________________

Sample mean difference is ___________Sample standard deviation of differences

is __________________n = number of differences = ________

Hypothesis Test

If exercise program has no effect, mean difference will be 0.HO: ________________

If exercise program is effective, mean difference will be positive.HA: ________________

Hypothesis Test

AssumptionsRandom sample Independent DifferencesNearly Normal Population

Test Statistic

P-value

P-value

Hypothesis Test

Decision:

Hypothesis Test

Conclusion:

Important Difference

If two values come from two independent samples

_____________________________________dependent samples (values collected twice

from same subject)_____________________________________

Second situation is called _______________________________

Example #1

The design of controls and instruments affects how easily people can use them. A student project investigated this effect by asking 25 right-handed students to turn a knob (with their right hands) that moved an indicator by screw action. Each student was tested on two different knobs, one turned clockwise and the other turned counterclockwise.

Example #1 (cont.)

Ob #1 – _________________________Ob #2 – _________________________Source – ________________________Inference –

Example #2

We would like to determine if students taking an ACT prep course will score better than students not taking the course. A random sample of 25 students was chosen who took the course and a random sample of another 25 students was chosen who did not take the course. At the end of the prep course, both groups were given the ACT.

Example #2 (cont.)

Ob #1 – ______________________________ Ob #2 – ______________________________ Source – _____________________________ Inference –

Example #3

We would like to determine if students can improve their ACT score by taking a prep course. A random sample of 25 students was chosen. They first took the ACT test. Then they spent 6 weeks taking the prep course. At the end of the 6 weeks, they took the ACT test again.

Example #3 (cont.)

Ob #1 – _________________________Ob #2 – _________________________Source – ________________________Inference –

Example #4

We would like to determine if students taking an ACT prep course will score better than students not taking the course. A random sample of 50 students was selected. All 50 students were first administered the ACT. Then the students were randomly split into two groups, one group took the prep course, and the other group did not. At the end of the prep course, both groups were again given the ACT.

Example #4 (cont.)

Ob #1 – _________________________Ob #2 – _________________________Source – ________________________

Example #4 (cont.)

Subjects split into two groups.Group 1: __________________________Group 2: __________________________

Inference –