Chapter 10, Part C

III. Matched Samples

This test is conducted twice with the same sample and results are compared.

For example, you might have two production methods and want to see which is faster. You have a sample of workers perform with method 1, then do the same with method 2.

Two ways to conduct

• Independent Sample Design: Choose n1 to use method 1. Choose n2 to use method 2. Then test the difference between the 2 means.

• Matched Sample Design: Choose only n1. Have n1 use one method, then switch to the other.

The Difference

We’re only concerned with the difference between methods 1 and 2.

n

dd

n

ii

1

The mean difference:

1

)(1

2

n

dds

n

ii

d

Standard deviation of the difference.

Hypothesis Tests

One possible two-tailed test is that the mean difference is zero, or the two methods are no different. In other words, µd = (µ1 - µ2) = 0.

H0: µd = 0

Ha: µd 0

Example

A company attempts to evaluate the potential for a new bonus plan by selecting a sample of 4 salespersons to use the bonus plan for a trial period. The weekly sales volume before and after implementing the bonus plan is shown on the next slide. Let the difference “d” be d = (after - before)

Weekly Sales

Salesperson Before After

1 48 44

2 34 40

3 38 36

4 42 50

Use =.05 and test to see if the bonus plan will result in an increase in the mean weekly sales.

The Set-Up

H0: µd <= 0 (the plan doesn’t increase weekly sales)

Ha: µd > 0 (if we reject Ho, the plan does increase weekly sales)

With 3 degrees of freedom, the critical value is t.05 = 2.353.

The Test

Calculate di for every observation and find the sample mean difference and standard deviation.

Your test statistic:n

dd

n

ii

1

1

)(1

2

n

dds

n

ii

d= 2 = 5.8878

)/( ns

dt

d

d =2/(5.8878/2) = .68

Your decision is that you can’t reject the null. The new policy doesn’t significantly increase weekly sales.