Chapter 11, Problem 14CR

To determine

To Describe: The usage of simulation to re-sample the data.

Answer to Problem 14CR

Repeatedly make new control and treatment groups and see how often you get differences between the new groups that are at least as large as the original mean.

Explanation of Solution

Given:

Depression score
Control group	49	45	43	47
Treatment group	39	40	39	37

Depression score
Control group	46	45	47	46
Treatment group	41	40	42	43

Calculation:

To re-sample the data, the first step is to combine the measurements from both groups and assign a number to each value. Let the numbers $1$ through $8$ represent the data in the original control group, and let the numbers $9$ through $16$ represent the data in the original treatment group, as shown.

Original control group	$4.5$	$4.5$	$4.8$	$4.4$	$4.4$	$4.7$	$4.3$	$4.5$	$4.1$	$4.2$
Assigned number	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$

Original treatment group	$4.6$	$4.8$	$5.0$	$4.8$	$4.7$	$4.6$	$4.9$	$4.9$	$4.8$	$4.4$
Assigned number	$11$	$12$	$13$	$14$	$15$	$16$	$17$	$18$	$19$	$20$

Now, use a random number generator. Randomly generate $16$ numbers from $1$ through $16$ without repeating a number.

For this, you can use $TI-84$ the plus calculator.

Press $MATH$

Press three times to reach the $PRB$ menu.

Select 8:randintNoRep (

Press

Press $ENTER$

  $)$

The table shows the results.

$13$	$5$	$3$	$4$	$6$	$15$	$7$	$16$	$17$	$19$
$11$	$10$	$2$	$12$	$14$	$8$	$9$	$1$	$20$	$18$

Use the first $8$ numbers to make the new control group, and the next $8$ to make the new treatment group. The results are shown in the table below.

New control group	$5.0$	$4.4$	$4.8$	$4.4$	$4.7$	$4.7$	$4.3$	$4.6$	$4.9$	$4.8$
New treatment number	$4.6$	$4.2$	$4.5$	$4.8$	$4.8$	$4.5$	$4.1$	$4.5$	$4.4$	$4.9$

Now, use the data to find the new experimental difference.

Repeatedly make new control and treatment groups and see how often you get differences between the new groups that are at least as large as the original mean.

Conclusion:

Hence, repeatedly make new control and treatment groups and see how often you get differences between the new groups that are at least as large as the original mean.