As another measure of effectiveness, the company has asked you to compare the nu

Question

As another measure of effectiveness, the company has asked you to compare the number of incident reports from the six months prior to the training (pre-training) to the six months after the training (post training). The number of incident reports for each employee for each of those periods is provided below:

Family Name

Incident Reports Pre-Training

     Incident Reports      Post-Training

Taub

3

3

Hadley

2

2

Cameron

2

1

House

10

8

Wilson

5

4

Cuddy

6

4

Foreman

9

5

Volakis

4

2

Chase

1

0

The company-wide average for number of incident reports filed over a six month period is 1.25. The company would like to know whether the number of incident reports filed after training for this department differs from the company-wide average. Determine whether there is a difference in the number of incident reports after training (Incident Reports Post-Training) compared to the company-wide average (hint: the company should be considered a population for this problem).

A.Calculate the appropriate test in SPSS (1.5 pt)

B.Report a formal test of the hypothesis (1.75 pts)

C.Calculate the effect size (if appropriate) BY HAND. Be sure to show all work. (1 pt)

D.Report a formal conclusion (1.5 pts)

Family Name

Incident Reports Pre-Training

     Incident Reports      Post-Training

Taub

3

3

Hadley

2

2

Cameron

2

1

House

10

8

Wilson

5

4

Cuddy

6

4

Foreman

9

5

Volakis

4

2

Chase

1

0

Explanation / Answer

The company-wide average for number of incident reports filed over a six month period is 1.25.  

For the given sample size of 10

average number of incidents post training = 3.22 and standard deviation of the sample = 2.386

Null Hypothesis : H0 : meandepartment = 1.25

ALternative Hypothesis : H1 : meandepartment 1.25

We will do t- test because population variance is unknown

test statistic => t = ( 3.22- 1.25)/ (2.3586/sqrt(10)) = 1.97/0.7458 = 2.64

so tcritical for degree of freedom = 9 is tcritical = 2.262

so t > tcritical so we can say that department has different average number of uincident reports after training compared to company wide average.

c. effect size = [ Mean of experimental Group - mean of control group] / standard deviation =

   = (4.67 -3.22) /sp

sp = sqrt [ {(n1 - 1 )s12 + (n2 - 1 )s22}/ (n1 +n2 - 2)] = 2.8012

(where n1 = n2 = 10 and s1 = 3.1622 and s2 = 2.3863)

effect size = (4.67 -3.22) /2.8012 = 0.52

Effect size is medium here.

D. Here we can conclude that the Null hypothesis is invalid and we can conclude that Incidence Reports Post- training in the given department or sample is significantly different from Comapny- wide average.

Family Name Incident Reports Pre-Training      Incident Reports      Post-Training Taub 3 3 Hadley 2 2 Cameron 2 1 House 10 8 Wilson 5 4 Cuddy 6 4 Foreman 9 5 Volakis 4 2 Chase 1 0 MEAN 4.666666667 3.222222222 STD. DEV. 3.16227766 2.386303511

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