A study was conducted to investigate the effect of management training on the decisionmaking

abilities of supervisors in a large corporation. Sixteen supervisors were selected
and eight were randomly chosen to receive managerial training. Four trained and
four untrained supervisors were then randomly selected to function in a situation in
which a standard problem arose. The other eight supervisors were presented with an
emergency situation in which standard procedures could not be used. The response
was a management behaviour rating for each supervisor as assessed by a rating scheme
devised by the study’s author. The data are shown on the next page.
2
Situation (B) Training (A)
Standard Trained Not trained Total
85 53 519
91 49
80 38
78 45
Emergency 76 40 473
67 52
82 46
71 39
Total 630 362 992
Figure 2: Management rating
[3] (a) What are the two factors considered in this study?
[2] (b) What are the levels of each factor?
[10] (c)Construct the ANOVA table for this study.
[3] (d) Is there a significant interaction between the presence or absence of training
and the type of decision making situation? Test at � = .05.
[3] (e) Do the data indicate a significant difference in behaviour ratings for the two
types of training categories? (Test at � = .05).?
[3] (f) Do the data indicate a significant difference in behaviour ratings for the two
types of situations? (Take � = .05).

(a) The two factors considered in this study are:

1. Training - whether the supervisors received managerial training or not.
2. Situation - whether the supervisors were presented with a standard problem or an emergency situation.

(b) The levels of each factor are:
1. Training:
- Trained: Supervisors who received managerial training.
- Not trained: Supervisors who did not receive managerial training.

2. Situation:
- Standard: Supervisors who were presented with a standard problem.
- Emergency: Supervisors who were presented with an emergency situation.

(c) To construct the ANOVA table, we need to calculate different sums of squares (SS) and degrees of freedom (df) as follows:

Source | SS | df | MS
-------------------------------------
Training | SSTr | 1 | MSTr = SSTr/dfTr
Situation | SSS | 1 | MSS = SSS/dfS
Interaction | SSInt | 1 | MSInt = SSInt/dfInt
Error | SSE | 12 | MSE = SSE/dfE
Total | SST | 15 |

Where:
- SST: Total sum of squares
- SSTr: Sum of squares for the Training factor
- SSS: Sum of squares for the Situation factor
- SSInt: Sum of squares for the interaction between Training and Situation
- SSE: Sum of squares of error
- dfTr: Degrees of freedom for the Training factor (1)
- dfS: Degrees of freedom for the Situation factor (1)
- dfInt: Degrees of freedom for the interaction (1)
- dfE: Degrees of freedom for error (12)

(d) To test for the significant interaction between training and the type of decision making situation, we need to perform an analysis of variance (ANOVA) and compare the MSInt value to the MSE value using the F-test. If MSInt is significantly larger than MSE, then there is a significant interaction.

(e) To test for a significant difference in behavior ratings for the two types of training categories, we can perform an independent samples t-test between the behavior ratings of trained supervisors and untrained supervisors.

(f) To test for a significant difference in behavior ratings for the two types of situations, we can perform an independent samples t-test between the behavior ratings of supervisors in standard situations and supervisors in emergency situations.