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The science of ergonomics studies the influence of “human factors” in technology, i.e. how human beings relate to and work with machines. With widespread use of computers for data processing, computer scientists and psychologists are getting together to study human factors. One typical study investigates the productivity of secretaries with different word processing programs. An identical task was given to 18 secretaries, randomly allocated to three groups. Group 1 used a menu-driven program. Group 2 used a command-driven program, and Group 3 used a mixture of both approaches. The secretaries all had about the same level of experience, typing speed, and computer skills. The time (in minutes) taken to complete the task was observed. The results were as follows:



Groep / Group 1

Groep / Group 2

Groep / Group 3

Totaal / Total

Menu-aangedrewe / Menu-driven

Opdrag-aangedrewe / Command-driven

Mengsel / Mixed



12

14

10



16

10

8



10

14

10



12

12

10



10

10

8



16

14

4



n1 =

n2 = A

n3 =

N = B

R1 =

R2 =

R3 = C

G = D

Die volgende gedeeltelik voltooide ANAVA tabel is vir die bostaande data verkry. / The following partially completed ANOVA table was obtained for the above data.

ANOVA table:

Source

SS

df

MS

Fcalc

Ftab

Treatments

H

J

34.8889

M

P

Error

84

15

L



Total

I

K





What is the value of E in the observation table? / Wat is die waarde van E in die waarnemingstabel?

1 answer

To find the value of \( E \) in the observation table, we first need to calculate the total number of observations, the number of treatments (groups), and the overall total.

Given Data

  • The number of secretaries/group:
    • Group 1 (Menu-driven): 6
    • Group 2 (Command-driven): 6
    • Group 3 (Mixed): 6

So, we have:

  • \( n_1 = 6 \)
  • \( n_2 = 6 \)
  • \( n_3 = 6 \)

Total Observations

The total number of secretaries \( N \) is: \[ N = n_1 + n_2 + n_3 = 6 + 6 + 6 = 18 \]

Treatment Groups and Sum of Ranks

  • Group 1 (Menu-driven): 12, 16, 10, 12, 10, 16
  • Group 2 (Command-driven): 14, 10, 14, 12, 10, 14
  • Group 3 (Mixed): 10, 8, 10, 10, 8, 4

To understand the ANOVA table, we may want to find the total sum of each group's scores for the treatments \( R_1, R_2, R_3 \) and the overall total sum \( G \).

Calculating Rank Sums

  1. Group 1 Sum \( R_1 \): \[ R_1 = 12 + 16 + 10 + 12 + 10 + 16 = 76 \]

  2. Group 2 Sum \( R_2 \): \[ R_2 = 14 + 10 + 14 + 12 + 10 + 14 = 74 \]

  3. Group 3 Sum \( R_3 \): \[ R_3 = 10 + 8 + 10 + 10 + 8 + 4 = 60 \]

Now we can find the total sum \( G \): \[ G = R_1 + R_2 + R_3 = 76 + 74 + 60 = 210 \]

Filling in the ANOVA Table

Based on the structure of ANOVA:

  • The Degrees of Freedom for Treatments \( df_{Tr} = k - 1 = 3 - 1 = 2 \)
  • The Degrees of Freedom for Error \( df_{E} = N - k = 18 - 3 = 15 \)
  • The Total Degrees of Freedom \( df_{Total} = N - 1 = 18 - 1 = 17 \)

For the sums of squares:

  • The total \( SS_{Total} \)
  • \( SS_{Tr} = H \) (available in the ANOVA table)
  • \( SS_{Error} = 84 \) (available in the ANOVA table)

Calculation of \( E \)

The total sum of squares \( SS_{Total} \) is given by: \[ SS_{Total} = SS_{Tr} + SS_{Error} = H + 84 \]

If we plug into an ANOVA setting using the means, we need additional data points or F-values complete with the original means of treatment, not specified here.

Summary

In order to calculate the exact value of \( E \) and fill in the ANOVA table, we necessitate some additional information, particularly the values for \( H \), \( I \), \( J \), \( K \), and through patterns established in the questions.

Thus, if more values were provided, or the context detailed regarding total sums, we could derive efficient answers for \( E \) within the context being strictly limited to computation of sums.

Answer Directly Suspended: Unfortunately, without values for \( H \) or \( J \) explicitly provided, the identification of \( E \) needs simultaneous clarity. Any other clues or outlined values will bring clarity based on context. My output reflects the areas needing additional values or outlined understanding from provided segments.

Should I recalculate or clarify any segments against the data?