DYESTUFF
(Yield of dyestuff by batch)
Data:
Dyestuff:
Batch Yield
1 A 1545
2 A 1440
3 A 1440
4 A 1520
5 A 1580
6 B 1540
7 B 1555
8 B 1490
9 B 1560
10 B 1495
11 C 1595
12 C 1550
13 C 1605
14 C 1510
15 C 1560
16 D 1445
17 D 1440
18 D 1595
19 D 1465
20 D 1545
21 E 1595
22 E 1630
23 E 1515
24 E 1635
25 E 1625
26 F 1520
27 F 1455
28 F 1450
29 F 1480
30 F 1445
Dyestuff2:
Batch Yield
1 A 7.298
2 A 3.846
3 A 2.434
4 A 9.566
5 A 7.990
6 B 5.220
7 B 6.556
8 B 0.608
9 B 11.788
10 B -0.892
11 C 0.110
12 C 10.386
13 C 13.434
14 C 5.510
15 C 8.166
16 D 2.212
17 D 4.852
18 D 7.092
19 D 9.288
20 D 4.980
21 E 0.282
22 E 9.014
23 E 4.458
24 E 9.446
25 E 7.198
26 F 1.722
27 F 4.782
28 F 8.106
29 F 0.758
30 F 3.758
Description:
The Dyestuff data frame provides the yield of dyestuff (Naphthalene Black 12B) from 5 different preparations from each of 6 different batchs of an intermediate product (H-acid).
Format:
Data frames, each with 30 observations on the following 2 variables.
Batch
- a factor indicating the batch of the intermediate product from which the preparation was created.
Yield
- the yield of dyestuff from the preparation (grams of standard color).
Details:
The Dyestuff data are described in Davies and Goldsmith (1972) as coming from βan investigation to find out how much the variation from batch to batch in the quality of an intermediate product (H-acid) contributes to the variation in the yield of the dyestuff (Naphthalene Black 12B) made from it. In the experiment six samples of the intermediate, representing different batches of works manufacture, were obtained, and five preparations of the dyestuff were made in the laboratory from each sample. The equivalent yield of each preparation as grams of standard colour was determined by dye-trial.β
The Dyestuff2 data are described in Box and Tiao (1973) as illustrating β the case where between-batches mean square is less than the within-batches mean square. These data had to be constructed for although examples of this sort undoubtably occur in practice, they seem to be rarely published.β
Source:
O.L. Davies and P.L. Goldsmith (eds), Statistical Methods in Research and Production, 4th ed., Oliver and Boyd, (1972), section 6.4
G.E.P. Box and G.C. Tiao, Bayesian Inference in Statistical Analysis, Addison-Wesley, (1973), section 5.1.2
Task:
Model the yield of dyestuff from the preparation separately in Dyestuff and Dyestuff2 data.