Question

A study is planned on the physiology of exercises with human subject volunteers. The two treatments in the study are two methods of aerobic exercise training (call the methods A and B). At the end of a ten-week exercise period, each subject will undergo a treadmill test for standard respiratory and cardiovascular measurements.

Nineteen volunteers are listed in the table by sex and age. All volunteers are in good health and in the normal weight range for their age, sex, and height. Eight individuals will be tested in each the methods (A or B), so that only 16 of the 19 volunteers will be used; a subject will participate only in one of the methods.

a. Explain how you would group the individuals prior assignment of treatments so that experimental error variance could be kept at a minimum. b. Explain why you grouped as you did. c. Show your final assignment of individuals to the treatment groups.

Answer 1

Solution

Back-up Concpts

Randomization is one of the important tools in experimental design. By assigning experimental units to treatment at random, the design ensures all units get equal chance of inclusion. This in turn ensures minimum, if not zero, error due to bias. The underlying assumption is that the set of available units is homogeneous with respect to all characteristics which may have an impact on the response variable. [If this assumption cannot be taken for granted, a stratification is employed and the randomization is used within each stratum.]

Now to work out the solution,

Part (a)

Randomly assign the 19 volunteers to three groups. [process described in Part (c)]. Volunteers assigned to Group 1 to be given Treatment A, those assigned to Group 2 to be given Treatment B, and the remaining 3 in Group 3 not to be assigned [possibly to be kept as stand-by] Answer

Part (b)

As explained under Back-up Concepts, this will ensure the error due selection bias is eliminated, or at least equally distributed between the two treatments. Answer

Part (c) Actual Assignment Process

* => rejected due to repetition; ** => rejected due to out of range

Trial #	Random #	Volunteer # and Group
1	73	16 2
2	73	*
3	5 4	16*
4	59	2   1
5	63	6   1
6	78	2*
7	13	13   2
8	4 6	8   1
9	38	19 3
10	73	*
11	13	*
12	4 6	8*
13	38	*
14	73	16*
15	02	2*
16	96	**
17	5 5	17   3
18	83	7     1
19	03	3    1
20	90	14    2
21	70	13*
22	82	6*
23	00	**
24	25	6*
25	98	**
26	85	9    2
27	9 2	16*
28	38	19*
29	51	13*
30	27	8*
31	96	**
32	5 6	18    3
33	23	4    1
34	94	18*
35	33	14*
36	66	9*
37	56	18*
38	35	16*
39	70	13*
40	64	7*
41	77	1    1
42	57	19*
43	84	8*
44	28	9*
45	81	5    1
46	66	9*
47	52	14*
48	64	7*
49	40	2*
50	20	1*
51	42	4*
52	20	1*
53	57	19*
54	20	1*
55	15	15     2
56	83	7*
57	84	8*
58	71	14*
59	74	17*
60	76	19*
61	86	10    2
62	61	4*
63	43	5*
64	30	11   2
65	14	14*
66	33	14*
67	08	8*
68	97	**
69	93	17*
70	34	15*
71	37	18*
72	08	8*
73	73	16*
74	05	5*
75	65	8*
76	22	3*
77	78	2*
78	15	15*
79	52	14*
80	24	5*
81	66	9*
82	81	5*
83	97	**
84	85	9*
85	73	16*
86	23	4*
87	16	16*
88	38	19*
89	16	16*
90	62	5*
91	07	7*
92	11	11    2
93	69	12

Random numbers used

Lines 10580–10594, columns 21–40, from

RAND Corporation - RAND's A Million Random Digits

73735 45963 78134 63873 02965 58303 90708 20025 98859 23851

27965 62394 33665 63570 64775 78428 81665 26440 20422 05720

15838 47174 76866 14330 89793 34378 08730 56522 78155 22466

81978 57323 16381 66207 11698 99314 75002 80827 53867 37797

99982 27601 62686 44711 84543 87442 50033 14021 77757 54043

46176 42391 80871 32792 87989 72248 30500 28220 12444 71840

DONE