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Sampling Table for TA Studies

Table 14.2 shows the number of spot observations necessary to estimate the frequency of an activity to within a fractional accuracy. It also tells you how many observations you need if you want to see an activity at least once with 95% probability.

Table 14.2 Number of Observations Needed to Estimate the Frequency of an Activity to within a Fractional Accuracy

True

frequency of activity

Number of observations needed to see the activity at a particular fraction of accuracy

To see activities at least once with 95% probability

f

0.05

0.10

0.15

0.20

0.30

0.40

0.50

0.01

152127

38032

16903

9508

4226

2377

1521

299

0.02

75295

18824

8366

4706

2092

1176

753

149

0.03

49685

12421

5521

3105

1380

776

497

99

0.04

36879

9220

4098

2305

1024

576

369

74

0.05

29196

7299

3244

1825

811

456

292

59

0.06

24074

6019

2675

1505

669

376

241

49

0.07

20415

5104

2268

1276

567

319

204

42

0.08

17671

4418

1963

1104

491

276

177

36

0.09

15537

3884

1726

971

432

243

155

32

0.10

13830

3457

1537

864

384

216

138

29

0.15

8708

2177

968

544

242

136

87

19

0.20

6147

1537

683

384

171

96

61

14

0.25

4610

1152

512

288

128

72

46

11

0.30

3585

896

398

224

100

56

36

9

0.40

2305

576

256

144

64

36

23

6

0.50

1537

384

171

96

43

24

15

5

SOURCE: H. R. Bernard and P D. Killworth, ''Sampling in Time Allocation Research,'' Ethnology, Vol. 32, p. 211. Copyright © 1993. Reprinted with permission.

Here’s how to read the table. Suppose people spend about 5% of their time eating. This is shown in the first column as a frequency, f, of 0.05. If you want to estimate the frequency of the activity to within 20%, look across to the column in the center part of table 14.2 under 0.20. If you have 1,825 observations, and your data say that people eat 5% of the time, then you can safely say that the true percentage of time spent eating is between 4% and 6%. (Twenty percent of 5% is 1%; 5%, plus or minus 1%, is 4%-6%. For the formula used to derive the numbers in table 14.2, see Bernard and Killworth 1993.)

Suppose you do a study of the daily activities of families in a community and your data show that men eat 4% of the time and women eat 6% of the time. If you have 300 observations, then the error bounds of the two estimates overlap considerably (about 0.02-0.06 for the men and 0.04-0.08 for the women).

You need about 1,800 observations to tell whether 0.06 is really bigger than 0.04 comparing across groups. It’s the same for other activities: If women are seen at leisure 20% of their time and caring for children 25% of their time, then, as table 14.2 shows, you need 1,066 observations to tell if women really spend more time caring for children than they do at leisure.

Oboler had 1,500 observations. It is clear from table 14.2 that her findings about men’s and women’s leisure and work time are not accidents. An activity seen in a sample of just 256 observations to occur 40% of the time can be estimated actually to occur between 40%, plus or minus 15% of 40%, or between 34% and 46%. Since men are seen working 38% of the time and about half of Oboler’s 1,500 observations were of men, her finding is solid.

 
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