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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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