Sampling in Time Allocation Research

Sampling behavior by direct observation is a common technique in field studies of behavior (Lehner 1979; Martin and Bateson 1986). There are two ways to sample behavior: (1) focus on individuals and monitor them continuously for a period of time; (2) record the behavior of individuals at random times throughout the period of research. The former technique is called focal-animal sampling; the latter is known as spot sampling. Spot sampling is the basis for time allocation studies in anthropology, though there remains some controversy in primate studies about its merits compared to focal-animal sampling (Altmann 1974; Rhine and Flanigon 1978; Harcourt and Stewart 1984). Spot sampling is based on a simple, appealing axiom: if you sample a representative number of moments in, say, a week or a year, and if you note what people are doing at those moments, then the percentage of times that people are seen doing things (eating, working, cooking, playing) is the percentage of time they spend doing those things (Erasmus 1955; Johnson 1975; Gross 1984). The axiom holds, of course, only if the sample of moments is in fact representative, which raises the question: How big is a representative sample of moments? It seems to us that this question can sensibly be interpreted in three ways: (1) If some activity is fairly rare, how many times must an observer plan to make observations in order to be reasonably certain of even seeing the activity at all? (2) How many times must observations be made so that the frequency of an activity can be estimated within some desired effort bounds? (3) How many times must observations be made so that the frequency of an activity can be known to be less than some desired amount, with reasonable accuracy? The statistics to answer all three questions are well known, but do not seem to have been used in the current connection. Accordingly, we derive and tabulate the answers to these three questions and discuss them in the light of previous work. ESTIMATING SAMPLE SIZE FOR SPOT OBSERVATION: AN EMPIRICAL SOLUTION Michael Baksh (1990) had 4,182 observations of Machiguenga (Peru) men in 41 households of twelve activities and 9,673 observations of Embu (Kenya) women in 169 households on fifteen activities. Baksh randomly selectrd 90 per cent of the cases in his Machiguenga data and compared the percentages for each of the twelve activities (eating, child care, idle, etc.) against the percentages in 100 per cent of his data. Tbe percentages were nearly identical. He repeated the exercise for random samples of 80 per cent of his data, 70 per cent of his data, and so on. All the percentages remained stable down to 20 per cent and changed dramatically only at 10 per cent of his data. In other words, he was able to recover the pattern of time allocation with a random sample of 137 observations. Baksh then examined one activity in his Embu data: eating. Relatively little time is devoted to this activity so, Baksh reasoned, estimates of time spent eating should be sensitive to changes in sample size. He ran 25 trials of randomly selected observations drawn for thirteen sample sizes: 50 per cent, 10 per cent, 2 per cent, and increments of 0.1 per cent down to 1 per cent. The mean eating time for the 50 per cent sample was 4.4 per cent and the mean eating time for the 1 per cent sample was 5.0 per cent. The difference in the means was insignificant but, of course, the range increased as the sample size decreased. Baksh plotted the per cent of sample size against the ranges for the estimates of mean eating time in all the samples. By inspection, he found that the range of the estimates remained at 4 per cent or less in samples that were 1.6 per cent or greater. Considering this acceptable, Baksh concluded that a sample of "about 150 observations" was sufficient to estimate Embu women's time use (1. …