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t in such a manner that a unit of space may be used, so that random sampling may be more easily carried out. For example, suppose the problem is to estimate the chlorophyll content of algae in a pond at a particular time of year. The measure- ment is upon algae, yet the sample consists of a volume of water. We could use our knowledge of the way the algae are spatially distributed or make some reasonable assumptions, tnen construct a random sampling scheme based upon a unit of volume (liter) as the basic sampling unit. It is not always a simple or straightforward matter to define sampling units, because of the dynamic nature of living populations. Many aquatic organisms are mobile, and even rooted or sessile forms change with time, so that changes occurring during the study often make data interpretation difficult. Thus the benefit to be derived from any attempt to consider such factors in the planning stage will be consider- able. Random sample selection is a subject apart from the selection of the study site. It is of use only after the study objectives have been defined, the type of measurements have been selected, and the sampling units have been defined. At this point, random sampling pro- vides an objective means of obtaining informa- tion to achieve the objectives of the study. One satisfactory method of random sample selection is described. First, number the universe or entire set of sampling units from which the sample will be selected. This number is N. Then from a table of random numbers select as many random numbers, n, as there will be sampling units selected for the sample. Random numbers tables are available in most applied statistics texts or books of mathematical tables. Select a starting point in the table and read the numbers consecutively in any direction (across, diagonal, down, up). The number of observations, n (sample size), must be determined prior to sampling. For example, if n is a two-digit number, select two-digit numbers ignoring any number greater than n or any number that has already been selected. These numbers will be the numbers of the sampling units to be selected. To obtain reliable data, information about the - t BIOMETRICS - RANDOM SAMPLING statistical population is needed in advance of the full scale study. This information may be obtained from prior related studies, gained by pre-study reconnaissance, or if no direct in- formation is available, professional opinion about the characteristics of the population may be relied upon. 2.1.1 Simple random sampling Simple (or unrestricted) random sampling is used when there is no reason to subdivide the population from which the sample is drawn. The sample is drawn such that every unit of the population has an equal chance of being selected. This may be accomplished by using the random selection scheme already described., 2.1.2 Stratified random sampling If any knowledge of the expected size or variation of the observations is available, it can often be used as a guide in subdividing the population into subpopulations (strata) with a resulting increase in efficiency of estimation. Perhaps the most profitable means of obtaining information for stratification is through a pre- study reconnaissance (a pilot study). The pilot study planning should be done carefully, perhaps stratifying based upon suspected varia- bility. The results of the pilot study may be used to obtain estimates of variances needed to establish sample size. Other advantages of the pilot study are that it accomplishes a detailed reconnaissance, and it provides the opportunity to obtain experience in the actual field situation where the final study will be made. Information obtained and difficulties encountered may often be used to set up a more realistic study and avoid costly and needless expenditures. To maxi- mize precision, strata should be constructed such that the observations are most alike within strata and most different among strata, i.e., minimum variance within strata and maximum variance among strata. In practice, the informa- tion used to form strata will usually be from previously obtained data, or information about characteristics correlated with the characteristic of interest. In aquatic field situations, stratifica- tion may be based upon depth, bottom type, isotherms, and numerous other variables sus- pected of being correlated with the character- 3