Forest research is primarily concerned with the behavior of plant crops with a long life span. For this reason it differs from agricultural research in several important respects. In agriculture it has often been possible to obtain conclusive results from research in a few years, because agricultural crops develop from seed to maturity within a single growing season. In the forest, observation of the behavior of a single crop from youth to old age, and determination of the response of that crop to various means of treatment, may require a period of fifty years or more. A single forest research project may be started by one individual or group of individuals, it may be continued by several successive groups, and it may be completed by men who were not born when the project was established.
There are, of course, certain classes of forestry problems, such as those arising in nurseries and plantations, regarding which valuable research results can be obtained in a short time. Many problems in mensuration can also be solved rapidly. But it remains true that the majority of forest research undertakings require a long time for their completion.
Since individual forest projects are observed by different men at different times, it is particularly important that plans for any forest research project be thought out with the greatest clarity before actual work is commenced and be set down on paper in the greatest detail. Unless this is done, it becomes practically inevitable that changes in methods of measurement, etc., will be introduced from time to time, with results very damaging to the validity of the eventual conclusions.
The importance of proper planning to the success of silvicultural research was emphasized in a recent report of the Subcommittee on Planning and Statistical Procedures of the Society of American Foresters. The Subcommittee draws special attention to the advantages to be gained from the use of modern statistical methods in the design and analysis of silvicultural research projects. Through the courtesy of the editors of the Journal of Forestry we have been permitted to summarize that part of the Subcommittee's report relating to planning and to quote in full the section dealing with the use of statistical methods.
Planning Silvicultural Research
Any program of silvicultural research consists of a number of individual studies or projects. Plans for the general program may consist chiefly of the definition of its objects and the principal problems which it is intended to solve. The program plan must then be supported by detailed plans for individual studies or projects. Each project plan must bear a direct relationship to the general program. The individual plans, taken together, should constitute a restatement in detail of the general program and of the means proposed for carrying it out.
The principal objects of a silvicultural research program are determined by the physical conditions and practical problems existing within the district or region to which the program is to apply. Since financial and other resources are always subject to limitations, it is necessary to decide which individual problems should be given the highest priority. Valid decisions must be based on accurate knowledge of the relative importance of different practical problems within the region. Given this knowledge, it is necessary to consider what research projects might be undertaken, regardless of practical limitations; what projects ought to be undertaken from the point of view of the practicing silviculturist; and what projects it is possible to undertake with the staff, money, and other facilities actually available.
When assigning relative priorities to different studies, preference should be given to those promising results of the greatest practical usefulness, those which will fill critical gaps in silvicultural knowledge, and those of the greatest importance to the development of further research programs.
The first step in developing a program is an examination of research studies already undertaken in the region concerned, and an assessment of their value. This is always necessary in order to avoid useless duplication of work.
The second step involves selection of specific projects to be undertaken. Selection is guided by considerations outlined in the previous paragraphs and also, and to a very important degree, by the capabilities and experience of the research staff. Since research programs are always limited in comparison with the need for new knowledge, it is most important that any work undertaken be done well. Therefore, every effort should be made to assign to individual members of the staff projects which engage their interest and lie within the range of their capabilities.
When a program has been planned and studies have been chosen, it is necessary to select methods appropriate to each individual project. Suitable working hypotheses must be developed, and these in turn influence the selection of methods.
Each research project is planned in the hope that it will provide complete or partial answers to some specific question. Proper formulation of the questions to be answered and of the hypotheses to be tested in seeking for the answers will provide a preliminary definition of the project.
Many forestry research projects involve repeated measurement of selected forest characteristics over long periods of time. To illustrate, it may be necessary to remeasure established sample plots at five-year intervals for twenty or thirty years. Under such circumstances it is particularly important that written plans define exactly what characteristics are to be measured, the methods of measurement, and the instruments to be used. Only thus can there be reasonable assurance that the results will be comparable with the original work and with each other.
A satisfactory working plan for an individual project should include:
(1) A clear, precise statement of the questions to be answered.
(2) Provision for review of the relevant literature.
(3) A statement of the hypotheses to be tested.
(4) A statement of the methods to be used, including details of the experimental design.
(5) Method of presenting the results.
Item 4 is of particular importance; correct design of an experiment is essential if significant results are to be obtained. The design of research projects which depend upon sampling, instead of complete measurement of the universe being studied, should be guided by the principles of modern statistical theory. Otherwise, there may be no sound basis for determining whether observed differences between different areas or apparent differences resulting from different treatments are-of real significance or are merely accidental. Failure to plan correctly has greatly reduced or even nullified the value of many research projects in silviculture.
The following discussion is reprinted from the report of the Subcommittee on Planning and Statistical Procedures, Society of American Foresters:
Statistical methods in silvicultural research
Why statistical methods are needed. If there could be one and only one answer to the question "What is the diameter of that tree?", and if a definite percent, no more, no less, of every lot of yellow-poplar seed were viable; in other words, if measurements were not subject to error and living things to unaccountable variation, there would be no need for statistical methods. But measurements are subject to error and living organisms do vary even under controlled conditions.
Experimental results are, therefore, not absolute, but variable; and so the basis for action they provide cannot be absolute or perfect; it is only more or less reliable. The evaluation of the reliability of experimental results is a function of statistical methods, along with the designing of efficient experiments and the skillful analysis and condensation of experimental results. Statistical methods are, however, not the whole of silvicultural research, or of any other kind of research. They are only an aid to, and not a substitute for, the right use of human reasoning power.
A model of variability. Just as mathematical models - paraboloids, cones, neiloids - are used to help in the calculation of the volume of tree trunks, so mathematical models have been set up to help in dealing with errors of measurement and the uncontrolled variation in living things. One such useful model is the "normal curve of error." Although we have not yet found ways to make trees grow more like paraboloids, or neiloids, we can make the variability of our forestry data approach the normal curve of error by properly collecting and handling such data. For example, treat the several thousand planted trees in a uniform plot alike.
Measure the heights of 30 of them. The heights will vary and the pattern of variation may look little like the normal curve. Take heights of 30 groups of 30 trees each. The 30 averages of the groups will vary, but the pattern will be closer to the normal curve of error than the 30 single measurements. The fact that the variability associated with our data fits the mathematical model better and better as the number of observations increases, strengthens our confidence in the model.
The normal curve of error is based on the laws of chance. If we are to make use of the formulae derived from it we must be sure that every one of the trees in our uniform plot had an equal chance of being selected for measurement in our samples, that is, they must have been chosen at random. This seems sensible, too, for we are well aware that if we picked tall trees only, we would get a biased average, no "honest" answer to the question: How well are the trees growing on that plot?
Over and above these and other evidences that the mathematical model set up by the statisticians does really fit the kind of variability we deal with in biological research, use of statistical methods has the great advantage that it compresses and distills, by standard procedure, masses of data that would be unmanageable in the raw. Condensation of data in a variety of ways, each research man using his own, would be confusing and inefficient - just as it would if each one used a language of his own. The accepted "language" not only of biological research, but of science in general is the statistical method. Workers in silvicultural research cannot afford to be unfamiliar with it.
Some statistical procedures useful in silvicultural research. It is not the purpose of the committee to teach the use of statistical methods, but rather to tell why this tool is needed-and to point out situations in which it is useful.
Consider now an experiment to determine the effect that the addition of organic matter to the soil has on the height of nursery seedlings at transplanting time. The average height of seedlings in the humus-treated bed is found to be greater - say 3 inches greater - than the average height of seedlings in the untreated bed. But the best seedlings in the untreated bed are taller than the poorest ones in the treated bed. How reliable is this 3-inch difference in the averages? Statistical methods provide a standard test - the test of the significance of differences - which, if the rules are followed, will measure the probability of so large a difference happening by chance. If it could have happened only very rarely by chance, that is, if it was not "just an accident," we would recommend the use of humus to increase, by about 3 inches, the height of seedlings at transplanting time. The same statistical procedure will, incidentally, furnish an estimate of the variability of results to be expected in the use of this treatment under the same conditions. The decision whether the 3-inch increase, with its liability to variation, is worth while and of practical importance is beyond the field of statistical methods.
Note that we made the prediction about the effect of adding humus on the assumption it would be used "under the same conditions." Conditions are, of course, never really the same. In fact, if we compared a single treated bed with a single untreated one, a part of the difference in height might have been due to differences in the original texture or fertility of the soil. If we had selected at random from all the beds in the nursery a number - say 6 - to which to add humus and the same number to leave without humus, we could then have determined how much seedling height at transplanting time varied in beds treated alike, and by a statistical procedure called the analysis of variance, could have arrived at a more precise measure of the effect of the humus treatment and of the variation associated with it. As a consequence, we could have predicted more reliably what to expect following use of the treatment. Go a step further. Suppose half the humus-treated beds and half the untreated beds had been watered. The analysis of variance would then enable us to evaluate the effect of watering and the effect of humus treatment separately, with the variation associated with each. We could also evaluate their combined effect; and their interaction, that is, determine whether response to watering is the same in humus-treated beds as in beds not humus-treated. More complex experiments to test the separate and combined effects of larger numbers of treatments and their interactions are readily handled by the method of analysis of variance.
Problems involving the relation of changes in one thing to changes in another are common in silvicultural research. How does the volume of even-aged Douglas-fir change as the stand grows older, If we measure the diameters, heights, and volumes of a number of loblolly pines, how can we analyze the data so as to estimate the volumes of other loblolly pines from measurements of their diameters and heights, The statistical procedure correlation is most useful in these and similar cases. The method of correlation has the advantage of being objective: it does not require the personal judgment that must be used to draw freehand curves. It can handle any number of variables: in graphic work two independent variables are about the limit. The procedure is standardized so that all workers using the same data would come out with the same result. It provides a measure of how much of the original variation in the dependent variable is accounted for by its correlation with the independent variables, and evaluates the error of estimate to be expected in making predictions.
Hardly a study can be made in silvicultural research without using sampling. In each of the examples described so far it was necessary. Not all the trees in the uniform planting could be measured, and certainly not all the seedlings in the nursery beds. Wherever measurement of a part of the individuals in a population must be made to serve instead of measurement of all the individuals, sampling is involved. This branch of statistical methods tells how to take unbiased samples, representative of the population; how to estimate the number of plots needed in an experiment; how to sample efficiently by using devices that increase the precision of sample averages without the need to increase the number of measurements; how to apply the results of sampling accurately, and to best advantage.
Finally, the design of experiments integrates the physical layout of the plots, trees, or other things being studied with the schemes that are to be used in analyzing the data. Experimental design dictates how the plots and trees are to be selected for treatment to avoid bias in the experimental results. Basic to all good experimental design are randomization and replication. That is to say, precautions must always be taken so that the personal judgment of the experimenter shall not determine which plots or trees are to be treated one way and which another, and always each of the treatments must be applied not to one plot or to one tree, but to a sufficient number so that the variability of the results can be measured.
In the humus-treatment experiment, outlined above, we used a simple experimental design involving 12 randomly selected plots in a nursery. Proper procedure would require that each of the 12 plots should have equal chance of being treated with humus or of being left without it. That is what we mean by saying that the treatment should be applied at random to half of the plots. Similarly, when we refine the experiment further by watering half of the beds, those to be watered must be selected entirely by chance - this can be accomplished by drawing numbers out of a hat, or in any other fashion that makes it impossible for the experimenter to decide ahead of time which plots are to be treated.
In this experiment four treatments were used: some plots received both humus and water; some received neither; on some humus was applied and water withheld; and on some humus was withheld and water applied. Note that each treatment was used three times. Thus the experiment was balanced and provision made to measure the variability of the results. Complex designs for more complicated situations are available in the textbooks.
Conclusion. The objective of all experimental design, as well as of statistical methods in general, is to get the greatest amount of accurate information for the outlay of manpower, time, and money. Without a working knowledge of statistical methods no worker in silvicultural research can expect to reach that goal.
Statistical methods applicable to biological research are described in an ever-increasing number of publications. The following selected list gives of some of them:
FISHER, R. A. (10th edition) 1946. Statistical Methods for Research Workers. Oliver and Boyd, London.
FISHER, R. A. (5th edition) 1949. The Design of Experiments. Oliver and Boyd, London.
SCHUMACHER, F. X. and CHAPMAN, R. A. 1948. Sampling Methods in Forestry and Range Management. Duke University, School of Forestry, Durham, North Carolina, U. S. A., Bulletin 7.
SNEDECOR, G. W. (4th edition) 1946. Statistical Methods Applied to Experiments in Agriculture and Biology. Collegiate Press, Inc., Ames, Iowa, U. S. A.
YATES, FRANK. 1949. Sampling Methods for Censuses and Surveys. Charles Griffin & Co., London.
