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# Evaluating Results: Statistics, Probability, and Proof (page 3)

By Thomas Moorman
John Wiley & Sons, Inc.

### Replicating and Expanding on Experiments

How could Alice "prove" more, besides just making statistical analyses of her data? She could replicate the experiment. This would raise the predictive power of her test if results were as good as the first test or better, even though it would still not finally prove anything. We must accept this because there is always uncertainty about the future. Some things are more highly probable than others, of course. We are all fairly sure that the sun will come up tomorrow, while we may not be so sure that another planting of corn, treated as Alice's was treated, will turn out the same. So we are always dealing in probabilities.

Scientists like to show that their findings allow them to predict, or generalize, in another way than in the simple replication of an experiment or other investigation. Alice could expand her research in several ways:

Plan A: One experimental level of urea, applied in water (Alice's first plan).

Planter Description
1 Control: no urea
2 Experimental: 2 g (grams) per liter of water used to water the plantings

Plan B: Three experimental levels of urea, applied in water

Planter Description
1 Control; no urea
2 Experimental: 2 g urea per liter of water
3 Experimental: 4 g urea per liter of water
4 Experimental: 6 g urea per liter of water

Plan C: Three experimental levels of urea, applied in soil

Planter Description
1 Control; no urea
2 Experimental: 109 urea mixed in the soil
3 Experimental: 20 g urea mixed in the soil
4 Experimental: 30 g urea mixed in the soil

If she were to test both variables—two ways of applying urea and three different levels of urea—at the same time Alice would need an arrangement of planters (or outdoor plots) as in figure 13.3.

You may be interested in figuring out how many different experiments would be needed to test each of these plans one at a time against a control and against each different level of urea. Also consider that there are other nitrogen compounds that should be compared with urea; each should be applied in different amounts. Then there are other kinds of soil, other varieties of corn, other planting methods, other methods of applying the fertilizer, and other chemicals that may be as important as nitrogen for promoting healthy growth in the corn. Many of these variables would best be tested in combination with certain other variables. Therefore, the designs in some cases would be more complicated than in the above Plan C. For the most significant results, most of the experiments would be conducted all the way through to the mature stage of the crop. Therefore, the testing would need to be done outdoors in plots of land large enough to accommodate farm equipment.

Surely under these expanded conditions there would be enough "population" to make the results prove something! Well, perhaps not surely, but more so. And yet these methods would create other problems. Rarely would individual plants be measured in order to determine results. Instead, more gross measures, such as weighing the grain from each plot or weighing the grain and other plant matter, would be used. This would increase our confidence in the results in that they would not be affected so much by variations among individual plants as in Alice's small groups. Nevertheless, the different plots might vary as to quality of soil, drainage conditions, and the like, and so scientists have found that each "treatment" must be used over several smaller plots that are spread in a randomized pattern around an entire field. For example, instead of two larger plots, one experimental and one control, the experimental plot is divided into five smaller experimental plots (each given the same treatment) and the control plot is divided into five smaller control plots. These plots are distributed randomly throughout the entire field. As a consequence, we find that we are dealing with a small number of things (five plots) as in Alice's experiment with five corn plants. While this gives important improvements to the overall plan, it still shows somewhat the same problem of a small sample (small number of plots). As a consequence, the statistical treatment for such a study must be highly developed if you are to squeeze the most meaning out of the results.

All said and done, there is still uncertainty about the evaluation or results as there is elsewhere in scientific method. We must not be disheartened about this uncertainty, however. Unfortunately, many people have been oversold on science and its powers for finding out the "truth" about things. Others have shown disappointment over the way science has not been able to solve more problems. It is important to understand that scientific methods are the best that have been found so far for learning about many things, and that they are superior to ordinary, everyday, "commonsense" methods. That's why scientific methods are called "scientific"—they are better than unscientific methods. Yet, by comparison, humankind has been working with scientific methods only a short time. Not all kinds of human problems can be solved by using scientific kinds of knowledge, but those problems that might be solved by scientific methods seem to be limitless. Nevertheless, in spite of the uncertainty of science and the limited speed with which scientists can move into new areas, we must use scientific methods to find out all we can about the world and the people and things in it. Even with its uncertainty, it is still the best we have for trying to resolve many of the problems of humankind.

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