The Way to Inference from Experimental Data

During the life span of an experiment, following the stages of conducting the experiment and collecting data, there comes a time when the experimenter, with his logbooks loaded with mea­surements, meter readings, and various counts of other kinds, will have to sit and ponder how reliable each bunch of observa­tions (measurements, readings, or counts) is for answering his questions, and how such answers fit together in the purpose for his experiment. At this stage, he will be analyzing the data, the purpose of which is to make decisions, predictions, or both about unobserved events. We may ask, What are such unobserved events? The answer is, They include all things that are yet to hap­pen in situations similar to the ones that are embodied in the experiment. The relevance of this answer becomes obvious if we recall that making generalizations is the major purpose of research. Based on what we observe happening, we feel embold­ened to predict what may happen in future and elsewhere under similar circumstances.

The experimenter, while analyzing the data, finds himself in a situation wherein such concerns as the following are all behind him in time:

• Standardizing the material
• Randomizing relative to the material, the subject, the sequence of experiments, and other relevant conditions
• Calibrating all measuring devices involved
• Designing the experiment (1) to avoid nuisance factors and (2) to account for factors that have combined effects

All that is now on hand are several bunches of observations, each observation being either a yes-no response or, more often, a number. We further imagine that each number is the output of an experimental inquiry, in the form of a dependent variable, the sys­tem responding to an input, in the form of one or more indepen­dent variables. The bunch of observations we referred to consists of several such outputs recorded while replicating the experiment.

Our discussion here is restricted to statistical inference, which means the process of making generalization about populations, having at our disposal only samples. In the context of experimen­tal research, each of what we called a “bunch of numbers” is a sample. If that is so, where is the population? It exists only as a possibility; the possibility of any person at any time in future, conducting a similar experiment and getting another bunch of numbers. Suppose the bunch of numbers we have on hand is 56.4, 56.4, . . ., all the n elements of the set being 56.4. The mean of this set is 56.4 and the standard deviation is 0. Then, we project that the population, however big, will have for its mean 56.4, and for its standard deviation, 0. But this situation practi­cally never occurs. Even if all possible controls are exercised in experimentation, individual numbers in the bunch (elements in the set) will have variation. And that is the reason why, and the occasion when, statistical inference is required. It consists of two parts: (1) trying to find statistical parameters of the population such as mean and standard deviation, and (2) formulating spe­cific assertions, known in statistics as hypotheses, to test in statisti­cal terms whether such assertions can be accepted or need to be rejected. The first part mentioned above is known as estimation, and the second as testing of hypothesis. It is necessary for the reader to distinguish further here between “hypothesis” as used in the logic of planning experiments, as was done in Chapter 18, and the meaning of the same word as used here in statistics and refer­ring to the data collected from experiments. The scope of the lat­ter, testing of (statistical) hypothesis, is rather limited. It is confined each time to deriving inferences from one set of numbers on hand, which is done in the following pages.

Source: Srinagesh K (2005), The Principles of Experimental Research, Butterworth-Heinemann; 1st edition.