Inferential Logic and Experimental Research

That logic is the art (or science?) of reasoning is a truism. The purpose of any research, particularly experimental research (so far as it can be distinguished from theoretical research), is to draw inferences from the results, as recorded or observed, of the exper­iments. The inferences can be in the form of either statements

Logical Fallacies in Experimental Research

Inasmuch as a given researcher, more often than not, bases his own research on the published research of others in the field, he needs to understand the way inferences are drawn. And when it is his turn to publish his own research, he should make every effort to make his inferences easily understood. In

Argument in Experimental Research

Argument is the intellectual process in which one or more pre­mises are used to arrive at a conclusion, which is, in fact, the inference of the argument. A premise is a statement asserting or denying, but not questioning, something, the truth-value of which is taken for granted. When a conclusion can be reached with

Categorical Propositions in Experimental Research

Propositions are statements. Categorical propositions are statements about categories, that is, about groups or classes. A class is a col­lection of all objects (or entities) that have some special character­istics in common. Categorical propositions are used both as premises and conclusions in the process of deductive argumenta­tion, in which the premises are expected to

Conventions, Symbolism, and Relations among Categorical Propositions in Experimental Research

The four forms of categorical propositions (1) through (4) men­tioned above are named, and often referred to, respectively, as A, E, I, and O propositions. The (verb) terms of affirmation (e.g., “is,” “are,” and “were”) and negation (e.g., “is not,” “are not,” and “was not”) are referred to as indicating the quality of affirmation

Diagrammatic Representation of Categorical Propositions in Experimental Research

Propositions otherwise expressed in words can also be picturized, using circles to represent classes; some of the symbolic representa­tions in traditional logic and their literal meanings are shown in Figure 13.2. A categorical proposition, having to refer to two classes, one each for the subject term and the predicate term, requires two cir­cles for

Categorical Syllogisms in Experimental Research

A categorical syllogism is a deductive argument. As mentioned ear­lier, it consists of three categorical propositions, the first two of these, in sequence, being premises and the third, the conclusion. The term that occurs as the predicate of the conclusion is called the major term; the premise that contains the major term is known

Ordinary Language and Arguments in Experimental Research

We will start this section with a set of rules as checkpoints appli­cable to standard-form categorical syllogism. In a valid syllogism, There should be only three terms (each used con­sistently). The middle term should be distributed in at least one premise. The terms in the conclusion should be distributed in the premises. Both premises

Need for Randomization

We may recall that in Chapter 7, discussing the experiment on the benefit of a hypothetical plant food, and also in other con­texts, we mentioned the word “random” quite a few times. We may now ask, Why random? Why not pick the first forty or so plants of one kind that the experimenter came

Applications of Randomization

Obtaining samples or specimens from a group (also known as a lot or population) of any kind is an activity wherein the applica­tion of randomness is of utmost significance. In the case of the study by pairing, a toss of the coin serves the purpose. Random­ization has applications beyond sampling, for example, in the

Methods of Randomization

Throwing the coin and wagering heads or tails is the simplest random process. If there are more than two possibilities, obvi­ously, throwing the coin is useless. Then, we may resort to the method of picking paper strips with hidden numbers, this being suitable for any number including two. In the hope of reducing the

Meaning of Randomization

After dealing with these various contexts—there are many more—of randomization, we may ask, What is really meant by randomization? The closest we can get to the meaning of “ran­dom” is “done without previous calculation” or “left to chance.” Any attempt to define randomization is known to be philosophi­cally hopeless for it begs the idea

Replication

We have already used this word, even before defining it, as we shall do now. Replication is repetition with some difference. When we speak of repetition, we normally imply a sequence in temporal order; what we do now, we may do after a lapse of time, no matter how long. This is replication of

Samples and Sampling

In Chapter 15 we dealt with the statistical properties of an arbi­trarily selected group of numbers, which can be considered a set. Every element of the set, in most cases, contributes toward deter­mining the required property. If the population of the set is too large to handle, or if economy in terms of time

Notions of Set

Set: is a collection of elements Capital letters (A, B, C . . .) are customarily used to symbolize sets. Elements: may be numbers, measurements, materials of any kind, plants, animals, men, or any other objects or entities. Lowercase letters (a, b, c, . . .) are customarily used to symbolize elements. X =

Permutations and Combinations

After doing sampling, the result of which is the set of a smaller number of elements, the relevant questions are In how many different ways can we arrange the given (small) number of elements of the set, deal­ing with all of them together? How many different subsets can we form out of a given

Quantitative Statement of Randomization

To illustrate this point, we deliberately work with a small set. Consider a population of six elements, a, b, c, d, e, and f out of which we want to have a random sample of two elements. The possibilities are fifteen subsets: This is the same as the number of combinations among six things,

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Sampling Methods

The following are typical, but by no means the only, methods used for sampling. Though there is wide variation among the methods used to suit the circumstances, there are some principles to which all sampling methods should conform to render the sam­ple worthy of statistical analysis. The sample should be representa­tive of the population,

Inference from Samples

The very idea of sampling is meaningful only when the popula­tion is large. When the population is very large, sampling is done to economize on time and expense. When the population involved is not only very large but also not practically accessible, as, for example, when finding the average height of tenth-grade boys in

Theoretical Sampling Distribution of X

When we encounter finite but large or infinite populations, sam­pling is inevitable. Suppose we are interested in knowing the pop­ulation mean, the only connection we have with the population being the sample; we have to depend on the sample mean, which is not an exact but a “probabilistic” value, meaning it is reason­ably close

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