Statistical Methods for. Research Workers. BY. R. A. FISHER, Sc.D., F.R.S.. Formerly Fellow oj Conville and Caius Colle/;e, Cambridge. Honorary Member. The prime object of this book is to put into the hands of research workers, Cite this chapter as: Fisher R.A. () Statistical Methods for Research Workers. Fisher, R. a. () Statistical Methods for Research Workers - Download as Word Doc .doc /.docx), PDF File .pdf), Text File .txt) or read online.

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Fisher, R. A.: Statistical Methods for Research Workers, Aufl., Oliver & Boyd, Edinburgh, London XIII, S., 12 Abb., 74 Tab., 40 s. E. Rödel. Statistical methods for research workers. By Sir Ronald A. Fisher. Edinburgh ( Oliver and Boyd), 12th Ed., Pp. xv, ; 12 Figs., 74 Tables. 16s. Trove: Find and get Australian resources. Books, images, historic newspapers, maps, archives and more.

If it disagrees with experiment it is wrong. In that simple statement is the key to science. It does not make any difference how beautiful your guess is.

It does not make any difference how smart you are, who made the guess, or what his name is—if it disagrees with experiment it is wrong. These are 1 assumptions made by scientists, 2 attitudes expected of scientists, and 3 formulation of scientific theory.

Science is based on the belief that all natural phenomena have antecedent factors. This assumption is sometimes referred to as universal determinism. Primitive people proposed supernatural causes for most of the events they observed. Modern science did not develop until people began to look beyond supernatural explanations and to depend on the observation of nature itself to provide answers.

This assumption underlies any statement that declares that under specified conditions certain events will occur. For example, the chemist can state that when a mixture of potassium chlorate and manganese dioxide is heated, the process will produce oxygen.

Behavioral scientists likewise assume that the behavior of organisms is lawful and predictable.

Related to this first assumption is the belief that the events in nature are, at least to a degree, orderly and regular and that people can discover this order and regularity of nature through the scientific method.

A second assumption is that reliable knowledge can ultimately derive only from direct and objective observation. Reliance on empirical observation differentiates science from nonscience. The scientist does not depend on authority or tradition as sources of knowledge but insists on studying empirical evidence. In the history of science we find many examples of scientists who rejected the prevailing notions of their day and proceeded with their observations and experimentation.

A corollary of this assumption is the belief that only phenomena that are subject to observation lie within the realm of scientific investigation. Universal determinism 2. Inductive reasoning 3. Deductive reasoning 4.

Hypothesis a. Proceeding from general to specific knowledge through logical argument b. Deriving general conclusions through direct observation c.

A statement describing relationships among variables that is tentatively assumed to be true d. The assumption that all natural phenomenal have antecedent factors Answers 1. Scientists are essentially doubters, who maintain a highly skeptical attitude toward the data of science. Scientists investigate questions concerning the relationships among natural phenomena. Their findings are regarded as tentative, however, and are not accepted by themselves or other scientists unless further investigations can verify them.

Verification occurs when repeated observations yield the same or similar results. Verification thus requires scientists to make their research measurements and procedures known so that others may replicate the study and verify, or fail to verify, the findings. Scientists are objective and impartial. In conducting observations and interpreting data, scientists seek knowledge and are not trying to prove a point. They take particular care to collect data in such a way that any personal biases they may have will not influence their observations.

They look for observable evidence and accept the findings even when those results are contrary to their own opinions. If the accumulated evidence upsets a favorite theory, then they either discard that theory or modify it to agree with the findings.

In reality, scientists are human like the rest of us. Some scientists have been known to report only findings that agreed with their preconceived ideas or have even made up data to support their contentions.

A notorious example occurred when Stalin ruled the Soviet Union. His secretary of agriculture, Lysenko, asserted that environment changed heredity. Those scientists who reported results supporting this contention got published, got to keep their jobs, and got promoted. They concluded that the phenomenon did not exist.

Scientists deal with facts, not values. Scientists do not indicate any potential moral implications of their findings; they do not make decisions for other people about what is good or what is bad.

Scientists provide data concerning the relationships among events, but you must go beyond scientific data if you want a decision about whether a certain consequence is desirable. Thus, although the findings of science may be of key importance in solving a problem about a value decision, the data themselves do not furnish that value judgment.

Scientists are not satisfied with isolated facts but seek to integrate and systematize their findings. They want to put the things known into an orderly system. Thus, scientists aim for theories that seek to bring together empirical findings into a meaningful pattern.

However, they regard these theories as tentative or provisional, subject to revision as new evidence appears. The ultimate goal of science is theory formation. Scientists, through empirical investigation, gather many facts, but facts by themselves are of limited usefulness.

As facts accumulate, scientists must integrate, organize, and classify to make the isolated findings meaningful.

They must identify and explain significant relationships in the data. That is where theory comes into play. Scientists formulate theories to summarize and order the existing knowledge in a particular area. A theory may be defined as a set of interrelated constructs and propositions that presents an explanation of phenomena and makes predictions about relationships among variables relevant to the phenomena.

Theories knit together the results of observations, enabling scientists to make general statements about variables and the relationships among variables. Theories range from a few simple generalizations to complex formulations of laws.

The theory not only summarizes previous information but also predicts other phenomena by telling you what to expect of any gas under any temperature change. Purposes of Theories Theories serve useful functions in the development of science. They 1 organize empirical findings and explain phenomena, 2 predict phenomena, and 3 stimulate new research.

A theory organizes the findings from many separate observations and investigations into a framework that provides explanations of phenomena. We would not have progress if science were composed only of multiple separate facts. A single theory can integrate many facts by showing what variables are related and how they are related.

Researchers have developed useful theories to explain motivation, intellectual and cognitive development, moral development, social development, and so on. From the explanatory framework of a theory, scientists can proceed to make predictions about what will happen in novel situations.

If these predictions are supported by scientific investigation, then science proceeds finally to control. As soon as a statement theory was made about the relationship between the Anopheles mosquito and malaria in humans, scientists could 1 explain why malaria was endemic in some areas and not in others, 2 predict how changes in the environment would entail changes in the incidence of malaria, and 3 control malaria by changing the environment. Researchers state and test hypotheses deduced from theories, which results in the development of new knowledge.

Deductions from a theory permit predictions of phenomena, some as yet unobserved. For example, astronomers predicted the existence of the outermost planets from theory long before they were actually observed. Testing the deductions from a theory serves to confirm and elaborate the theory.

If, however, research findings do not support the theory, scientists revise it and then collect more data to test the revised theory.

Criteria for Theories To serve its purpose in science, a theory should satisfy certain criteria. The following are some of the characteristics of a sound theory: 1. A theory should be able to explain the observed facts relating to a particular problem.

This explanation of the events should take the simplest form possible. Scientists favor a theory that has fewer complexities and assumptions over a more complicated one. This rule is called the principle of parsimony.

A theory should be consistent with observed facts and with the already established body of knowledge. Scientists build on what has already been found. They look for the theory that provides the most probable or the most efficient way of accounting for the accumulated facts.

A theory should provide means for its verification.

Scientists achieve this for most theories by making deductions in the form of hypotheses stating the consequences that you can expect to observe if the theory is valid. Scientists can then investigate or test these hypotheses empirically to determine whether the data support the theory. The acceptance or rejection of a theory depends primarily on its utility, or usefulness.

A theory is useful or not useful depending on how efficiently it leads to predictions concerning observable consequences, which are then confirmed when the empirical data are collected. Even then, any theory is tentative and subject to revision as new evidence accumulates. You may recall the old theory of formal discipline, which stated that the mind is like a muscle that can be strengthened through exercise.

Subjects such as logic, Latin, and Greek were once included in the curriculum because educators believed them to be best for strengthening the mind. Thorndike, William James, and Charles Judd challenged and abandoned it. A theory should stimulate new discoveries and indicate further areas in need of investigation. The goal of theory formation has been achieved to a far greater extent in the physical sciences than in the social sciences, which is not surprising because they are older sciences.

In the early days of a science, the emphasis typically is on empiricism; scientists are concerned with collecting facts in particular areas. Only with maturity does a science begin to integrate the isolated knowledge into a theoretical framework. Although there are marked differences in the number and power of the theories that have been established in the physical and social sciences, theory has the same role to play in the progress of any science. Regardless of the subject matter, theory works in essentially the same way.

It serves to summarize existing knowledge, to explain observed events and relationships, and to predict the occurrence of unobserved events and relationships. Theories represent the best efforts to understand the basic structure of the world in which we live.

The following are among the proposed explanations: a. The sun is a god miraculously creating heat. The heat comes from combustion like a log burning in a fireplace. The sun is an enormous ball of gas. The pressure created by gravity on this great mass creates great heat. Questions 1. Which of the explanations are subject to disproof through observation? Which are scientific theories? Later, it was shown that if c was true, the sun could only produce heat for a short period of time. Should the publishers of these textbooks apologize for publishing c because it has now been shown to be inadequate for explaining the phenomenon?

Have we finally reached the correct explanation? Answers 1. Science is dynamic, never claiming that a theory is the ultimate truth. There is no shame in embracing a theory and then discarding it when a better explanation comes along. We do not know. Currently, it fits the facts. It may be the ultimate answer, but scientists remain open to the possibility that future research may produce a better explanation. The social sciences have not established generalizations equivalent to the theories of the natural sciences in scope of explanatory power or in capacity to yield precise predictions.

Frequently, researchers in the social sciences disagree on what the established facts are or what explanations are satisfactory for the assumed facts. Perhaps the social sciences will never realize the objectives of science as completely as the natural sciences. Certainly, we must stress that using the scientific approach is not in itself a sufficient condition for scientific achievement. Several limitations hinder the application of the scientific approach in education and the other social sciences.

Complexity of Subject Matter A major obstacle is the inherent complexity of subject matter in the social sciences. Natural scientists deal with physical and biological phenomena.

A limited number of variables that can be measured precisely are involved in explaining many of these phenomena, and it is possible to establish universal laws. In contrast, social scientists deal with the human subject. They must consider many variables, acting independently and in interaction, in any attempt to understand complex human behavior. Each individual is unique in the way he or she develops, in mental ability, in social and emotional behavior, and in total personality.

The behavior of humans in groups and the influence of the behavior of group members on an individual must also be dealt with by social scientists. A group of first-graders in one situation will not behave like first-graders in another situation. There are learners, teachers, and environments, each with variations that contribute to the behavioral phenomena observed in a setting.

Thus, researchers must be extremely cautious about making generalizations because the data from one group or in one situation may have limited validity for other groups and other settings. Difficulties in Observation Observation, the sine qua non of science, is more difficult in the social sciences than in the natural sciences. Observation in the social sciences is often less objective because it more frequently involves interpretation on the part of the observers.

Motives, values, and attitudes are not open to inspection. Observers must make subjective interpretations when they decide that behaviors observed indicate the presence of any particular motive, value, or attitude. The problem is that the personal values and attitudes of social scientists may influence both what they choose to observe and their assessment of the findings on which they base their conclusions. Natural scientists study phenomena that require less subjective interpretation.

The findings can be reported and the observations can be easily replicated by others. Replication is much more difficult to achieve in the social sciences.

Statistical Methods for Research Workers

Even within a single school building, one cannot reproduce a given situation in its entirety and with precision. Social phenomena are singular events and cannot be totally repeated for purposes of observations. Interaction of Observer and Subjects An additional problem is that mere observation of social phenomena may produce changes that might not have occurred otherwise.

Researchers may think that X is causing Y, when in fact their own observation of X may cause Y. For example, in the well-known Hawthorne experiments, changes in worker productivity stemmed not from the varying working conditions but from the mere fact that the workers knew they had been singled out for investigation. Investigators are human beings, and their presence as observers in a situation may change the behavior of their human subjects.

The use of hidden video cameras and audio cassettes may help minimize this interaction in some cases, but much social science research includes the responses of human subjects to human observers.

Difficulties in Control The range of possibilities for controlled experiments on human subjects is much more limited than in the natural sciences. The complexities involved in research on human subjects present control problems that have no parallels in the natural sciences. In the latter, rigid control of experimental conditions is possible in the laboratory. Such control is not possible with human subjects; social scientists must deal with many variables simultaneously and must work under conditions that are much less precise.

They try to identify and control as many of these variables as possible, but the task is sometimes very difficult. Problems of Measurement Systematic research must provide for measurement of the variables involved. The tools for measurement in the social sciences are much less perfect and precise than the tools of the natural sciences. Social science has nothing that can compare with the precision of the ruler, the thermometer, or numerous laboratory instruments.

We have already pointed out that an understanding of human behavior is complicated by the large number of determining variables acting independently and in interaction.

The multivariate statistical devices available for analyzing data in the social sciences take care of relatively few of the factors that obviously are interacting.

Furthermore, these devices permit you to attribute the variance only to factors operating at the time of measurement. Factors that have influenced development in the past are not measurable in the present, even though they may have significantly influenced the course of development. It is often necessary to conduct several studies in an area before attempting to formulate generalizations. If they consistently confirm initial findings, then researchers can be more confident in making broad generalizations.

Despite the handicaps, education and the social sciences have made great progress, and their scientific status can be expected to increase as scientific investigation and methodology become more systematic and rigorous. It is a way to acquire dependable and useful information. Its purpose is to discover answers to meaningful questions by applying scientific procedures.

To be classified as scientific research, an investigation must involve the approach we described in the previous section. Although it may take place in different settings and may use different methods, scientific research is universally a systematic and objective search for reliable knowledge. Educational research is the way in which people acquire dependable and useful information about the educative process. Educators usually conduct research to find a solution to some problem or to gain insight into an issue they do not understand.

The ultimate goal is to discover general principles or interpretations of behavior that people can use to explain, predict, and control events in educational situations—in other words, to formulate scientific theory. The acceptance of the scientific approach in education and the other social sciences has lagged far behind its acceptance in the physical sciences.

In , J. Rice, a pioneer in educational research, found himself in a situation similar to that described by the quotation attributed to Bacon previously in this chapter. Rice reported, To my great surprise, the question threw consternation into the camp. The first to respond was a very popular professor of psychology engaged in training teachers in the West.

He said, in effect, that the question was one which could never be answered; and he gave me a rather severe drubbing for taking up the time of such an important body of educators in asking them silly questions. He also pointed out that many words children were required to learn how to spell had little practical value. His work led other investigators, such as Edward L. Thorndike, to use documentary analysis to determine the frequency of use of words in the English language. Their work in turn led to improvements in language arts texts and curricula.

The scientific approach is widely regarded as the single most reliable source of new knowledge.

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The scientific approach rests on two basic assumptions: 1 People can derive truth from observation, and 2 phenomena conform to lawful relationships. Scientific inquirers seek not absolute truth but, rather, theories that explain and predict phenomena in a reliable manner. They seek theories that are parsimonious, testable, and consistent, as well as theories that are themselves stimuli for further research.

The scientific approach incorporates self-correction, inasmuch as every theory is tentative and may be set aside if a new theory better fits the evidence.

Investigators have used the scientific approach to explain, predict, and control physical phenomena for centuries. As a science, educational research uses investigative methods consistent with the basic procedures and operating conceptions of scientific inquiry.

The complexity of educational variables and difficulties in making reliable observations impeded scientific inquiry in education. However, since the beginning of the movement early in the 20th century, scientific inquiry in education has enjoyed increasing acceptance and increasing success in both theoretical and practical research.

Identify the source of knowledge—deductive reasoning, inductive reasoning, or the scientific approach—most prominently used in the following examples: a. After extensive observation of reactions, Lavoisier concluded that combustion is a process in which a burning substance combines with oxygen.

His work was the death blow to the old phlogiston theory of burning. Dalton, after much reflection, concluded that matter must consist of small particles called atoms. His early assumptions became the basis for the atomic theory. They found support for the atomic theory. After studying reinforcement theory, a teacher hypothesizes that using a tutorial computer program will lead to superior achievement in arithmetic. She devises a study in which the tutorial is used with two sixth-grade classes, whereas conventional materials are used with two other sixth-grade classes.

What is the role of theory in scientific inquiry? What is the difference between an inductive theory and a deductive theory? Give examples of the use of authority and experience as sources of knowledge. All graduating seniors with high GPAs study Latin. John is a senior with a high GPA. Therefore, John studies Latin.

All vertebrates have backbones. This animal has a backbone. Therefore, this animal is a vertebrate. Evaluate the following inductive arguments: a. Animals with backbones are vertebrates. I am reasonably certain that this animal is a vertebrate. This is a student who studies very hard. Students who make good grades tend to study hard. This student probably makes good grades. Which characteristic attitudes expected of scientists are violated in the following statements?

This study was undertaken to prove that the use of marijuana is detrimental to academic achievement. It proved conclusively that this is the case. The results show that marijuana is evil. What are the characteristics of a useful theory?

Which of the following would contribute to theory development in education? Evidence that supports the hypothesis of a study b. Evidence that refutes the hypothesis of a study c. Inductive reasoning b. Deductive reasoning c. Scientific approach d. Deductive reasoning e. Scientific approach f. Scientific approach 2.

Theory integrates findings, summarizes information, provides leads for new research, and enables people to explain and predict phenomena. An inductive theory serves to explain previous observations, whereas a deductive theory is developed before extensive observations have been made. Answers will vary. The argument is flawed; the major premise is not valid.

Statistical Methods for Research Workers

The argument is correct. The argument is flawed; cannot state that because the student studies hard, he or she makes good grades. The scientist is objective and impartial. The scientist is skeptical and regards findings as tentative. The scientist deals with facts, not values. A useful theory explains the phenomena in the simplest form possible, is consistent with observation and the established body of knowledge, provides means for its verification, and stimulates new investigation.

The technique of study. Somewhat arbitrarily, Fisher chose to define statistical significance as a difference that had less than a. A researcher who wanted to determine whether a new teaching method was effective might examine the test scores of a group of randomly chosen students educated in the new way against those who did not.

His logic proved to be flawed. Many experimental findings in disciplines that use the. One large study, published in the journal Science, found that fewer than half of the findings published in three major psychology journals held up when replicated.

Though the. A new proposal, authored by 72 prominent statisticians, economists, psychologists and medical researchers, offers a simple answer: Use. Benjamin says that the solution, while not perfect, could do a lot of good in the short term. The paper presents research suggesting that it could reduce the number of false results in economics and psychology by half. Benjamin admitted that choosing. A common interpretation of evidence falling below the.The correlation is therefore significant.

The internal evidence thus suggests that the technique was satisfactory. Much wisdom passed from generation to generation is the result of experience. They must consider many variables, acting independently and in interaction, in any attempt to understand complex human behavior. How you are affected by an event depends on who you are. Although there are marked differences in the number and power of the theories that have been established in the physical and social sciences, theory has the same role to play in the progress of any science.

With extensive material appropriate for biometrical investigations there is little danger of false conclusions being drawn. No eye observation of such diagrams. Melton observed that individuals feeling positive affects performed significantly worse on a set of syllogisms i.