# Chapter 12

**FORMULATION OF A HYPOTHESIS **

**Definition and Purpose of a Hypothesis **

A hypothesis is a researcher’s tentative prediction of the results of the research findings. It states the researcher’s expectations concerning the relationship between the variables in the research problem. Since many studies contain a number of variables, it is not common to have more than one hypothesis for a research topic. The researcher does not then set out to prove his or her hypothesis, but rather, collects data to determine whether the hypothesis is supported or not supported by the data. Hypotheses are essential to all quantitative research studies, with the possible exception of some descriptive studies whose purpose is to answer certain specific questions.

The hypothesis is formulated from a theory or the review of related literature prior to the execution of the study. It logically follows theory or the review, because it is based on the implications of the theory or the previous research. The related literature leads one to expect a certain relationship. For example, studies finding white chalk to be more effective than yellow chalk in teaching mathematics would lead a researcher to expect it to be more effective in teaching physics, if there were not other findings to the contrary. A theory that suggested that the ability to think abstractly was quite different for 10-year-olds versus 15-year-olds night suggest a hypothesis stating that there would be a difference in the performance of 10-and 15-year-olds on a test of abstract reasoning.

Hypotheses precede the study proper because the nature of the study is determined by the hypothesis, every aspect of the research is affected by the hypothesis, including participants. Although all hypotheses are based on theory or previous knowledge and are aimed at extending knowledge, they are not all of equal worth. A number of criteria can and should be applied to a given hypothesis to determine its value.

A hypothesis is a specific statement of prediction. It describes in concrete (rather than theoretical) terms what you expect will happen in your study. Not all studies have hypotheses. Sometimes a study is designed to be exploratory. There is no formal hypothesis, and perhaps the purpose of the study is to explore some area more thoroughly in order to develop some specific hypothesis or prediction that can be tested in future research.

Actually, whenever we talk about a hypothesis, we are really thinking simultaneously about *two * hypotheses. Let's say that you predict that there will be a relationship between two variables in your study. The way we would formally set up the hypothesis test is to formulate two hypothesis statements, one that describes your prediction and one that describes all the other possible outcomes with respect to the hypothesized relationship. Your prediction is that variable A and variable B will be related (you don't care whether it's a positive or negative relationship). Then the only other possible outcome would be that variable A and variable B are *not * related. Usually, we call the hypothesis that you support (your prediction) the *alternative * hypothesis, and we call the hypothesis that describes the remaining possible outcomes the *null * hypothesis. Sometimes we use a notation like H_{A} or H_{1} to represent the alternative hypothesis or your prediction, and H_{O} or H_{0} to represent the null case. You have to be careful here, though. In some studies, your prediction might very well be that there will be no difference or change. In this case, you are essentially trying to find support for the null hypothesis and you are opposed to the alternative.

**Characteristics of a Hypothesis **

A good hypothesis has the following characteristics:

- It is based on sound reasoning
- It provides a reasonable explanation for the predicted outcome.
- It clearly states the expected relationship between defined outcome.
- It is testable within a reasonable time frame.

It should be clear that *a hypothesis should be based on a sound rationale* . It should follow from previous research or theory and lead to future research; its confirmation or disconfirmation should contribute to educational theory or practice. Therefore, a major characteristic of a good hypothesis is that it is consistent with theory or previous research.

The previously stated definition of a hypothesis indicated that it is a tentative prediction of the results of the research outcomes. *A good hypothesis provides a reasonable explanation for the predicted outcome* . If your students are not able to speak English fluently after years taking English course, you might hypothesize that it is because your students never pay attention to your teaching, or they never memorize the vocabulary that you assign; such a hypothesis would not be a reasonable explanation. A reasonable hypothesis might be that you did not give the right techniques, methods, or approaches. Or another reason might be that you never motivated our students to practice their English more and more. In a research study, a hypothesis suggesting that children with freckles pay attention longer than children without freckles would not be reasonable explanation for attention behavior. On the other hand, a hypothesis suggesting that children who have a good breakfast pay attention longer would be.

*A good hypothesis states as clearly and concisely as possible the expected relationship (or difference) between two variables and defines those variables in operational, that is, measurable, terms* . A simply but clearly stated hypothesis makes it easier for readers to understand, simplifies its testing, and facilitates formulation of conclusions. The relationship expressed between two variables may or may not be a causal one. For example, the variables anxiety and math achievement might be hypothesized to be significantly related (there is a significant correlation between anxiety and math achievement), or it might be hypothesized that on math problems high-anxiety students perform better than low-anxiety students.

This example also illustrates the need for operational definitions. What kind of math problems? What is a high anxiety student? What does it mean to perform better? In this example, *high-anxiety students* might be defined as any student whose score on the Acme Anxiety Inventory is in the upper 30% of student scores. A low-anxiety student might be defined as any student who scores in the lowest 30% of students on the Acme Anxiety Inventory.

A well-stated and defined hypothesis must be testable (and it will be if it is well-formulated and stated). It should be possible to test they hypothesis by collecting and analyzing data, it would not be possible to test a hypothesis that indicated that some students behave better than others because some have an invisible little angel on their right shoulder and some have an invisible kittle devil on their left shoulder. There would be no way to collect data to support the hypothesis. In addition to being testable, *a good hypothesis should normally be testable within some reasonable period of time* .

**Types of Hypotheses **

Hypotheses can be classified in terms of how they are derived (inductive versus deductive hypotheses) or how they are stated (declarative versus null hypotheses). An inductive hypothesis is a generalization based on observed relationships. The researcher observes that certain patterns or associations among variables occur in a number of situations and uses these tentative observations to form an inductive hypothesis. For example, a researcher observes that in many eighth-grade classrooms students who are given essay appear to show less testing stress than those who are given multiple-choice tests. This observation could become the basis for an inductive hypothesis.

Deductive hypotheses are generally derived from theory. The results of the study generally supported this hypothesis. In deriving a hypothesis from a theory, you should be sure that your hypothesis is a logical implication of theory, not a wild, unsupported inferential leap.

A research hypothesis states an expected relationship or difference between two variables. In other words, it specifies the relationship the researcher expects to verify in the research study. Research, or declarative, hypotheses can be nondirectional or directional. A nondirectional hypothesis simply states that a relationship or difference exists between variables. A directional hypothesis states the expected direction of the relationship or difference. For example, a nondirectional hypothesis might state:

There is a significant difference in the achievement of 10th-grade biology students who are instructed using interactive multimedia and those who receive regular instruction only.

The corresponding directional hypothesis might state:

Tenth-grade biology students who are instructed using interactive multimedia achieve at a higher level than those who receive regular instruction only.

The nondirectional hypothesis states that there will be a difference between the 10th-grade groups, while the directional hypothesis states that there will be a difference and that the difference will favor interactive media instruction.

A directional hypothesis should onle be stated if you have a basis to believe that the results will occur in the stated direction. Nondirectional and directional hypotheses involve different types of statistical tests of significance.

Finally, a null hypothesis states that there is no significant relationship or difference between variables. For example, a null hypothesis might state:

There is no significant difference in the achievement level of 10th-grade biology students who are instructed using interactive multimedia and those who receive regular instruction.

The null hypothesis is the hypothesis of choice when there is little research or theoretical support for a hypothesis. Also, statistical tests for the null hypothesis are more conservative than they are for directional hypotheses.

The disadvantage of null hypotheses is that they rarely express the researcher’s true expectations based o literature, insights, and logic regarding the results of a study. One approach is to state a research hypothesis (either directional or non-directional), analyze your data assuming a null hypothesis, and then make inferences concerning your research hypothesis based on your testing of a null hypothesis. Given that few studies are really designed to verify the nonexistence of a relationship, it seems logical that most studies should be based on a non null hypothesis.

Hypotheses are critical aspects of quantitative research approaches; they focus the study on the methods and strategies needed to collect data to test the hypotheses. As noted previously, the aims and strategies of qualitative research differ from those of quantitative research. As a general rule, qualitative researchers do not state hypotheses to guide the conduct of their studies. They rarely test hypotheses at all. Rather than testing a priori hypotheses, qualitative researchers are much more likely to generate new hypotheses as a result of their studies. In simple terms, it is generally appropriate to say that a strength of quantitative research is in testing hypotheses, while that of qualitative research is in generating hypotheses.

**Stating the Hypotheses **

A good hypothesis is stated clearly and concisely, expresses the relationship between two variables, and defines those variables in measurable term. A general model for stating hypotheses for experimental studies is as follows:

P who get X do better on Y than

P who do not get X (or get some other X)

This model should help you to understand the statement of a hypothesis. Further, this model, sometimes with variations, will be applicable in many situations. In the model,

P refers to the participants,

X refers to the treatment, the causal or independent variable (IV), and

Y refers to the observed outcome, the effect or dependent variable (DV).

Study the following topic statement and see if you can identify the P, X, and Y:

The purpose of this study is to investigate the effectiveness of 12th-grade mentors on the absenteeism of low-achieving 10th-graders.

In this example,

P = low-achieving 10th-graders,

X = presence or absence of a 12th-grade mentor (IV), and

Y = absenteeism (days absent or, stated positively, days present) (DV).

A review of the literature might indicate that mentors have been found to be effective in influencing younger students. Therefore, the directional hypothesis resulting from this topic might read:

Low-achieving 10th-graders (P) who have a 12th-grade mentor (X) have less absenteeism than low-achieving 10th graders who do not.

As another example, suppose your topic statement was as follows:

The purpose of the proposed research is to investigate the effectiveness of different conflict resolution techniques in reducing the aggressive behaviors of high school students in an alternative educational setting.

For this topic statement,

P = high school students in an alternative educational setting,

X = type of conflict resolution (punishment or discussion) (iv), and

Y = instances of aggressive behaviors (DV).

You related nondirectional hypothesis might read:

There will be a difference in the summer of aggressive behaviors of high school students in an alternative educational setting who receive either punishment or discussion approaches to conflict resolution.

Let’s try one more. Topic statement:

This study investigates the effectiveness of token reinforcement, in the form of free time given for the completion of practice worksheets, on math computation skills of ninth-grade grade general math students.

P = ninth-grade general math students,

X = token reinforcement in the form of free time for completion of practice worksheets, and

Y = math computation skills.

Hypothesis:

Ninth-grade general math students who receive token reinforcement in the form of free time for the completion of practice worksheets have higher math computation skills than ninth-grade general math students who do not receive taken reinforcement for completed worksheets.

For a null hypothesis, the paradigm is:

There is no difference in Y between P who do not get X (or get some other X).

**Testing the Hypothesis **

The researcher selects the sample, measuring instruments, design, and procedures that will enable her or him to collect the data necessary to test the hypothesis. Collected data are analyzed in a manner that permits the researcher to determine whether the hypothesis is supported. Note that analysis of the data does not lead to a hypothesis being proven or not proven, only supported or not supported for this particular study. The results of analysis indicate whether a hypothesis was supported or not supported for the particular participants, context, and instruments involved. Many beginning researchers have the misconception that if their hypothesis is not supported, then their study is a success. Neither of these beliefs is true. It is just as important to know what variables are not related as it is to know what variables are related. If a hypothesis is not supported, a valuable contribution may be made in the form of a revision of some aspect of a testing contributes to the science of education primarily by expanding, refining, or revising its knowledge base.

Thu, 12 May 2011 @12:31