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Analyzing the Structure and Substance of

Hypotheses

In: Quantitative Research in Education: A Primer

By: Wayne K. Hoy

Pub. Date: 2012

Access Date: May 7, 2019

Publishing Company: SAGE Publications, Inc.

City: Thousand Oaks

Print ISBN: 9781412973267

Online ISBN: 9781452272061

DOI: https://dx.doi.org/10.4135/9781452272061

Print pages: 67-90

This PDF has been generated from SAGE Research Methods. Please note that the pagination of the

online version will vary from the pagination of the print book.

https://dx.doi.org/10.4135/9781452272061

Analyzing the Structure and Substance of Hypotheses

We turn to hypotheses in this chapter. What is a hypothesis? What are the criteria of a good hypothesis? We

build on our understanding of variables and focus on relations between variables in the form of hypotheses.

We examine the notions of “theoretical hypotheses“ or “substantive hypotheses” and “statistical

hypotheses,” such as a “null hypothesis.” We explore simple hypotheses as well as more complex ones.

Our goal is to diagram hypotheses in the way a grammarian diagrams sentences. We begin by defining a

hypothesis and its elements. Then we conclude by constructing a framework for diagramming hypotheses

and applying it to multiple hypotheses. Oh yes, we will also apply the statistical knowledge we learned in the

previous chapter to our analysis of hypotheses.

Hypotheses

We concluded the second chapter by defining a research problem as a query that asks what the relationship

is between two or more variables. Typically, researchers begin their work with scientific problems, that is,

questions about relations between variables. For example, what is the relationship between bureaucratic

structure and teacher sense of alienation? Not all questions, however, are scientific questions. Consider the

question “What makes a good principal?” Although the question may be interesting to you, it is not a scientific

problem because it is not a question of the relationship between variables. Contrast this query with the

following question: “What is the relation between administrative drive and organizational effectiveness?” In the

last interrogative, we have the rough beginnings of a research problem because it deals with the relationship

between two variables—administrative drive and organizational effectiveness.

Studies begin with research questions, are transformed and guided by hypotheses, and culminate with the

testing of the hypotheses. Problems and questions need answers. A hypothesis is the proposed answer

to a research problem. To be more specific, a hypothesis is a conjectural statement that indicates the

relationship between at least two variables. Hypotheses are conjectures; they specify how the variables relate

to each other (see “Elements of a Proposal,” Appendix A). Note the following essential characteristics of good

hypotheses:

• They are declarative statements, not questions.

• They are tentative—conjectures that await empirical evidence.

• They must have at least two variables.

• They must be testable.

• They are statements of the relation between variables.

Hypotheses are usually more specific than research problems because in the search for responses to the

questions, researchers examine the literature, conceptualize the problem, and specify their concepts (see

“Elements of a Proposal,” Appendix A, for an outline of this process in a dissertation proposal). In answer to

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the question “What is the relationship between bureaucratic structure and teacher sense of alienation?” the

researcher might generate the following two hypotheses:

H.1: Schools with a hindering bureaucratic structure have a greater sense of faculty

powerlessness than schools with an enabling structure.

H.2: Schools with a hindering bureaucratic structure have a greater sense of faculty

meaninglessness than schools with an enabling structure.

These are both answers to the same general research question, but they are more specific than the research

question because they suggest the conceptual schemes used to capture the meaning of bureaucratic

structure (hindering vs. enabling structures) and alienation (powerlessness and meaninglessness). Note also

that the hypotheses are written in the present tense and they relate concepts, not measures.

There are many ways to express hypotheses. Consider the following as illustrative: If x, then y; x causes y;

x and y covary; x facilitates y; x is related to y; as x increases, y increases; and y is a function of x. There

are many other ways to state the hypothesis, but the important point is that you need to select the form of the

hypothesis statement that best fits your variables and your study. Without a very strong theory, you would be

well advised not to state the hypothesis as a direct casual relation (x causes y). Instead, the hypothesis might

be stated as a relational one such that the greater x, the greater y. Causation is a complex, thorny issue,

which is well beyond the scope of this book. Be careful not to claim direct causation without strong reason

and evidence.

In summary, a good hypothesis has a number of features; make sure your hypothesis has them:

• The hypothesis must have at least two variables.

• The hypothesis must specify a relation between the variables.

• The hypothesis must be testable.

• The hypothesis should be written in the present tense.

• The hypothesis should be conceptual—relate concepts, not measures.

• The hypothesis should be stated simply and clearly (see “A Few Writing Tips,” Appendix B).

One final thought—the best hypotheses are derived from theory; they are deduced from theory as a way to

test empirically a theoretical explanation. Theories are heuristic: They suggest many propositions that are

in need of examination. Thus, good theories are your best source for generating sound hypotheses. As you

grapple with your research problem, seek theories that spread light on the concepts that you are interested in

studying.

Kinds of Hypotheses

Just as there are many ways to classify variables, there are also a variety of kinds of hypotheses. One

distinction that is useful is between substantive hypotheses and statistical hypotheses. The substantive

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hypothesis is the statement of the hypothesis in conceptual or theoretical terms; a declarative statement

describes the relation between the concepts or variables. All the hypotheses illustrated thus far are

substantive hypotheses, which are also called theoretical or research hypotheses.

Eventually, however, we will want to test our theoretical hypotheses. To test them, we must transform them

into statistical hypotheses; that is, we specify each hypothesis in terms of the measures of the variables.

There are two forms of the statistical hypothesis—the null and the alternative. The null hypothesis states that

there is no relation between the measures of the variables. For example, if we are predicting that the students

taught using a discovery approach will achieve at a higher level than those taught using a lecture approach,

then our null hypothesis would take the following statistical form indicating a chance model explanation—no

difference between the means of the two groups:

The directed, alternative hypothesis would take the following statistical form

The directed, alternative hypothesis predicts that the mean score for the group taught by the discovery

approach is significantly higher than the mean score of the group taught using the lecture approach.

You know from the previous chapter, however, that statistics are used to reject the chance model. That is,

statistical tests are used to reject the null hypothesis. Depending on the nature of the variables, the null

hypothesis can take the form Ma = Mb, r = 0, χ 2 is not significant, t is not significant, F is not significant,

and so on. If the null hypothesis (chance model) is rejected, then we are in a position to accept the directed,

alternative hypothesis. We repeat—you can only use statistics to reject the null in anticipation of accepting

the predicted alternative. Regardless of how the hypothesis is stated, it is the null hypothesis that is tested

statistically. Remember—rejecting the null hypothesis supports the alternative hypothesis.

Imposter and Misconceived Hypotheses

There are many traps that must be avoided by students as they both read the research and develop their

own hypotheses. Many hypotheses are poorly constructed, vague, misleading, and sometimes not really

hypotheses (see Charters, 1992).

Imposters: Only One Variable

One will occasionally find in the literature, but more often in dissertations, statements that masquerade

as hypotheses. Let's consider some imposters. One student recently came to me proud to present his

original hypothesis: Charismatic educational leaders make a difference in American schools. At first blush,

the statement may seem like a reasonable beginning hypothesis, but it is not. Although it is a declarative

statement, what are the two variables? Charismatic leadership style might be a variable, but what is the other

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variable? Difference is not a variable. Different in what respect? We need a second variable to make this

statement a legitimate hypothesis. If there are not at least two variables, then it is not a hypothesis.

Consider the following statement: High school principals of this state rarely focus their attentions on school

safety. Again, what are the two variables? The extent to which principals spend time on school safety might

be one variable, but that is the only variable. Here is yet another example of the same ilk. The researcher

proposes to test the hypothesis that American public schools have cultures of pessimism. The degree of

pessimism in the school culture might be a variable, but what is the other variable? Finally, consider the

following proposal: The purpose of this research is to test the hypothesis that New Jersey school boards are

composed of professionals rather than nonprofessionals. A descriptive study might be able to address this

proposition, but it is no hypothesis because it does not examine the relation between two or more variables.

Incomplete Hypotheses: Something Missing

Some propositions offered as hypotheses are simply incomplete. The statements do not give us enough

information to decide what the second variable is—even though a second variable is implied. For example,

consider the following:

Administrative teams with appointed leaders have more cohesion among team members.

The statement suggests that appointed leader teams have more cohesion than what—than teams with

elected leaders? Than leaderless teams? Than nonappointed leader teams? This statement can be readily

transformed into a hypothesis with two clearly identifiable variables, but as it stands now, it does not pass

muster. There is no excuse for this kind of slipshod writing; in fact, it likely shows carelessness in writing, a

lack of understanding of a hypothesis, or fuzzy thinking—none of which bodes well for the research. Take a

minute and develop a good hypothesis using the concepts implied in this description of administrative teams.

Here is a similar example: Elementary teachers are more humanistic in American schools. Again, the problem

is one of comparison. Clearly the dependent variable is the degree of humanism, but what is the independent

variable? We don't know what or whom to compare the elementary teachers with—secondary teachers or

principals, or is it a comparison of American and Russian schools or some other set of schools? Let's take

the statement and develop some clear hypotheses. Consider the following:

H.3: Elementary teachers are more humanistic than secondary teachers in American schools.

H.4: Elementary teachers are more humanistic than their principals in American schools.

H.5: Elementary teachers are more humanistic in American schools than their counterparts are in

Russian schools.

You probably can figure out what the researcher means in a great many cases if you read the work and

carefully examine the statistical analysis and discussion, but it should be neither this difficult nor ambiguous.

Then again, sometimes you will find that the researcher really does not have a hypothesis and is simply

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describing the character of American schools, in which case there are not two variables, and you are

confronted with an imposter hypothesis.

Tautologies: Nothing New

In too many cases, what appear to be hypotheses are nothing more than tautologies; that is, they are of

the variety “if x, then x.” The independent and dependent variables are the same. Consider the following

statement: Teachers who are alienated are dissatisfied. Can it be any other way? Is not alienation a form

of dissatisfaction? The proposition appears to have two variables—alienation and satisfaction—but in the

end, they are both descriptions of the same general state. The statement tells us nothing new; hence, it is a

tautology, not a hypothesis.

Sometimes the research uses two different words to refer to the same property and claims a relation. In the

example above, it is easy to see the tautology, but in other cases it is more difficult. For example, I once had a

student who developed the perfectly reasonable theoretical hypothesis that the more hierarchical the school

structure, the greater the sense of powerlessness of the teachers. Check this hypothesis—a declarative

statement, two variables, clearly stated, a relation, and testable. It seems that it has all the criteria of a good

hypothesis. Yet in the end, the statement turned out to be a tautology and not a hypothesis. How could that

be, you ask. Clearly, the hypothesis seemed to have “the right stuff,” yet it was a tautology. Examine the

operational measures for each variable, and you find the flaw. In this case, the operational measures turned

out to be composed of items that were virtually the same for the two concepts. Here is a tip: If the correlation

between two variables is very high (above .90), then check to see how the measures of the two variables

differ. Don't be surprised if the variables are masquerading as different properties but in reality are the same

property with different names—a tautology by any other name.

Unspecified and Untestable Hypotheses

Sometimes, declarative statements express a relationship between two variables, but the relation cannot be

tested because it is unspecified. For example, consider the following relation: Teacher loyalty is a function

of the personality of the principal. Let us examine this proposed hypothesis more closely. Personality is a

variable, but what are the types of personality? How does personality vary? Along a continuum? By category?

What are the categories of personality? As the hypothesis is stated, it cannot be tested; furthermore, it is

difficult to understand just what the researcher is proposing; it is too vague. Moreover, are we to expect a

positive or negative relation? Just what is the prediction? It is hard to tell. Unspecified relations or hypotheses

where the categories of the variables are unknown obfuscate rather than guide. Consider the following

hypotheses based on the unspecified relation above:

H.6: Principals who are extroverts have more loyal faculties than those who are introverts.

H.7: Open-minded principals have more loyal faculties than do closed-minded principals.

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Note that these hypotheses specify the categories of personality and transform the unspecified relation

between personality and loyalty into two testable hypotheses; in fact, the two are quite different.

Unspecified hypotheses are common. Here are a few more examples for your consideration. Turn them into

testable hypotheses.

• The racial composition of the community is an important factor in determining the success of

elections to raise tax levies.

• Faculty morale is positively related to the type of authority structure of the institution.

• The effectiveness of resident dorm counselors is dependent on the social relations that they have

with resident students.

In sum, make sure that the hypotheses have two variables and clearly describe the relation between the

variables. Beware of tautologies. Finally, make sure that the hypotheses are specified and can be tested.

Finding Hypotheses in Research Studies

In the next chapter, we will discuss how to generate original hypotheses, but here we are concerned with

finding and analyzing hypotheses in the research literature. One would think that is no problem, but often it is

an issue. About half the research articles in education do not state the hypotheses clearly. You have to dig to

find them, and most often you have to construct them yourself! Look for the statement of the purpose. What

are the variables of the study, and how are they measured? Which are the independent variables, and which

are dependent variables? Look for the reasoning that leads to the analysis. What statistics are used? Look at

the conclusions in the discussion. What propositions are proposed in the discussion? We will shortly present

a framework for diagramming hypotheses that organizes these questions and will lead you to the hypotheses.

Even if the hypotheses are explicitly stated, as Charters (1992) warns, don't count on them having a proper

structure.

Good hypotheses are clear guides that direct your reading of the research. Among other things, they suggest

how the variables are conceptualized and measured; they underscore a body of related literature; they lead

to the correct study design; they suggest appropriate statistics for the analysis; and in general, they provide a

useful direction by focusing on the important aspects of the study—what the study is all about (see “Elements

of a Proposal,” Appendix A).

Analyzing and Diagramming Hypotheses

After we find the hypothesis of a study, we need to do a careful and comprehensive analysis of it, which

includes the following:

• Identify the independent and dependent variables by name.

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• Determine the kind of each variable—categorical or continuous.

• Elaborate each variable (elaboration)—What do the numbers mean?

• Specify the relation of the hypothesis (specification)—How are the variables related?

• Decide on the appropriate unit of analysis—What is the object of the study?

• Select the appropriate statistical test—What statistic do I use to test the null?

These items provide the elements of a framework and schema for analyzing and diagramming hypotheses

(see Table 4.1). The schema builds on and refines the framework first introduced by Charters (1992) to dissect

hypotheses.

Case I: Dichotomous Independent Variable and Continuous Dependent

Variable

What are the independent and dependent variables that form the hypothesis? What is the presumed

causal (independent) variable and presumed effect (dependent) variable? Which variable is “manipulated” or

changed to examine its impact on the dependent variable? What are the names of each variable, and how

is each conceptualized? This is the first set of questions in need of answers. I suggest that you clearly write

down the hypothesis. Then begin your analysis by answering the preceding questions.

Let's illustrate the process with the first hypothesis proposed in this chapter.

H.1: Schools with a hindering bureaucratic structure have a greater sense of faculty

powerlessness than do schools with an enabling structure.

This hypothesis is clearly stated, and so the identification and names of the variables are straightforward. The

hypothesis suggests that the independent variable (x) is bureaucratic structure and the dependent variable (y)

is sense of powerlessness. It is reasonable to assume that bureaucratic structure influences powerlessness.

So far so good!

What kind of variable is each? This is an important question because the answer will explain why we have two

variables and not three. Beginning students often get confused with this kind of hypothesis, thinking that there

are three variables (hindering, enabling, and powerlessness) when there are only two variables (bureaucratic

structure and powerlessness). The independent variable, bureaucratic structure, is a categorical variable,

whereas the dependent variable is a continuous variable.

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Table 4.1 Hypothesis Diagramming Table

As we elaborate each variable, it becomes clear why there are only two variables. Bureaucratic structure

has two categories, hindering and enabling; that is, there are only two variations of structure. The dependent

variable, powerlessness, is a continuous variable that varies along a continuum such that the higher the

number, the greater the sense of powerlessness. It is important to make sure that a high number means what

you think it means. In this case, we are claiming that the higher the score on the powerlessness variable, the

greater the powerlessness.

A good rule for stating hypotheses is to make sure that the numerical value of the variable is consistent

with the name of the variable; that is, the higher the value of the variable, the more of the property it has.

In this case, the name of the variable is sense of powerlessness, and so a high value should mean more

powerlessness. The same measure of powerlessness could be used as a measure of sense of power, in

which a small value would represent a large sense of power. The key point is to be sure that the value of the

measure and the name of the variable are running the same way. When you construct a hypothesis, make

sure that the name of the variable and its measure are consistent; that is, the higher the value, the more of

the property; this practice is good form.

Next, we make sure that we understand the unit of analysis. This can be a little tricky sometimes. In this case,

we are claiming that the school is our object of study. We are concerned with the relation between structure

and powerlessness. Let's explain the consequences of such a claim. We are studying and measuring school

properties here. One school gives us one data point for each variable. Thus, School A has one score

on bureaucratic structure (either a hindering or an enabling structure) and one score on faculty sense of

powerlessness. In other words, the dependent variable is a school score, not an individual score. Even though

we ask teachers to respond, we will have one school score on powerlessness, which is an average score for

the school. To repeat, the school score is what we are concerned with, not individual scores per se. When

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researchers study school properties, both the independent and the dependent variables are school properties

because the unit of analysis is the school.

Finally, what is the null hypothesis that we are trying to reject? The directed hypothesis says that the mean

powerlessness score for hindering structures will be greater than the mean powerlessness score for enabling

structures; therefore, the null hypothesis is that the two means will be the same; that is, there is no difference.

The appropriate statistical test of the null is either a t test or an F test. The complete diagram of the hypothesis

is summarized in Table 4.2.

This diagram contains the elements that you need for a careful and systematic analysis of a hypothesis. It

is a guide that you should commit to memory. Use the diagram as you analyze hypotheses in this chapter.

One suggestion: When you elaborate a variable or specify the relations, use shorthand descriptions that you

understand. Understanding is the key. Don't let the symbols confuse you. In this diagram, you could have just

as easily used the statement “Powerlessness is greater in hindering than enabling structures.”

Case II: Continuous Independent and Continuous Dependent Variables

To illustrate a hypothesis with two continuous variables, consider the following: The greater the degree of

hindering bureaucratic structure in schools, the greater is the sense of faculty powerlessness. This hypothesis

describes the same relationship as the previous one; that is, the concepts are the same—bureaucratic

structure and powerlessness—but the statement clearly implies that both variables are continuous. Table 4.2

presents the diagram of this hypothesis. Compare Tables 4.2 and 4.3.

Table 4.2 Diagram of H.1

The two hypotheses (H.1 and H.1a) capture the same relation between x and y, and the unit of analysis is

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the same; however, the independent variable in H.1a is continuous and varies from low to high, and thus the

relation is specified differently. The null hypothesis is tested by a correlation coefficient and not an F or a t

test. Study the two hypotheses and their diagrams to make sure you understand the difference.

One thing should be clear—the way the independent and dependent variables are measured affects their

elaboration, the specification of their relation, and the null hypothesis and statistical test. Review Table 4.4,

which we developed in the previous chapter. You need to know the content to diagram the hypotheses that

are examined in this chapter in order to select the appropriate statistics. See Table 4.4 for a summary of the

nature of variables and the appropriate statistical test for each type.

Case III: Categorical Independent and Categorical Dependent Variables

Sometimes both the independent and the dependent variables are categorical. Such hypotheses are often

difficult to express because it means that you need to specify the relationships between every pair of cells in

the contingency table. Sociologists are most likely to develop and test hypotheses with categorical variables

because their data are often reported as frequencies, often frequencies of demographic data. Generally

speaking, it is wise to use continuous variables when you can because they are easier to write and talk about.

Table 4.3 Diagram of H.1a

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Table 4.4 Types of Variables and Appropriate Statistical Tests

In a simple relationship in which both variables are dichotomous, expressing the relation is not too difficult.

Consider the following hypothesis:

H.8: Being Republican as contrasted with Democrat in the U.S. Senate leads to a conservative

voting record on bills, whereas being Democrat leads to a liberal voting record.

Let's first sketch the contingency table (a 2 × 2 cross break) for the hypothesis:

Conservative Vote Liberal Vote

Republican

Democrat

What goes in each cell in the above contingency table? Frequencies—the number of people who were

Republican and voted conservative, the number of Democrats who voted conservative, the number of

Republicans who voted liberal, and the number of Democrats who voted liberal. If there is a relation between

the two variables, then we expect that there will be disproportionate frequencies in the cells as suggested by

the hypothesis.

Let's analyze and diagram the hypothesis (H.8). The independent variable is party affiliation—Republican

or Democrat. The dependent variable is voting record in terms of a conservative vote or liberal vote. Both

variables are categorical with two variations—hence the four cells in the contingency table. The relation is

specified because Republicans are more likely to vote conservative while Democrats are more likely to vote

liberal. The unit of analysis is clearly the individual; individual senators are the objects of the study. What kind

of statistical test is appropriate when both variables are categorical? A chi-square (χ2) is the appropriate test

for the null hypothesis. The analysis for this hypothesis is summarized in Table 4.5.

We have examined a simple case of two variables in which both were categorical with only two variations.

As we suggested earlier, it gets difficult to write the hypothesis when all the variables are categorical,

especially if the variables have more than two categories. Yet you will encounter such relationships in the

literature. In such cases, your statistical analysis will begin with some kind of chi-square test. Remember

that measurement of the variables directly affects the kind of statistical analysis needed to test the relations.

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Clearly, you don't have any control over how others conceptualize and measure their variables, but if you

are doing the research, try to design your measures so they are continuous, at least the dependent variable,

because it will simplify things and make your statistics more easily managed and often more powerful.

Table 4.5 Diagram of H.8

After you have studied Table 4.5, try diagramming the following hypothesis:

H.9: Rioters are more likely to be men, whereas nonrioters are more likely to be women.

How many variables are there in this hypothesis? What kind of variables are they? What are the implications

of the answers to these questions for testing the hypothesis? How likely is it that the hypothesis will be

supported? Why? Can you develop a theoretical rationale to support this hypothesis?

Case IV: Categorical Independent (With More Than Two Categories) and

Continuous Dependent Variables

The first case we examined was a hypothesis with a dichotomous independent variable and a continuous

dependent variable (Case I). Now we extend that case by specifying an independent categorical variable with

more than two categories and a continuous dependent variable. Consider the following hypothesis:

H.10: College students develop greater critical thinking skills in instructor-led discussion classes

than in student-led discussion classes, but students in student-led discussion classes will develop

greater critical thinking skills than those in instructor lecture classes.

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Using our hypothesis diagram as a guide, we ask what the independent and dependent variables are. The

dependent variable, the presumed effect variable (y), is critical thinking skill. Critical thinking is predicted

to be greater or lesser dependent on the type of classroom instruction; thus, type of classroom discussion

is the presumed causal variable (x), the independent variable. The fact that the hypothesis states that the

dependent variable (critical thinking skill) will be “greater” under different conditions of teaching suggests

that the dependent variable is continuous; that is, its numerical value varies along a continuum from low to

high. The independent variable is a categorical variable with three variations. We elaborate and summarize

the variables a little more. The independent variable, classroom instruction, is defined and measured by

three kinds of classroom instruction: teacher-led discussion, student-led discussion, and teacher lecture. The

dependent variable of critical thinking skill varies in degree along a continuum from low to high: The higher

the value, the greater is the critical thinking skill.

Next, we turn to the relationship—its specification, the unit of analysis, the null hypothesis, and the statistical

analysis. How do we specify this relation? The key here is to make sure you understand the relation and

specify it in a shorthand way. Let's use the following symbols: CT = critical thinking skill, ID = instructor-led

discussion, SD = student-led discussion, and IL = instructor lecture. What does the hypothesis predict? First,

the hypothesis predicts a significant difference among critical thinking in the three groups, but more than that,

it specifies where the differences rest. For critical thinking skills (CT), ID > SD and SD > IL (or ID > SD > IL).

Finally, we turn to the null hypothesis, which states that there is no relationship between type of classroom

instruction and critical thinking; that is, CT mean of ID = CT mean of SD = CT mean of IL. The statistical

test of the null is an ANOVA because the independent variable is categorical and the dependent variable is

continuous (review Table 4.2). The F ratio will tell us whether the results are due to chance or not. If the F

ratio is significant, then we will have to use special t tests (e.g., Scheffé or Bonferroni test) for the pairs of

means to see which groups are significantly different. The hypothesis analysis is summarized in Table 4.6.

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Table 4.6 Diagram of H.10

Case V: Hypotheses with More than Two Variables

Thus far in our analyses, we have been concerned with bivariate analyses—one independent and one

dependent variable. We now turn to hypotheses with more than two variables. We will assess three kinds

of hypotheses in this case: (1) compound hypotheses, (2) contingent hypotheses, and (3) hypotheses with

multiple independent variables predicting one dependent variable. Some researchers call the latter type of

hypothesis multivariate, but technically, multivariate analysis has both multiple independent and dependent

variables. Suffice it to say that we will not go beyond multiple independent variables in this research primer.

Compound hypotheses. For lack of a better term, compound hypotheses are multiple, bivariate hypotheses

that are combined into a single statement. Sometimes, the researcher will take a set of bivariate relations

and combine them into one hypothesis, which can mislead the beginning student. Consider the following

hypothesis:

H.11: Relations-oriented leaders have more loyal, committed, and satisfied subordinates than do

task-oriented leaders.

If you are not careful, you can be misled by such hypotheses. As you begin your analysis, you should quickly

find the problem. What is the independent variable? Leadership style is the independent variable, which has

two variations: (1) relations oriented and (2) task oriented. What is the dependent variable? At this point,

you should begin to see the problem—there are three dependent variables in this hypothesis that have been

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combined in one relation. To analyze the hypothesis, it is best to separate the compound hypothesis into its

three component relations:

H.11a: Relations-oriented leaders have more loyal subordinates than do task-oriented leaders.

H.11b: Relations-oriented leaders have more committed subordinates than do task-oriented

leaders.

H.11c: Relations-oriented leaders have more satisfied subordinates than do task-oriented

leaders.

Now the analysis is simple: There are actually three hypotheses, each with an independent categorical

variable and a dependent continuous variable. Analyze one, and the pattern is the same for the rest.

Contingent hypotheses. Occasionally, the researcher will find or predict a relationship that is contingent or

dependent on another variable, a contingent hypothesis. Such hypotheses are more complicated, but they

are also more interesting and reveal the complexity of the relation. A moderator variable (z) changes the

relationship between two variables, x and y, as it changes. It is easiest to understand a moderator variable

when it is categorical, but theoretically, moderator variables can be continuous or categorical. Examine the

following hypothesis:

H.12: When the leader has influence with superiors, task-oriented leaders have more loyal

subordinates than do relations-oriented leaders, but when the leader has no influence with

superiors, then relations-oriented leaders have more loyal subordinates than do task-oriented

ones.

As you read this hypothesis, you should sense immediately that this is more complicated than most bivariate

hypotheses. How many variables are there in this hypothesis? The answer is three—influence with superiors,

loyalty, and leadership style. What are the independent and dependent variables? The independent variable

is leadership style, which is categorical with two variations—task and relations oriented. The dependent

variable is loyalty, which is a continuous variable ranging from low to high loyalty; the higher the numerical

value, the greater is the loyalty. What about influence with superiors? You guessed it—influence is a

moderator variable because it changes the relation between leadership style and loyalty; that is, the relation

is contingent on the influence with superiors. Moderator variables change the relation between x and y. This

hypothesis predicts that the relation between x and y will differ depending on the value of z. The hypothesis

says that when we have one condition of z, we have one relation between x and y, but when we have another

condition of z, we have a different relation between x and y.

Let's analyze and diagram this contingent hypothesis. We have already defined the independent, dependent,

and moderator variables. The independent variable and moderator variables are categorical variables, each

with two variations. The dependent variable is a continuous variable. Now we need to specify the relations.

When the leader has influence (I), then task-oriented leaders (TO) have more loyal (L) subordinates than do

relations-oriented leaders (RO), but when the leader has no influence (NI), then relations-oriented leaders

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(RO) have more loyal subordinates than do task-oriented leaders (TO).

The unit of analysis is a little trickier. You might think that the unit of analysis is the individual because we

are talking about leaders and followers. But each leader is the leader of the group, and it is the loyalty of that

group that we will be analyzing, and so the group is the unit of analysis. The null hypothesis is that there is

no difference between the groups regardless of the value of the moderator. The statistical test here is a more

complex ANOVA, which we have not explained but which is conceptually the same idea. We summarize our

analysis in Table 4.7.

Here is another hypothesis; you analyze and diagram it.

H.13: Principals who are task oriented are more effective than principals who are relations

oriented when school conditions are chaotic, but when conditions are moderately favorable, then

relations-oriented principals are more effective; however, when conditions are very favorable,

principals who are task oriented are more effective than those who are relations oriented.

Hypotheses With Multiple Independent Variables. Sometimes researchers are interested in a set of

independent variables as they relate to a single dependent variable. Suppose that the researcher is interested

in predicting student achievement. Instead of only examining one independent variable, here the researcher

may choose a set of independent variables to find the combined effect on the dependent variable, student

achievement. Let's select a set of variables that might be relevant. The socioeconomic status (SES) of

parents seems important because, in general, we expect that parents of higher SES spend more time helping

their children with schoolwork, provide them with more resources, and are more supportive of academic

pursuits. A second variable that seems likely to predict achievement is intelligence as measured by IQ.

The motivation level of students also seems a reasonable predictor of achievement. Thus, the following

hypothesis can be made:

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Table 4.7 Diagram of H.12

H.14: SES of parents, and intelligence and motivation of students combine to increase the level

of student achievement.

This hypothesis has three independent variables—SES, intelligence, and motivation—and one dependent

variable, student achievement. Without further comment, the hypothesis is analyzed in Table 4.8. Study the

diagram to make sure you understand the analysis.

Note that all the variables are continuous. The statistic we are computing is a multiple coefficient of

correlation, which tells us if the linear combination of the three independent variables has a significant

influence on the dependent variable, student achievement. Although the hypothesis does not predict it, the

regression analysis will also tell us if each of the independent variables is related to the dependent, holding

constant all the other independent variables; the regression coefficient for each variable can be tested for

significance by the appropriate t test.

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Table 4.8 Diagram of H.14

The Invisible Condition: “Other Things Being Equal“

Charters (1992) makes the important point that although most hypotheses don't state the condition, a basic

assumption made in the statement of any hypothesis is that “other things are equal.” In fact, he suggests

that beginning researchers ought to add to their hypotheses the condition cet. parib., which is Latin for “other

things being equal.” The phrase other things refers to other relevant things. It is good to consider other

variables that may be important to your hypotheses. If the researcher is aware of other variables that may

be related to the dependent variable, it behooves the researcher to control for their influence. Such variables

are called control variables; they are variables believed to be related to the dependent variable, and if not

attended to and “controlled,” they might be mistaken for the effect of the independent variable. For example,

SES is a strong causal variable of student achievement, and so any study with student achievement as the

dependent variable should control for SES either statistically or in the research design. If a researcher finds

that any organizational property of a school is related to student achievement, he or she must make sure

that SES has been “controlled for.” Otherwise, the researcher may mistakenly conclude that the variable

affects school achievement when in reality the relation is spurious because it is the SES that is producing the

significant relation, not the independent variable.

Summary

The purpose of this chapter was to examine the nature and meaning of hypotheses; the following propositions

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summarize the major ideas:

• A hypothesis is a conjectural statement that suggests the relationship between two or more variables.

• A good hypothesis is declarative, clear, has at least two variables, and must be amenable to testing.

• A substantive hypothesis is a declarative statement that describes the relation between the

concepts—it is theoretical. Strong substantive hypotheses evolve from sound theory and are explicit

in predicting the direction of the relation.

• Substantive hypotheses, however, must be transformed into statistical hypotheses to be tested.

• There are two kinds of statistical hypotheses: the null and the alternative.

• A null hypothesis is a statement that indicates that there is no relation between the measures of

the variable, whereas the alternative hypothesis specifies the relation between the measures of the

variables.

• Simply put, the idea is to reject the null and accept the directed alternative hypothesis.

• There are many declarative statements that masquerade as hypotheses, but in reality they are often

imposters, tautologies, or misconceived, incomplete, or untestable relations.

• We have proposed a scheme for diagramming and critiquing hypotheses that ferrets out the

imposters. The diagramming scheme has six steps:

Identify the independent, dependent, and moderating variables.

Determine the nature of each variable (categorical or continuous).

Elaborate each variable (What does the number mean?).

Specify the relation.

Decide on the unit of analysis.

Determine the appropriate statistical test for the null.

Check Your Understanding

Below are a series of hypotheses. Carefully analyze and diagram each one.

H.1: Teachers who are not people oriented are more likely to leave teaching than are those who

are people oriented, whereas teachers who are people oriented are more likely to stay than are

those who are not people oriented.

H.2: People-oriented teachers have a higher rate of termination from teaching than do non-

people-oriented teachers.

H.3: Task-oriented leaders are more effective than relations-oriented leaders when the group is

cohesive, but relations-oriented leaders are more effective than task-oriented leaders when the

group is noncohesive.

H.4: The more open a supervisor is to a teacher, the more open the teacher is to his or her

students.

H.5: The greater a parent's sense of powerlessness in school affairs, the stronger is the parent's

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opposition to the school-district budget referenda.

H.6: Organic school bureaucracies have more open organizational climates than do enabling

ones, but enabling bureaucracies are more open in climate than are mechanistic ones, and

mechanistic bureaucracies are more open in climate than are autocratic ones.

H.7: Democratic supervisors have teachers who demonstrate more creativity and enthusiasm in

teaching than do those teachers who have autocratic supervisors.

H.8: The greater the size of a community college's instructional faculty, the greater the degree of

centralization in their decision making.

H.9: Principals are more humanistic in their pupil control orientation than are their faculties.

H.10: The greater the academic optimism of a school's culture, the higher is the level of student

achievement of the school.

H.11: Schools with high levels of trust in parents have higher school achievement levels than do

schools with low levels of trust in parents.

H.12: In urban schools, custodial pupil control is positively related to student achievement, but in

suburban schools, custodial pupil control is negatively related to student achievement.

H.13: Teachers who have high academic optimism have higher levels of classroom student

achievement than do teachers with low academic optimism.

H.14: In urban schools, task-oriented teachers are more effective than relations-oriented

teachers, but in suburban schools, relations-oriented teachers are more effective than task-

oriented teachers.

H.15: The more diversity on the board of education, the more comprehensive is the curriculum of

the school district.

H.16: Democratic senators are more likely to vote liberal, whereas Republican senators are more

likely to vote conservative.

Key Terms

Alternative hypothesis (p. 70)

Compound hypothesis (p. 84)

Contingent hypothesis (p. 84)

Control variable (p. 88)

Elaboration of variables (p. 75)

Enabling structure (p. 68)

Good hypothesis (p. 67)

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Null hypothesis (p. 67)

Specification of the hypothesis (p. 75)

Statistical hypothesis (p. 67)

Tautologies (p. 72)

Theoretical hypothesis (p. 67)

http://dx.doi.org/10.4135/9781452272061.n4

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http://dx.doi.org/10.4135/9781452272061.n4

Analyzing the Structure and Substance of Hypotheses

In: Quantitative Research in Education: A Primer