Hypotheses

EDUR 7130
Educational Research On-Line

Hypotheses

A hypothesis is, very simply, a guess one makes about what will happen. For example, if one were asked to predict which students would obtain higher achievement scores on a test, a group who used cooperative learning or a group who received lecture-only, most would guess--hypothesize--that the cooperative learning group would obtain the higher achievement scores.

In most research situations, a hypothesis represents an educated, an informed, guess. Often the hypothesis is based on theory or logic; sometimes it is based on prior experience or data. When formulating a hypothesis, there are characteristics that will make it reasonable and acceptable to most readers.

Characteristics of Hypotheses

Consistent with previous research: Hypotheses that contradict previous research, especially a large body of research, must have sound reasoning in order for it to be acceptable by the reader. For example, it would seem odd, using the example above, to hypothesize that the lecture group would have higher achievement scores given that much of the research on cooperative learning supports the notion that cooperative learning results in better student achievement.
Clearly and concisely stated: No need to elaborate on this.
Testable: To be testable means that the hypothesis can be addressed by collecting and analyzing data; that is, data can be used to determine whether the hypothesis is or is not supported. If one's hypothesis cannot be addressed by collecting data, then it is not testable.
Variables: Like problem statements, the important variables to be studied should be presented in the hypotheses.
Relationships: Also similar to problem statements, relationships among the variables studied should be clear--that is, one should be able to identify which are the independent and dependent variables in the hypothesis.

Placement: Normally it is best to introduce the reader to the logic and history of the problem to be studied before introducing the hypotheses, so this suggests that hypotheses should come after the literature review and just prior to the methods section.

Type of Hypotheses

Hypotheses may be either directional, non-directional, or null. The specific wording of the hypothesis will depend upon whether the independent variable in question is qualitative or quantitative. In general, if the independent variable is qualitative, the hypothesis refers to group differences. For example, there will be differences between boys and girls in reading achievement. If the independent variable is quantitative, the hypothesis is written in the format of relationships among variables rather than group differences. For example, reading achievement is related to verbal recall ability. Specific differences among directional, non-directional, and null hypotheses are presented below, but first it is necessary to explain the types of relationships one may find among quantitative variables.

When one wishes to express the nature of the relationship between two quantitative variables, there several possible variations on types of relationships. In most cases, at least in education and the social sciences, relationships among quantitative variables will follow either a positive, negative (inverse), or no relationship pattern. Others are possible (e.g., non-linear relationships).

A positive relationship exists when two variables covary together in a similar manner; that is, when increases in one variable are associated with increases in another variable. So, in simpler terms, when one variable goes up , the other variable also goes up . For example, people with high levels of intelligence are expected to have higher grades in school; those with higher levels of motivation complete more work; the more publications a professor has in a given year, the higher the merit pay for that year.

A negative relationship represents two variables that covary in opposite directions. Thus, when one variable increases , the other variable decreases . A negative relationship is also referred to as an inverse relationship. Two examples of inverse relationships are: the greater one's belief in one's ability to learn, the lower one's anxiety about a course; the more associated one feels with school, the less likely one will drop out of school.

Below is a matrix that identifies the type of hypothesis by the type of independent variable. More detailed descriptions of each type follow the matrix.

Matrix of Hypotheses
(Assuming the dependent variable is quantitative.)

Type of Hypothesis	Type of Independent Variable
	Qualitative (Categorical)	Quantitative (Continuous)
Directional	Group differences exist; one group expected to perform better than the other group(s). Example: Group A will do better than group B.	Either a positive or negative relationship will exist. Example: Higher scores on A are associated with higher scores on B. Example: Higher scores on A are associated with lower scores on B.
Non-directional	Group differences exist, but it is not clear which group will do better. Example: There will be a difference between groups A and B.	Relationship will exist, but it is not clear if it will be positive or negative. Example: Variable A is associated with variable B.
Null	No difference expected; groups will do the same. Example: There is no difference between groups A and B.	No relationship expected. Example: Variable A is not associated with variable B.

A directional hypothesis indicates that one expects a group to over- or under-perform relative to other groups, or for there to be a positive or negative relationship among variables. To know when to refer to group differences or relationships among variables, it is necessary to know whether the independent variable is qualitative or quantitative. As noted above, if the independent variable is qualitative, the hypothesis is written in a manner that indicates one group's superior (or inferior) performance. If the independent variable is quantitative, reference in the hypothesis is to positive or negative relationships among variables.

To illustrate a directional hypothesis, the following indicates that one group will perform better in achievement that another. Note that the independent variable is qualitative.

Directional Hypothesis 1: Students exposed to cooperative learning will score higher on an achievement test that students exposed to lecture.

The following directional hypothesis indicates a positive relationship among the variables. Note that the independent variable is qualitative.

Directional Hypothesis 2: Students with higher levels of intelligence will score higher on tests designed to measure mental abilities. (The higher the intelligence, the better the test score.)

The following directional hypothesis indicates a negative relationship among the variables. Note that the independent variable is quantitative.

Directional Hypothesis 3: Students with higher levels of test anxiety will score lower on an achievement test. (So, as anxiety increases, performance decreases.)

For qualitative independent variables, a non-directional hypothesis indicates that groups will differ, but does not specify which groups will be superior or inferior. For quantitative independent variables, the non-directional hypothesis simply indicates that a relationship exists, but does not specifies the nature (positive or negative) of the relationship.

Non-directional Hypothesis 1: There will be a difference in achievement between students exposed to cooperative learning and students exposed to lecture.

Note that for non-directional hypotheses with qualitative independent variables, it is important to specify that one expects a difference among the groups. This manner of writing non-directional hypotheses with qualitative independent variables is preferred over simply stating that the variables are related. But for non-directional hypotheses with quantitative independent variables, indicating that an association or relationship is expected is acceptable, as illustrated below.

Non-Directional Hypothesis 2: There is a relationship between a student's level of intelligence and his or her score on a test designed to measure mental abilities.

For null hypotheses, one simply indicates that there will be no difference (for qualitative independent variables) or that no relationship exists (for quantitative independent variables).

Null Hypothesis 1: There will be a no difference in achievement between students exposed to cooperative learning and students exposed to lecture.

Null Hypothesis 2: The is no relationship between a student's level of intelligence and his or her score on a test designed to measure mental abilities.

Sometimes one may read of a research hypothesis. A research hypothesis is nothing more than one the researcher expects to find in his or her study. Also, one may occasionally see reference to a statistical hypothesis. A statistical hypothesis is simply a null hypothesis.

Practice Exercise

For each of the following hypotheses, determine the following:

the independent (IV) and dependent (DV) variables;
indicate if IV is qualitative or quantitative, and if qualitative, indicate the categories of the IV;
whether the hypothesis is directional, non-directional, or null;
and for directional hypotheses, specify which group is expected to do better or whether a positive or negative relationship is expected.

Illustrated Example 1:

Hypothesis: Students who enter educational research with prior research experience will demonstrate greater achievement than students who enter educational research without research experience.

IV is research experience, DV is achievement (the DV is not greater achievement)
IV is qualitative since there are two groups, and the two groups are (1) those with research experience and (2) those without research experience
hypothesis is directional (specifies that one group will do better than the other group—those with research experience will do better)
IV has categories (i.e., groups), and those with research experience are expected to have greater achievement.

Illustrated Example 2:

Hypothesis: The more a student studies, the better that student will do on achievement tests.

IV is amount of studying, DV is performance on achievement tests
IV is quantitative (amount of studying can be ranked from more to less)
hypothesis is directional
positive relationship is expected--as studying increases, so does achievement

Practice Hypotheses: Identify each component for the hypotheses that follow. Answers are provided below.

Children taught by the vocabulary method will learn more than children taught by the experimental method.

The greater one's retention ability, the more one’s learning from related prose will increase.

Given equal prior learning, corrective and non-corrective instruction are likely to produce different levels of achievement among fourth-grade students.

Programs offering stipends will be just as successful at retaining students as programs not offering stipends.

In a middle-class, suburban, public school district in which a child is expected to meet the standards of a set curriculum, a child who is under five years of age upon entrance to kindergarten is less likely to be ready for first grade in one year than a child who is five years of age or more at the time of entrance to kindergarten.

Fourth grade students who participate in computer assisted instruction (CAI) will have higher mathematics achievement scores than fourth grade students who do not participate in CAI.

Teachers who establish rapport with their students will be more effective in motivating students to study than teachers who do not establish rapport with their students.

Students with higher SAT scores will also have higher GRE scores; similarly, students with lower SAT scores will have lower GRE scores.

Under intangible reinforcement conditions, middle-class children will learn more than lower-class children.

The average achievement group and the low achievement group will show the same level in ratings of self-worth.

Classroom intellectual composition was expected to directly influence students’ academic achievement; the higher the classroom intellectual composition, the greater the academic achievement.

There will be no difference in mathematics achievement between the computer and tutor group, the computer-only group, and the traditional instruction group.

Students’ confidence in their academic ability and their intelligence are both related to achievement.

Test-taking experience affects test performance.

Students who receive individually guided instruction will demonstrate greater gains in reading achievement than students who receive group based instruction.

Students exposed to the read, visualize, and draw condition are expected to comprehend more of the biology text than are students in the read and visualize condition or the read only condition.

Science achievement is independent of academic self-efficacy.

Perceptions of the characteristics of the "good" or effective teacher are in part determined by the perceiver’s attitudes toward education.

Academic performance in school is related to dropping out of school.

Perceived autonomy in the classroom predicts student evaluations of instruction. (Note: Perceived autonomy is measured by several responses to Likert scaled items. Reposes to each item range from 1 "strongly disagree" to 5 "strongly agree.")

Practice Exercise Answers

1. Children taught by the vocabulary method will learn more than children taught by the experimental method.

IV is method of instruction, DV is amount learned

qualitative, categories are vocabulary and experimental

directional

vocabulary learns more

2. The greater one's retention ability, the more one’s learning from related prose will increase.

IV is retention ability, DV is amount learned
IV is quantitative (retention ability ranges from high to low, so it is quantitative)
direction
positive relationship

3. Given equal prior learning, corrective and non-corrective instruction are likely to produce different levels of achievement among fourth-grade students.

IV is type of instruction, DV is achievement (note, prior learning and fourth-graders are not variables, they do not vary since everyone referred to in the hypothesis has prior learning and is a fourth grader, therefore these two are constants)
qualitative, categories are corrective and non-corrective
non-directional
not applicable (n/a)

4. Programs offering stipends will be just as successful at retaining students as programs not offering stipends.

IV is whether stipends are offered, DV is retention of students
qualitative, stipends offered vs. not offered
null -- no difference in retention between the two types of programs
n/a

5. In a middle-class, suburban, public school district in which a child is expected to meet the standards of a set curriculum, a child who is under five years of age upon entrance to kindergarten is less likely to be ready for first grade in one year than a child who is five years of age or more at the time of entrance to kindergarten.

IV age of child, DV is readiness for first grade
qualitative, two categories, under 5 vs. 5 or over (if you argue that age is quantitative you are technically correct since these categories can be ranked, but since there are only two categories, I treat age as a qualitative variable)
directional
5 or over more ready

6. Fourth grade students who participate in computer assisted instruction (CAI) will have higher mathematics achievement scores than fourth grade students who do not participate in CAI.

IV is participation in CAI, DV is mathematics achievement (fourth grade and student are not variables, they are constants)
qualitative, two categories, use CAI and not use CAI
directional
those who use CAI have higher scores

7. Teachers who establish rapport with their students will be more effective in motivating students to study than teachers who do not establish rapport with their students.

IV is establishment of rapport, DV is motivation to study
qualitative, two categories, those who establish rapport and those who do not
directional
teachers who establish rapport better at motivating students

8. Students with higher SAT scores will also have higher GRE scores; similarly, students with lower SAT scores will have lower GRE scores.

IV is SAT, DV is GRE (if you are not familiar with SAT and GRE, then you will not be able to identify which is IV and DV; usually SAT is a test taken in high school, GRE is taken in college, therefore SAT precedes GRE in chronological order)
IV is quantitative, scores from SAT can be ranked from high to low
directional
positive relationship; as scores from SAT increase, so too do scores from GRE

9. Under intangible reinforcement conditions, middle-class children will learn more than lower-class children.

IV is class status, DV is learning (intangible reinforcement conditions is a constant, all of these children are under this situation; children are not a variable since all participants in the hypothesis are children)
qualitative, categories are middle and lower (if you thought this was a quantitative variable, you would also be correct since class status can be ranked, but I identify it as qualitative since there are only two categories)
directional
middle-class learn more

10. The average achievement group and the low achievement group will show the same level in ratings of self-worth.

IV is achievement group, DV is self-worth
qualitative, categories are average and low (if you thought this was a quantitative variable, you would also be correct since average level and low level can be ranked, but I identify it as qualitative since there are only two categories)
null
n/a

11. Classroom intellectual composition was expected to directly influence students’ academic achievement; the higher the classroom intellectual composition, the greater the academic achievement.

IV is intellectual composition, DV academic achievement
quantitative, intellectual composition varies and can be ranked (note, the higher--er--signifies comparative form of the word and therefore represents degrees of quality or amount, hence intellectual composition varies by degree so is quantitative)
directional
positive, the great intellectual composition, the greater the learning

12. There will be no difference in mathematics achievement between the computer and tutor group, the computer-only group, and the traditional instruction group.

IV is type of instruction (group), DV is mathematics achievement
qualitative, categories are tutor, computer-only, and traditional instruction
null
n/a

13. Students’ confidence in their academic ability, and their intelligence, are both related to achievement.

IVs are confidence in academic ability, and intelligence, DV is achievement
both confidence and intelligence are quantitative (most likely), since they both vary by degree (can be ranked from high to low)
non-directional, no specific positive or negative relationship identified
n/a

14. Test-taking experience affects test performance.

IV is experience, DV is performance
quantitative, experience can be ranked from more to less
non-directional, the exact relationship is not specified
n/a

15. Students who receive individually guided instruction will demonstrate greater gains in reading achievement than students who receive group based instruction.

IV type of instruction, DV reading achievement
qualitative, guided and group
directional
guided will do better in reading

16. Students exposed to the read, visualize, and draw condition are expected to comprehend more of the biology text than are students in the read and visualize condition or the read only condition.

IV is type of condition, DV is comprehension
qualitative, with three categories, (a) read, visualize, and draw, (b) read and visualize, and (c) read
directional
those using read, visualize, and draw comprehend more

17. Science achievement is independent of academic self-efficacy.

IV academic self-efficacy, DV is science achievement; this one may be confusing for some. One way to identify the IV and DV is to read the hypothesis again, but to change the word INdependent to DEPENDENT, so: "Science achievement is dependent upon academic self-efficacy." In this sentence it should be clear that achievement is dependent on self-efficacy. Whenever it is stated that variable A is independent of variable B, then variable A is the dependent variable.
quantitative, self-efficacy may be ranked from high to low
null, stating that one variable is independent of another indicates no relationship between the two
n/a

18. One's perceptions of an effective teacher are in part determined by the perceiver’s attitudes toward education.

IV is attitude, DV is perception
difficult to determine whether attitude is qualitative or quantitative without more information about how this variable was defined and measured
non-directional
n/a

19. Academic performance in school is related to dropping out of school.

IV is academic performance, DV is dropping out
quantitative
non-directional
n/a

20. Perceived autonomy in the classroom predicts student evaluations of instruction.(Note. Perceived autonomy is measured by several responses to Likert scaled items. Reposes to each item range from 1 "strongly disagree" to 5 "strongly agree.")

IV is perceived autonomy, DV is student ratings of instruction
quantitative
non-directional
n/a