KPOLOVIE Hypothesis Postulation

Journal of Education in Developing Areas (JEDA) Vol. 19, No. 1.

HYPOTHESIS POSTULATION: THE WHAT, WHY, HOW AND WHICH?

By

Dr. Peter James Kpolovie

Department of Psychology, Guidance and Counselling, Faculty of Education,

University of Port Harcourt

Abstract

The great need for refocusing of education in Nigeria in this century and beyond can best be met with execution of more and more quantitative empirical research. Execution of such research demands postulation and testing of apposite hypotheses. Unfortunately however, it doubtlessly seems that many educational practitioners and researchers have lost or are loosing focus on the enormous role of hypothesis in education and knowledge advancement. Therefore, this paper has thoroughly presented the meaning, the eight uses, the five characteristics and the two types as well as the two forms of hypothesis in addition to the seven steps for testing it. When educational researchers and practitioners acquire and apply the mastery knowledge of hypothesis as lucidly elucidated in this article, the quality of their research works will be tremendously improved and this will absolutely be reflected in refocusing of education in Nigeria.

March , 2011 JOURNAL OF EDUCATION IN DEVELOPING AREAS (JEDA) VOL.19 (1).

w w w . j e d a - u n i p o r t . c o m

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Introduction

There is a great need to refocus education in Nigeria. Refocusing education in

Nigeria in the 21st century can best be accomplished with execution of more and

more quantitative empirical research. “Research can satisfactorily be defined as the

logical, systematic and objective collection, analysis, synthesis, evaluation and

recording of accurate and controlled observations for the development of

generalizations, principles or theories that are ultimately aimed at description,

explanation, prediction and control of natural phenomena to meet specific needs of

man” Kpolovie (2010, 3). Execution of research necessarily demands postulation and

testing of apposite hypotheses. Unfortunately however, a critical examination of

educational journal articles tends to show that great majority of the articles are not

based on empirical works that duly tested appropriate hypotheses. The number of

position papers (several of which do not truly qualify for any scholarly position)

tends to far outweigh well researched articles that formulated and tested the right

hypotheses on the basis of relevant data collection and analyses. For instance,

several of the position papers utterly fail to meet the basic requirements for “review

articles”, “theoretical articles”, “methodological articles” or “case studies” as specified

in the publication manual of the American Psychological Association (American

Psychological Association, 2002, 7–9).

Furthermore, some of the position papers do not even set forth “a set of

principles, a description of policy, or (workable) recommendations for action on a

specific issue” which is a compulsory requirement as defined in the New

International Webster’s Comprehensive Dictionary of the English Language, Read

(2004, 985). Even some of the articles that claim to report empirical studies

demonstrate that substandard hypotheses were formulated as they do not meet the

fundamental requirements for international best practices. For instance, a statement

that contains only one variable, or a proposition which cannot serve the various

uses of hypothesis or a postulation that does not contain the characteristics of

hypothesis as thoroughly articulated in this paper; cannot and should never be

scholarly considered as a hypothesis. It doubtlessly seems that many educational

practitioners and researchers have lost or are losing focus on the enormous role of

hypothesis in education and knowledge advancement. In order to refocus education

in Nigeria in the current century and beyond through empirical research, this article

has proffered and lucidly elucidated answers to the ever fresh important questions of

‘what, why, how and which?’ about hypothesis. In other words, in this paper, the

meaning, uses, characteristics and types of hypothesis as well as the steps for

testing it are thoroughly rationalized.



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Definition

The definition here deals with ‘What?’ about hypothesis. Hypothesis is a tentative

proposition about the nature and workability of a phenomenon in terms of

independent and dependent variables, and which is subject to refutation or rejection

by empirical evidence via statistical testing and criticism by rational argument. It

can also be seen as a tentative solution to the research problem or answer to the

research question, and which its tenability or otherwise is to be tested statistically

after due collection and analyses of requisite data for the investigation. Simply put,

hypothesis is a rational guess about the relationship between two variables or

among more than two variables in a given population in order to arrive at empirical

solution to the problem under investigation on the basis of testing its tenability

statistically. In the words of Jackson (2006, 8), hypothesis is “a prediction regarding

the outcome of a study, often involving the relationship between two variables.”

Hypothesis is formulated to adequately cover the research problem under study;

such that valid, reliable and dependable solutions to the problem can be attained

after due subjection of data collected to the appropriate statistical tests. This

accounts for why problem identification and hypothesis formulation constitute the

first step in the scientific approach to knowledge acquisition. That is, no

researchable problem can conclusively be said to have been identified without

postulation of the apposite hypotheses in the scientific quest for knowledge

discovery (Kpolovie, 2010; Best and Kahn, 2007; Cohen, Manion and Morrison,

2008; Banyard and Grayson, 2000; Fraenkel and Wallen, 2003 and Kpolovie, 2011).

Formulation of hypotheses that attempt to explain and predict relationships

amongst variables of interest, and actually testing their authenticity statistically on

the basis of adequate randomly collected data, is a very crucial aspect in every

empirical research. In fact, hypothesis testing is the central theme in most research

works in education and the behavioural sciences as it is in the pure sciences.

Hypothesis testing is so crucial in research because it is the systematic procedure

for deciding whether the results of a research, which investigates a randomly drawn

sample, support a particular theory or practical innovation in the entire population.

In research, data on the variables of interest are collected mainly from a

representative sample of the population. Data in research are not just collected for

their own sake. Hypothesis testing is the most important reason for which data are

collected in research. This accounts for the indispensability of hypothesis testing in

research, as data obtained from a representative sample must be subjected to

statistical hypothesis testing, for accurate, valid and reliable generalizations to be

made to the population (Kpolovie, 2011; Howitt and Cramer, 2008; Babbie, 2007;

Graziano and Raulin, 2007 and Koul, 2009). Ary, Jacobs and Razavieh (2002, 97)

have therefore posited that:

The hypothesis is a powerful tool in scientific inquiry. It enables

researchers to relate theory to observation and observation to



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theory. Today the use of hypothesis enables people, in the

search for knowledge, to employ both the ideas of the inductive

philosophers, with their emphasis on observation, and the logic

of the deductive philosophers, with their emphasis on reason.

The use of hypotheses has united experience and reason to

produce a powerful tool for seeking knowledge.

Uses of Hypothesis in Research

Specifying the necessity of good hypothesis in research, Howell (2002, 96) posited

that: “We do not go around obtaining sampling distributions, either mathematically

or empirically, simply because they are interesting to look at. We have important

reasons for doing so. The usual reason is that we want to test some hypothesis.”

Stressing the indispensability of hypothesis in research and statistical analysis,

Kpolovie (2011, 38) averred that: “Hypothesis formulation as well as testing is so

central and crucial in the making of conclusive conclusions, inferences and

generalizations from the sample studied to the population to the extent that an

empirical research cannot be considered to have been well executed without

hypothesis”. He rationalized that hypothesis is used in research for the following

eight major reasons which serve as the ‘Why?’ of hypothesis postulation.

i. Proposition of relationship between two variables

Scientific investigation deals with at least one independent variable and one

dependent variable. The nature of the relationship that exists between the

independent and dependent variables is tentatively proposed with hypothesis. The

most accurate prediction and explanation of the phenomenon of interest in a

research is succinctly expressed by the researcher from the beginning of the study

with hypothesis. In other words, hypothesis provides the best tentative solution to

the problem under investigation. At the end of data collection and analysis, the

tenability of the hypothesis is determined. Thus, with the use of hypothesis, the

researcher is able to bring together information for making tentative rational

statement about the relationship that exists between the dependent and

independent variables in such a way that allows for rejection or otherwise on the

basis of unbiased data collected and analyzed at the end of the investigation.

ii. Hypothesis provides direction to research

An excellently formulated hypothesis provides a direction on the type of data to be

collected, the population and sample to be studied, the research design to apply and

the method of data analysis that is most suitable for the study. On the basis of the

postulated hypothesis, the investigator becomes certain of whether to collect

nominal, ordinal, interval or ratio data for the study. The population to which

findings of the research are to be appropriately generalized, is specified in the

hypothesis. Decision on or choice of the most suitable research design for an

investigation can best be made on the basis of the hypothesis that guides the work.



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Whether the hypothesis is stated in terms of ‘difference’ or ‘relationship’ is a clue to

the type of research design that could possibly be applied. The appropriate

statistical test for data analysis in a research depends on the way that hypothesis

for the study is formulated. It is with the hypothesis that the scope of an

investigation is best known, as it prevents the work from being too broad by

restricting it to only the variables under investigation and the population from which

the sample was randomly drawn.

iii. Hypothesis conveys empirically testable rational statement

Hypothesis is an embodiment of a rational proposition or statement that is directly

testable by the researcher on the basis of empirical data and statistical inference.

Hypothesis is the only type of statement in research that automatically calls for

collection and analysis of relevant data for the testing of its authenticity. The title of

a study, purpose of the study, literature review, research question, significance of

the study, and so on, do not lend themselves individually or collectively to statistical

tests on the basis of data collected for tenability. It is the hypothesis alone that is

testable to ascertain the degree or extent to which the occurrence of the

phenomenon under study in the population is not merely by chance. While testing a

hypothesis provides answer to the corresponding research question and meets the

purpose of the investigation; answering a research question alone cannot serve as

hypothesis testing and therefore can never meet the purpose of the study that calls

for determination of characteristics of a phenomenon in the entire population from

the sample characteristics. The fact remains that for the purpose of a research work

that studies sample, randomly drawn from the population to be met, hypothesis

must be tested.

iv. Hypothesis determines the quality of a research

Hypothesis is the main determinant of the quality of a research because the

findings, conclusions and generalizations of a research cannot be more or better

than what was proposed in the hypothesis. A work with poorly stated hypothesis is

bound to produce correspondingly poor, unauthentic, invalid and ungeneralizable

results. For instance, if an amateur researcher states hypothesis that is not testable

in an investigation, then certainly, the work cannot produce valid or tenable result.

Furthermore, a work with wrongly stated hypothesis that does not contain any or

one of the variables under investigation, or does not propose a relationship between

the two variables, cannot in any way yield result that conclusively states that there

is a relationship between the independent and dependent variables in the population

at a given level of significance or certainty from the sample studied. This accounts

for why well-informed academic project, thesis or dissertation supervisors, external

examiners, or research assessors can on the basis of excellently postulated

hypotheses conclude rightly that the researcher has sufficient knowledge in the area

or field that the investigation is embarked upon.



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v. Hypothesis embodies the essence of research

The essence of research in the discovery of knowledge is encapsulated in hypothesis.

It is the hypothesis that shows that research is not concerned merely with whether

there is a difference between two groups of individuals or objects with respect to a

given attribute, but with whether such difference is significant statistically.

Hypothesis reveals that knowledge discovery is concerned with whether a

statistically significant relationship actually exists between two variables, and not

with whether there is a relationship between the two variables. That there is a

difference between two groups with respect to psychological construct, or that a

relationship exists between the two variables, cannot be considered conclusively as a

newly discovered knowledge or an expansion of knowledge because such ‘difference’

or ‘relationship’ found within the sample drawn for the study could most probably

be as just a function of sampling error, measurement error or chance occurrence in

the parent population. Rather, what counts validly as discovery or expansion of

knowledge is when the ‘difference’ or ‘relationship’ is statistically significant at a

predetermined level of significance. This accounts for why statement of hypothesis

usually contains explicitly or implicitly, the term ‘significant’ or the phrase,

‘statistically significant’.

vi. Hypothesis stimulates research endeavour

Hypothesis stimulates research endeavour that culminates in accumulation of new

knowledge because hypothesis proposes tentative explanations for phenomena.

Hypotheses enable the researcher to, either inductively or deductively, postulate

explanations for the phenomena of interest and finally verify the credibility or

authenticity of such explanations. Accumulation of inductive explanations for

phenomena with hypotheses testing could eventually result in postulation of theory

about the phenomena. Conversely, accumulated deductive explanations of

phenomena with hypotheses prove the workability of the different aspects of a theory

in real life or practical setting. With hypothesis, the researcher is stimulated to

relate theory to observations and observations to theory, and successfully unite

experience with reason to produce knowledge.

vii. Hypothesis facilitates the research report writing

In writing of a research report, the results and conclusions are written around the

hypothesis. In other words, hypotheses serve as the basis for the findings and

conclusions, as well as the basis around which research results, discussions,

conclusions and generalizations of the research are reported. The last chapter of a

research dissertation or thesis, as well as the entire summary of the research work

into articles for publication in journals; are usually written around each of the

hypotheses.

viii. Hypothesis testing is the core of inferential statistics

Inferential statistics are used for the main purpose of hypothesis testing. It is for the



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purpose of hypothesis testing that each statistical test was developed and is in use.

It is on this basis that Colman (2003, 704) defined statistical test strictly as “a

procedure for deciding whether or not to reject the null hypothesis and conclude

that an observed difference or relationship is not due to chance”. The entire logic of

inferential statistics revolves round hypothesis testing. In empirical research, each

hypothesis has a statistical test that is most suitable for testing its tenability. For

example, when a hypothesis involves comparison of two independent samples with

respect to an attribute, the independent samples t-test is used. When the hypothesis

compares the same group of individuals with regard to their performance in two

different measures, the correlated samples t-test is most appropriate. When the

hypothesis involves comparison of three or more groups with respect to an attribute,

ANOVA becomes most suitable. If a hypothesis seeks to establish the main effects

and interaction effect of two or more independent variables contemporaneously on a

dependent variable, two-way ANOVA is necessitated. For a hypothesis that is on the

magnitude and nature of relationship between two variables, product moment

correlation becomes most handy. When the hypothesis expresses determination of

the effect of an independent variable on a dependent variable, with the effect of

pretest or any other covariate removed; the statistical analysis automatically called

for, is ANCOVA. If the hypothesis is postulated in a way that elicits the magnitude

and direction of relationship between two variables, when the influence of a third or

nuisance variable is held constant, adjusted for or removed; partial correlation is

necessarily required. When relationship among three or more variables is

hypothesized; application of multiple correlation is called for. Whenever prediction of

a criterion variable on a predictor variable is hypothesized, simple regression

inferential statistical technique becomes most appropriate. Multiple regression is

used when the hypothesis is aimed at predicting a group of individuals’ performance

in one variable on the basis of their performance in other two or more variables,

taken together. Therefore, hypothesis is a precondition for application of statistical

or inferential tests in research.

Characteristics of Hypothesis

Since hypothesis is a very crucial tool for execution of research, great care must be

taken in stating it so that it can maximally serve all the eight purposes that have

been explained for which hypothesis is used. Characteristics of hypothesis deal with

the very pertinent issue of the ‘How?’ on statement of hypothesis. An excellently

postulated hypothesis must possess certain basic characteristics. According to

Kpolovie (2011), only a statement which has the five characteristics outlined

hereunder that can be considered as a hypothesis.

i. Testability

Testability is the most important characteristic that a good hypothesis must

possess. A hypothesis is said to be testable when it is empirically verifiable. This

demands that it must be carefully stated in such a way that enough unbiased data



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or observations can be collected and statistically analyzed to either nullify it or

support it in virtually an unquestionable manner for decisions, conclusions and

inferences to be confidently made. A testable hypothesis must contain or relate only

variables that are operationally defined definitively and measured validly and

reliably by the researcher. If a variable in the hypothesis cannot be reliably and

validly measured, then quantitative data cannot be gathered for testing the tenability

of the relationship or difference proposed in the hypothesis. The indicators of each of

the variables in a hypothesis must have been defined operationally by the

researcher, who must actually obtain all the necessary data and measure the

variables subsequently. Recall that operational definition is that which clearly states

the procedures for necessarily measuring the variable in question in a reliable, valid,

and an unbiased and unambiguous way. A good hypothesis must not use any

variable that would be difficult or impossible to define in terms of identifiable and

observable behaviour, and measured accurately. A hypothesis must be stated in a

way that automatically lends itself to statistical testing on the basis of adequate data

collection. A hypothesis stated only in the alternative or research form cannot be

tested. Therefore, it must also be stated in the null form.

ii. Formulation of provisional relationship between variables

Each hypothesis must formulate provisional relationship between variables. The

relationship that the researcher expects between the independent and dependent

variables must be stated in every hypothesis. The quality that sets a hypothesis

apart from all other propositions is that it provisionally conjectures a specific

relationship between at least two variables in an empirically verifiable manner. This

implies that a hypothesis must have at least one independent variable and one

dependent variable as well as one deductive or inductive proposition, expectation,

suspicion or belief about the relationship between the two variables. The crucial

decision on whether to reject the proposition as false or retain (accept) it as the

truth, must wait for collection of empirical observations or data and subjection of

the data to the necessary statistical analyses at a given alpha (significance level) that

will reveal reasonably unquestionable preponderance of evidence.

iii. Mutually exclusive propositions

Hypothesis must be stated in two mutually exclusive propositions, called (a)

alternative hypothesis or research hypothesis (H1) and (b) null hypothesis (H0).

While the alternative or research hypothesis states that there is a significant

relationship between two variables of interest, the null hypothesis states that there

is no significant relationship between the two variables. In other words, while the

research hypothesis proposes that a valid relationship exists between the two

variables under study, the null hypothesis proposes that valid relationship does not

exist between the two variables that are under investigation. In terms of difference,

the research hypothesis postulates that there is a significant difference between two

or more groups with respect to a variable; the null hypothesis posits that there is no



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significant difference between the two or more groups with respect to a variable. The

only difference between these mutually exclusive ways of stating hypothesis is that

while the research hypothesis (H1) cannot be tested statistically, the null hypothesis

(H0) can directly be tested statistically and its tenability can be either ‘rejected’ or

‘not rejected’. When the null hypothesis, on the basis of inferential statistics, is

rejected; it means that the corresponding alternative or research hypothesis is

upheld, tenable, valid or accepted. Conversely, when the null hypothesis is retained

or not rejected (is accepted) on the basis of the appropriate inferential statistics, it

means that the available evidence is not sufficient to warrant its rejection, therefore

the alternative hypothesis cannot be tenable, valid or acceptable without further

observations or data collection and subsequent analysis. In short, when the null

hypothesis is retained, it means simply that the study is inconclusive. Simply put,

the two mutually exclusive statements of a hypothesis are used so that when the

testable null hypothesis is rejected, the research or alternative hypothesis is

accepted; and when the null hypothesis is ‘accepted’ (this is colloquially used to

actually mean ‘fails to be rejected’), the alternative hypothesis is rejected, at least

until when further empirical evidence will prove otherwise.

The stating of one hypothesis in both the research form and the null form is

anchored on the principle that what the researcher actually wants to ascertain or

prove is the alternative hypothesis that there is a significant ‘relationship’ or

‘difference’, but since this cannot be inferentially or statistically tested as all the

possible evidence cannot be or have not been gathered; the null hypothesis of ‘no

significant relationship’ or ‘no significant difference’ that can be tested with

inferential statistics is used so that its rejection will automatically confirm the

authenticity, validity, credibility and tenability of the corresponding research

hypothesis. On the other hand, if the null hypothesis is not rejected, it means that

the proposed ‘relationship’ or ‘difference’ is not statistically significant on the basis

of the quantum of observations made and data collected from the sample. This does

not absolutely mean that there is no element of relationship or difference at all in

the observation made, but that the study is inconclusive. In other words, it means

that the evidence gathered is not statistically preponderant or overwhelmingly large

enough to reject the null hypothesis.

The logic of formulating a single hypothesis in both the research form and null

form for the latter to be rejected in favour of the former is in order to authenticate

the true existence of a relationship or difference, is analogous to our legal system

which rejects the innocence of a person accused of criminal acts only when his or

her evidence of guilt is proved beyond all reasonable doubts. This is a scenario that

a null hypothesis is rejected. Conversely, when the null hypothesis is retained or not

rejected, the analogy with criminal trials in the legal system is like where lack of

evidence of guilt beyond all reasonable doubts against an accused, results in a

verdict of ‘not guilty’. Though the accused here is declared ‘not guilty’, it does not

prove that he or she is absolutely innocent of all the charges.



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On the logic of confirmation and disconfirmation or acceptance and rejection of

a hypothesis, Frank and Althoen (1994, 328) likened statement of hypothesis in

both the research and null forms to legal proceedings during criminal trials thus:

A prosecutor suspects that a defendant is guilty of a crime, but under

the American system of criminal justice the accused person is presumed

innocent. In order to obtain a conviction, the prosecutor must therefore

‘disconfirm’ the hypothesis of innocence in favor of the alternative

proposition that the defendant is guilty. To accomplish this, the

prosecution presents ‘factual’ evidence that is both implausible under

the hypothesis of innocence and consistent with the hypothesis of guilt.

If the prosecution fails, the defendant is found “not guilty”. That is, the

jury ‘rejects’ the hypothesis of ‘guilt’. This does not in any way imply

that the jury ‘accepts’ the hypothesis of ‘innocence’. It means only that

the evidence is insufficient to sustain a conviction.

iv. Clarity

Hypothesis must be stated in utmost clarity, without the least element of ambiguity

in proposing the relationship between the variables under investigation. It must be

stated in as simple and as concisely as possible. It must be a complete, yet simple,

clear and concise declaration that relates the independent and dependent variables

of interest. Terms or words employed in postulation of a hypothesis should be the

simplest acceptable to best convey the intended meaning that provides the essential

explanation of the phenomenon being investigated. Avoid use of constructs that are

vague, ambiguous, clumsy, not measurable, and which require assumptions in the

statement of hypothesis. One hypothesis should be stated to cover each of the

relationships that are being investigated in the work. One hypothesis should not be

compounded with any complexity of combining two or more relationships that the

research is on. Hypothesis must be stated specifically such that only one

relationship is covered by each hypothesis.

v. Consistency with existing body of knowledge

Hypothesis should be stated in a way that is consistent with existing body of

knowledge. Statement of good hypothesis requires the researcher to compulsorily

study existing theoretical and empirical literature on the variables of interest very

widely and thoroughly. When hypothesis is formulated on the basis of such

extensive review, the likelihood that it would be outright contradiction of theories

and previously well-established knowledge, on the one hand; and that it would be on

what has been over investigated conclusively in the population that the work covers,

on the other hand, will be less. It must however be noted, and emphatically too, that

it is from exhaustive review of related literature, that the researcher can spot

knowledge gap or an aspect of the phenomenon that urgently needs to be

investigated and which existing theories and or empirical works have left to be filled.

Hypothesis should not be totally contrary to what is known about the nature of a



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phenomenon; rather it should be consistent with previous knowledge so that it will

be worth pursuing. Probably, it would be unprofitable to hypothesize an absence of

relationship between two variables that existing preponderance of evidence supports

the presence of such relationship. It is of great importance to formulate truly

revolutionary hypothesis for reorganization of the existing knowledge into a more

satisfactory whole or theory as renowned scientists like Newton, Einstein, Darwin

and Copernicus did. Conclusively, hypothesis could be formulated on the basis of

grand theory or mini-theory as well as from prior empirical observation, playful

speculation, scientific hunches, serendipity, unbridled conjecture, and whimsical

inspiration that are affectionately known in some scientific circles as Scientific Wild

Intuitive Guesswork (SWIG).

Types of Hypothesis

There are two types of hypothesis, the research hypothesis (H1) and the null

hypothesis (H0). Each of these is very briefly explained here to adequately address

the question of ‘Which?’ about hypothesis.

The Research Hypothesis

The research hypothesis is also known as the alternative hypothesis, as it is indeed

the alternative to the null hypothesis. Research hypothesis is stated in positive or

affirmative terms about the proposed or expected ‘relationship’ or ‘difference’ that

exists between independent and dependent variables for the explanation of the

phenomenon under study. Statement of hypothesis in this form restricts or limits

the focus of the study to a definite target and determines the observations that will

most probably be made. The research hypothesis is actually the statement that

assertively expresses the ‘relationship’ or ‘difference’ between variables that the

researcher truly expects to find as a result of the research. However, the researcher

cannot collect all the evidence, which might be infinite in the population, to prove its

authenticity or validity because observations or data are collected from a randomly

drawn sample instead. Also, research hypothesis cannot be tested because the

affirmative proposition does not lend itself automatically to inferential statistical

analysis that could eliminate the possibility of chance occurrence of the said

‘relationship’ or ‘difference’ between the variables. Generally, it is technically and

classically necessary to preferably reformulate the research hypothesis in the null

form that allows for statistical testing.

The research hypothesis can be stated in two possible ways, either a

nondirectional form or a directional form. As the term implies, a nondirectional

research hypothesis simply states that a relationship or difference exists between

the variables of interest, without specifying the nature or direction of the expected

relationship or difference. An example of a nondirectional research hypothesis is:

There is a significant difference between male and female final year students’

performance in mathematics. The side that the proposed difference will favour is not

indicated, as it can go either way. Directional research hypothesis, on the other



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hand, is a statement or proposition that specifies the nature or direction of the

expected relationship or difference between the variables of interest in the

investigation. Example of directional research hypothesis can be given as: Male final

year students perform significantly better than their female counterparts in

mathematics. It can also take the other way round that: Female final year students

perform significantly better in mathematics than their male counterparts. You can

see that in this case (directional H1), the side that the expected gender difference in

mathematics performance favours, is specified in the proposition.

The Null Hypothesis

The null hypothesis is postulated in negative, no or not terms with regard to the

relationship or difference between the independent and dependent variables of

interest in the population, and that any such relationship or difference found in the

sample is attributable exclusively to chance or sampling error. Simply put, the null

hypothesis is formulated as a direct negation of the ‘relationship; or ‘difference’ that

the researcher actually expects as a result of the investigation. With the null

hypothesis, the researcher is able to ascertain whether apparent relationships or

differences observed in the sample are indeed genuine or are most likely due to

chance. Null hypothesis is anchored on the fact or principle that results of a study

could easily have occurred by chance; and therefore subject the data collected to

inferential statistical test to either rule out the possibility of chance or retain the

chance probability with a given percentage of certainty. If the statistical tests

indicate that data collected and analyzed have preponderance of evidence that is

overwhelmingly large enough or sufficiently adequate to prove beyond all reasonable

doubts that the observed relationship or difference is credible, valid, genuine,

authentic and certainly not a function of chance occurrence, then the null

hypothesis is rejected. Rejection of the ‘no’ proposition (i.e., the H0) means

automatically that its corresponding alternative or research hypothesis is accepted.

Statement of null hypothesis is so important that Cohen (2008, 125) personified it

and stated that “whenever you run an experiment… and write up the results and

send them to a journal to be published, the first person to see your article (no

matter which journal you send it to) is Dr. Null.” This implies that the first

requirement of an experimental investigation is how well the null hypothesis is

stated before results of the study can be published. Aron, Aron and Coups (2006)

also emphasized the indispensability of null hypothesis in every empirical

investigation as it entails the best and most appropriate way that data collected can

be summarized and generalized to the population from which sample was drawn.

In a situation that the statistical tests reveal that the data collected and

analyzed are not sufficient or not large enough to rule out possibility of chance in

determination of the observed relationship or difference; the null hypothesis is

retained (not rejected). This implies that the corresponding research hypothesis is

not sustainable or tenable in the population on the basis of the data obtained from

the random sample that was drawn. In other words, the observed difference or



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relationship was not significant statistically. Such study could be said to be

inconclusive, as obtaining and analyzing more and more data from the population

might indicate otherwise. So, what the investigator hoped to show as posited in his

or her research hypothesis is yet to be ascertained or authenticated.

To further illustrate null hypothesis, if a researcher wishes to show the effect of

a specific experimental treatment, the investigator randomly draws two samples of

equal mean from the population. Using research hypothesis, he/she postulates that:

At the end of the experiment, there will be a significant difference in the means of

the sample which received the experimental treatment and the sample that did not

receive. Recall that this is stated in a nondirectional form. Formulating the research

hypothesis in a directional form is: At the end of the experiment, the mean of the

sample that received experimental treatment will be significantly greater than the

mean of the sample that served as control group. Now, recasting the research

hypothesis in the null form for nondirectional will be thus: At the end of the

experiment, there will be no significant difference in the means of the sample which

received the experimental treatment and the sample that did not receive the

treatment. Then in a directional form, the null hypothesis will be: At the end of the

experiment, the mean of the sample that received experimental treatment will not be

significantly greater than the mean of the sample that served as control group.

If on the basis of the observations made and data collected and statistically

analyzed, the nondirectional null hypothesis is rejected, then the nondirectional

research hypothesis is sustained. If the directional null hypothesis is rejected, it

automatically means acceptance of the directional research hypothesis. Conversely,

if the nondirectional null hypothesis is retained, then the nondirectional alternative

hypothesis is not sustained for lack of significant evidence. If the directional null

hypothesis failed to be rejected, then the directional research hypothesis is rejected,

at least temporarily, on the basis of lack of statistical significance with the data

collected.

It is the null hypothesis that is, as a matter of necessity, subjected to inferential

statistical analysis for testing its tenability; which will definitely be either rejected or

retained. The research hypothesis cannot be directly tested statistically as pointed

out earlier. It must also be emphasized that in statement of a null hypothesis, ‘no’ or

‘not’, denoting negativity or nullity, and ‘significant’ should necessarily be used.

The term ‘significant’ has to be used because in research or hypothesis testing, the

investigator is not concerned merely with whether a relationship or difference exists

between the variables of interest, but crucially with whether the magnitude of the

relationship or difference is large enough to exclude the possibility that it was

caused by chance or sampling error. It is only when the relationship or difference is

overwhelmingly large enough to exclude every plausible explanation other than the

manipulation or condition of the independent variable, that the difference or

relationship is said to be significant, and again at a specified probability level.

Sampling error refers to the inevitability of variations in the means of several



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samples of the same size, each drawn randomly from the same population with

respect to any specific variable that is normally distributed in the population.

There are two forms of null hypothesis, namely, nondirectional and

directional. A nondirectional null hypothesis states that a relationship or difference

does not exist in the variables under study in the population. It does not lean to any

direction. For example: there is no significant difference between male and female

final year students’ performance in mathematics. A directional null hypothesis

indicates that a specific nature or direction of relationship or difference does not

exist in the variables of interest in the population. For example, male final year

students do not perform betters significantly in mathematics than their female

counterparts. Put the other way round, it will be: female final year students do not

perform significantly better in mathematics than their male counterparts.

Generally, in research, one hypothesis is not stated in both the nondirectional

and the directional forms. The researcher chooses to formulate a hypothesis either

in the nondirectional form or in the directional form. But the two types of hypothesis

(research, H1 and null, H0) should be stated for each hypothesis. There should be

consistency in the use of the research hypothesis and the null hypothesis. When the

research hypothesis is formulated in the nondirectional form, the null hypothesis

too must be postulated in the nondirectional form. If the research hypothesis is

proposed in the directional form, postulation of the null hypothesis too must

correspondingly be in the directional form. Each of the two forms that hypothesis

could be stated (nondirectional or directional) has its special implication in

determination of the critical value at which its tenability is tested.

Steps for Testing Hypothesis

Hypothesis testing requires observing the following steps carefully as presented in

Kpolovie (2011, 57-58).

Step 1: Restate the research question of the investigation as both research

hypothesis and null hypothesis

Step 2: Choose the most appropriate statistical test for the analysis of data collected.

Such statistical test should be in line with the hypothesis as well as the

research method or design employed for the investigation.

Step 3: Choose the level of significance at which tenability of the null hypothesis will

be tested. A 0.05 or 0.01 level of significance is conventionally appropriate in

most cases.

Step 4: Execute the statistical data analysis to obtain the sample characteristics for

the variables under investigation.

Step 5: Obtain the critical value for the statistics at the chosen level of significance

and the appropriate degrees of freedom. Critical values are found in



Page 14

statistical tables.

Step 6: Decision-making: compare the calculated value of the statistics and its

critical value. Reject the null hypothesis if the calculated value is equal to or

greater than the critical value; or retain the null hypothesis if the calculated

value is less or smaller than the critical value.

Where the data are analyzed with statistical software like SPSS, the

decision rule is: whenever the probability of the test result is equal to or less

than the chosen level of significance, reject the null hypothesis (i.e., reject H0

if p < .05 or if p < .01, as the case may be). Conversely, whenever the

probability of the statistical test result is greater than the chosen

significance level, retain the null hypothesis (i.e., retain H0 if p > .05 or if p >

.01), depending on the chosen alpha for the investigation.

Step 7: Briefly interpret the decision to show the side or direction that it favours,

and report it.

Summary

This article has exhaustively elucidated the meaning (what), uses (why),

characteristics (how) and types (which) of hypothesis as well as the steps for testing

it. Hypothesis is defined as a tentative proposition about the nature and workability

of a phenomenon in terms of independent and dependent variables, and which is

subject to refutation or rejection by empirical evidence via statistical testing and

criticism by rational argument. Hypothesis is stated for the purposes of (a) proposing

relationship between two variables, (b) providing direction to research, (c) conveying

empirically testable rational statement, (d) determining the quality of a research, (e)

encapsulating the essence of research, (f) stimulating research endeavour, (g)

facilitating research report writing and (h) applying of the most suitable inferential

statistics. The characteristics that a hypothesis must possess are testability,

provisional relationship between variables, mutually exclusive propositions, clarity

and consistency with existing body of knowledge. There are two types of hypothesis;

the research hypothesis and the null hypothesis, each of which could either be

stated in the directional form or nondirectional form. Seven steps for testing of

hypothesis are also given. When educational researchers and practitioners acquire

and apply the mastery knowledge of hypothesis as thoroughly presented in this

paper, the quality of their research works will be tremendously improved and this

will absolutely be reflected in refocusing education in Nigeria in the current century

and beyond.

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KPOLOVIE Hypothesis Postulation