Research: Hypothesis

Dr. Ranjul Rastogi

Definition

the word hypothesis is derived form the Greek words

..is a hunch, assumption, suspicion, assertion or an idea about a phenomena, relationship, or situation, the reality of truth of which one do not know

a researcher calls these assumptions, assertions, statements, or hunches hypotheses and they become the basis of an inquiry.

In most cases, the hypothesis will be based upon either previous studies or the researchers own or someone elses observations

Hypothesis is a conjectural statement of relationship between two or more variable (Kerlinger, Fried N, Foundations of Behabioural Research , 3rd edition, New York: Holt, Rinehart and Winston, 1986)

Definition

A tentative statement about something, the validity of which is usually

unknown (Black, James A & Dean J Champion, Method and Issues in Social

Research, New York: John Wiley & Sons, Inc, 1976)

Hypothesis is proposition that is stated is a testable form and that predicts a

particular relationship between two or more variable. In other words, ie, we

think that a relationship exists, we first state it is hypothesis and then test

hypothesis in the field (Baily, Kenneth D, Methods of Social Research, 3rd

edition, New York: The Free Press, 1978)

Hypotheses are predictions about the relationship among two or more variables or

groups based on a theory or previous research (Pittenger, 2003)

Hypotheses are assumptions or theories that a researcher makes and tests.

Definition

A hypothesis is written in such a way that it can be proven or disproven by

valid and reliable data in order to obtain these data that we perform our

study (Grinnell, Richard, Jr. Social Work Research and Evaluation, 3rd edition,

Itasca, Illinois, F.E. Peacock Publishers, 988)

A hypothesis may be defined as a tentative theory or supposition set up and

adopted provisionally as a basis of explaining certain facts or relationships and

as a guide in the further investigation of other facts or relationships (Crisp,

Richard D, Marketing Research, New York: McGraw Hill Book Co., 1957 )

Why are hypotheses important?

HYPOTHESIS - Formulation

A well

formulated

HYPOTHESIS

should

Contain conceptual clarity

Be specific and precise

Relate to a body of knowledge

Relate to the Research question

Functions

Bringing clarity to the research problem

Serves the following functions

provides a study with focus

signifies what specific aspects of a research problem is to investigate

what data to be collected and what not to be collected

enhancement of objectivity of the study

formulate the theory

enable to conclude with what is true or what is false

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Symbols used in Hypotheses

M= mean (mu: mew)= population mean

Roman Letters (e.g., A, B, C, D) are used to represent statistics

Greek Letters (e.g., , ) are used to represent parameters

= significance level; probability of committing a Type I Error (= .05)

p= probability value (p= .05) Null Hypothesis= (H0: 1 - 2 = 0 or H0: 1 = 2)

Alternative Hypothesis= (H1: 1-2 0 or H1: 1 2 ) Sometimes you may see it noted as HA

Typologies

Three types

working hypothesis

Null hypothesis

Alternate hypothesis

Working hypothesis

The working or trail hypothesis is provisionally adopted to explain the

relationship between some observed facts for guiding a researcher in the

investigation of a problem.

A Statement constitutes a trail or working hypothesis (which) is to be tested and

conformed, modifies or even abandoned as the investigation proceeds.

Typologies

Null hypothesis

A null hypothesis is formulated against the working hypothesis; opposes the

statement of the working hypothesis

....it is contrary to the positive statement made in the working hypothesis;

formulated to disprove the contrary of a working hypothesis

When a researcher rejects a null hypothesis, he/she actually proves a working

hypothesis

In statistics, to mean a null hypothesis usually Ho is used. For example,

Ho Q = O where Q is the property of the population under investigation

O is hypothetical

Typologies

Alternate hypothesis

An alternate hypothesis is formulated when a researcher totally rejects null

hypothesis

He/she develops such a hypothesis with adequate reasons

The notion used to mean alternate hypothesis is H1 Q>O

i.e., Q is greater than O

Example

Working hypothesis: Population influences the number of bank branches in a

town

Null hypothesis (Ho): Population do not have any influence on the number of

bank branches in a town.

Alternate hypothesis (H1): Population has significant effect on the number of bank branches in a town. A researcher formulates this hypothesis only after

rejecting the null hypothesis.

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Statistical versus Research hypotheses

Statistical hypotheses

(null hypotheses): states that there is no relationship between independent and dependent variables

Research hypothesis

(scientific hypothesis): a statement of expected relationship between the variables. It can be directional or nondirectional

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The type of research design; experimental or non-experimental, will influence the wording of the hypothesis

In case of an experimental design, the hypothesis will reflect cause effect relationship

e.g. incidence of . will be greater in subjects after . than after .

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Hypothesis related to non-experimental designs reflect associative relationship statements

e.g. there will be a positive relationship between and .

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Testing Hypotheses Cont.

We use a variety of statistical procedures

to test null hypotheses. The choice of which procedure we use depends on a variety of factors including: the research hypothesis, the data, the sampling strategy, and what we want to be able to say as a result

of our testing.

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Types of Tests

Statistical procedures that are commonly used for hypothesis testing include: correlation, analysis of variance (ANOVA), analysis of covariance (ANCOVA), regression, multivariate analysis of variance (MANOVA), t-tests, and Chi-Square. Each of these procedures has an associated test statistic, which is used to determine significance. For example ANOVA, ANCOVA, and regression use F statistics and their associated p-values.

Multivariate procedures, like MANOVA, use a variety of test statistics with interesting names, like Wilks lambda. These are then related to a more common test statistic, like F.

The secret here, for the layperson, is that all test statistics are eventually related to a probability distribution and a p-value. These p-values mean the same thing across test statistics.

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Error Types

In hypothesis testing, we must contend with two types of errors -- Type I and Type II. Errors are mistakes that we can make when judging the

null hypothesis

Type I error is what happens when the tested

hypothesis is falsely rejected. (It is when you say you found something, but that something is really an error.) A type I error is a false positive.

Type II error is what happens when a false tested hypothesis is not rejected (Hays, 1986). (It is when you dont find something that is, in fact, there.) A type II error is a false negative.

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Error Types Cont.

Alpha is the level of probability (pre-set by the researcher) that the tested hypothesis will be falsely rejected. Alpha is the pre-set risk of a Type I error. In other words, alpha is the degree of risk that you accept, in advance of conducting the study, that what you find will be an error.

Beta is the probability (often neglected by the researcher) that a false null hypothesis will not be rejected. Beta is the probability that you wont find what you are looking for if, in fact, it is really there.

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Error Types Cont.

Error Types Chart

Decision

H0 is True H1 is True

Reject H0

Type I

Correct

1-

Fail to Reject

(decide in favor of H0)

Correct

1-

Type II

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Example

Do we use Null Hypotheses in the real world?

Innocent until Proven Guilty

Defendant Innocent

Defendant Guilty

Reject Presumption of Innocence (Guilty Verdict)

Type I Error

Correct

Fail to Reject Presumption of Innocence (Not Guilty Verdict)

Correct Type II Error

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Test Statistics, Probability, and

Significance

In order to test a hypothesis, we compare the obtained value of a test statistic (e.g., the obtained F) to a critical value of the test statistic (e.g., a critical F) that is associated with the preset significance level (alpha).

If the obtained value of the test statistic is greater than the critical value, we determine that there is a significant difference or relationship.

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Test Statistics, Probability, and

Significance Cont.

Test Statistic: The specific statistic (i.e., the tool) that is chosen to test the null hypothesis. Examples include F, t, r.

Obtained Value: The actual value obtained when applying the test statistic to the data of interest. The probability value associated with the obtained value is p.

Critical Value: The critical value of the test statistic that is associated with the chosen significance level (alpha). If the obtained value is greater that the critical value, the result is significant.

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Test Statistics, Probability, and

Significance Cont.

Probability Value: The probability that observed relationships or differences are due to chance.

Alpha: Alpha is also known as significance level or rejection region. It is the level of probability set by the researcher as grounds for rejection of the null hypothesis (Williams, 1986, p. 58). Alpha is the probability level associated with the critical value of the test statistic.

In other words, alpha is our predetermined risk that differences that we declare to be real are actually due to chance.

Obtained: This is also known as the obtained probability (p): significance of the test statistic. It is the probability that the data could have arisen if Ho were true (Cohen, 1994, p. 998).

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Test Statistics, Probability, and

Significance Cont.

Significance: What happens when the obtained probability p is less than our predetermined alpha. Significance also occurs when the obtained value of the test statistic is greater than the critical value of the test statistic.

Test Statistic Probability Value Critical Value Significance Level (alpha) Obtained Value Obtained or Actual Probability (p) Note that larger obtained values of test statistics are

generally related with smaller values of p. If Obtained Value > Critical Value, then * Significance * If p < Alpha, then * Significance *

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Revisiting the Bell Curve

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Steps in Hypothesis Testing for

Quantitative Research Designs

Hypothesis testing is a 4 phase procedure:

Phase I: Research Hypotheses, Design, and Variables

Phase II: Statistical Hypotheses

Phase III: Hypotheses Testing

Phase IV: Decision/Interpretation

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Phase I: Research Hypotheses, Design,

and Variables

1. State your research hypotheses. 2. Decide on a research design based on your

research problem, your hypotheses, and what you really want to be able to say about your results (e.g., if you want to say that A caused B, you will need an experimental or time-series design; if probable cause is sufficient, a quasi-experimental design would be appropriate).

3. Operationally define your variables. Recall that one variable can have more than one operational definition.

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Phase II: Statistical Hypotheses

1. Consider your chosen statistical procedures.

2. Write one statistical null hypotheses for each operational definition of each variable that reflects that statistical operations to be performed.

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Phase III: Hypotheses Testing

Complete the following steps for each statistical null hypothesis:

1. Select a significance level (alpha).

1. Compute the value of the test statistic (e.g., F, r, t).

1. Compare the obtained value of the test statistics with the critical

value associated with the selected significance level or compare the obtained p-value with the pre-selected alpha value.

1. If the obtained value of the test statistic is greater than the

critical value (or if the obtained p-value is less than the pre-selected alpha value), reject the null hypothesis. If the obtained value is less than the critical value of the test hypothesis, fail to reject the null hypothesis.

Another way of looking it: If p is less than or equal to

alpha, reject the null hypothesis.

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Phase IV: Decision/Interpretation

1. For each research hypothesis, consider the decisions regarding the statistical null hypotheses.

2. For each research hypothesis, consider qualitative contextual information relating potential plausibility.

3. Cautiously explain your findings with respect to the research hypotheses.

4. List and discuss the limitations (threats to valid inference). Note: Null hypothesis testing is currently under

scrutiny (see e.g., Cohen, 1994; Kirk, 1996).

It is generally recommended that you report the effect size along with the value of the test statistic and the p-value. An alternative is to report confidence intervals.

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Points to Consider about Hypotheses

Testing

FISHING IN LAKE ALICE

We dont prove the null hypothesis.

If you go fishing on Lake Alice and you dont

catch fish, you cannot conclude that there are no fish in the lake!!!

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Points to Consider about Hypotheses

Testing Cont.

Returning to hypothesis testing:

Failure to reject the null hypothesis cannot be interpreted as proof that no differences or relationships exist. Existing differences or relationships might be obscured by: 1. insensitive outcome measures (the wrong

fishnet),

2. inappropriate statistical designs,

3. poor sampling strategies, and

4. low statistical power.

SA 4

RESEARCH QUESTION

A Research Question

embodies a gap in the

literature. It is a Question or

Questions posed so that an

answer or answers to it will

add knowledge in a particular

area or subject

What is a

RESEARCH

QUESTION

RESEARCH QUESTION & HYPOTHESIS

RESEARCH

QUESTION and

HYPOTHESIS

is

The early identification of a Research Question will help in the formulation of a hypothesisypothesis

THE IMPORTANCE OF THE

RESEARCH QUESTION The research question is the starting point

of the study. Everything flows from the research question. It will determine the population to be studied, the setting for the study, the data to be collected, and the time period for the study. A clear and concisely stated research question is the most important requirement for a successful study.

Origins of a Research Question

Careful Observation of People

Application of New Technology

The Annoyance Principle

Build on Experience

Scientific Communications

Skeptical Attitude (questioning peers and status quo)

Characteristics of a good research

question

FINER Feasible

Adequate numbers of subjects?

Adequate technical expertise?

Affordable in time and money?

Is it possible to measure or manipulate the variables?

Interesting

To the investigator?

Novel

To the field?

Ethical

Potential harm to subjects?

Potential breech of subject confidentiality?

Relevant

To scientific knowledge/theory?

To organizational, health or social management and policy?

To individual welfare?

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Exploratory studies usually have research questions not hypotheses

The outcome of an exploratory study may help in formulating hypotheses for future studies

Qualitative research studies are guided by research questions rather than hypotheses

The descriptive findings of qualitative studies can provide the basis for future hypothesis-testing studies

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Some studies may have research questions and hypotheses. In such case, research questions do not pertain to the proposed outcomes, rather, they may

provide additional information that may enrich the study and

may provide direction for further study

Research question and Hypotheses

Examples

RQ: Is a happy worker a productive worker?

H1: Happier workers are more productive than unhappy workers.

RQ: Does increasing the happiness of workers make them more productive?

H1: Increasing the happiness of workers does not increase productivity.