Download - Research -Hypothesis
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Research: Hypothesis
Dr. Ranjul Rastogi
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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)
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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.
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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?
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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
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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
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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.
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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
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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
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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.
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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
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RESEARCH QUESTION & HYPOTHESIS
RESEARCH
QUESTION and
HYPOTHESIS
is
The early identification of a Research Question will help in the formulation of a hypothesisypothesis
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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.
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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)
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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
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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.