16 hypothesis testing

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Research Methodology Dr. Nimit Chowdhary, Professor

Saturday, April 14, 2012 1© Dr. Nimit Chowdhary

© Dr. Nimit Chowdhary Research Methodology Workshop p. 2

Saturday, April

14, 2012

‘X’ is innocent‘X ‘ is Guilty

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© Dr. Nimit Chowdhary Research Methodology Workshop p. 3 Saturday, April 14, 2012

We all operate on basis of theories we hold A theory is a set of systematically interrelated

concepts, definitions, propositions that are advanced to explain and predict phenomena (fact)

Theories tend to be abstract and involve multiple variables

Hypothesis is simple, two-variable propositions involving concrete instances


Research Test theory TheorizeTheory Suggest a system to researcher to impose on

data

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Theory Concepts Constructs

Research Variables

A concept is a bundle of meanings or characteristics associated with certain events, objects, conditions, situations, etc.

Variables accept numerical values for empirical testing and measurementVariable is used synonymously for construct

A construct is an image or idea specifically invented or created for a given research and/ or-theory building purpose

© Dr. Nimit Chowdhary

Research

Methodology

Workshop p. 6Saturday, April 14, 2012

Theory The abstract statements that make claims about the world and how it work. Research problems are usually stated at a theoretical level

Example “poverty leads to poor health”

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© Dr. Nimit Chowdhary

Research

Methodology

Workshop p. 7Saturday, April 14, 2012

Concepts The building blocks of theory which are usually abstract and cannot be directly measured Descriptive/ nominal/ conceptual definition Operational definition

Example “poverty”

Concept Descriptive definition

Operational definition

Customer A patron of firm ‘x’ or one who buys products and services from firm ‘x’

One who has purchased at least one third of his family’s need from firm ‘x’ during the last 3 months

Year A twelve month period Financial year, April 1 through March 31

Boy A male youth A male of 12-16 years of age

Small-scale unit An industrial undertaking which manufactures some product/s on a small scale

An industrial unit with investment in plant and machinery less than 3 crores

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What is ‘rural’ as in rural tourism?


© Dr. Nimit ChowdharySaturday, April 14, 2012

Constructs The phenomenon which point to the existence of the concept

Example “poor living conditions”

Remember that ‘poverty’ was the concept. ‘Poverty’ is explained as ‘poor living conditions’

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Variables The components of the constructs which can be measured

Example “provision of sanitary facilities”

Construct ‘poor living conditions’ can be construed from a number of ‘measurable’ variables like ‘provision on sanitary facilities’


Value The actual units or methods of measurement of the variables. These are data in their most concrete form

Example “number of people per toilet”

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Identify variables Relate variables Nature of relationship Degree of relationship

Create a system of variables (Model) Predict variables


Dichotomous variables Discrete variables Continuous variable

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Independent variables Dependent variables


A moderating variable is a second independent variable that is included because it is believed to have a significant contributory or contingent effect on the originally stated IV-DV relationship.The introduction of a 4-day week (IV) will lead to higher productivity (DV) especially among younger workers (MV)

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An almost infinite number of extraneous variables (EV) exist that might conceivably effect a given relationship. Some can be treated as IV or MV, but most must either be assumed or excluded from the study.In routine office work (EV) the introduction of a 4-day week (IV) will lead to higher productivity (DV) especially among younger workers (MV)


The intervening variables (IVV) are factors that may theoretically affect the observed phenomenon but cannot be seen, measured, or manipulated; its affects must be inferred from the effects of the independent and the moderator variables on observed phenomenon.The introduction of a 4-day week will lead to higher productivity by increasing job satisfaction (IVV).

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Proposition (Problem) is a statement about concepts that may be judged as true or false if it refers to observable phenomenon.When a proposition is formulated for empirical testing, we call it a hypothesis. As a declarative statement, a hypothesis is of a tentative and conjectural nature.

Is an assumption about relations between variables

Is a predictive statement that relates an independent variable to a dependent variable.

Are tentative, intelligent guesses as to the solution of the problem


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Is a specific statement of prediction. It describes in concrete terms what you expect to happen in the study

Is an assumption about the population of study

Delimits the area of research and keeps the researcher on right track



Descriptive Hypothesis- state existence, size, form, or distribution of some variablePeople in equatorial regions (cases) have less than average heights (variables)

Relational Hypothesis- that describe relationship between two variables with respect to some case Correlational Hypothesis

Foreign cars are perceived by American consumers to be of better quality than domestic quality Explanatory hypothesis

An increase in family income leads to an increase in the percentage of income spent on junk food

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Null Hypothesis- is an hypothesis of ‘no difference’. It states that no difference exists between the parameter and the statistic being compared to or no relationship exits between the variables being compared. Ho: There is no relationship between a family’s income and its expenditure

on junk food Alternative (Research) Hypothesis- describes the

researcher’s prediction that, there exists a relationship between two variables.H1: Family’s expenditure on junk food increases with rise in family

income.

Consider mean demand for computers during assembly lead time. Rather than estimate the mean demand, our operations manager wants to know whether the mean is different from 350 units. In other words, someone is claiming that the mean time is 350 units and we want to check this claim out to see if it appears reasonable


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That the standard deviation [σ]was assumed to be 75, the sample size [n] was 25, and the sample mean [ ] was calculated to be 370.16


X

We can rephrase this request into a test of the hypothesis:

H0: = 350Thus, our research hypothesis becomes:

H1: ≠ 350


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For example, if we’re trying to decide whether the mean is not equal to 350, a large value of (say, 600) would provide enough evidence.

If is close to 350 (say, 355) we could not say that this provides a great deal of evidence to infer that the population mean is different than 350.


X

X

The two possible decisions that can be made:Conclude that there is enough evidence to support the alternative hypothesis(also stated as: reject the null hypothesis in favor of the alternative)Conclude that there is not enough evidence to support the alternative hypothesis(also stated as: failing to reject the null hypothesis in favor of the alternative)NOTE: we do not say that we accept the null hypothesis if a statistician is around…

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Null hypothesis: ‘X’ is innocent Alternate: ‘X’ has committed theft Either there is enough evidence to conclude that

‘X’ has committed theft (Accept alternative hypothesis..police may generate evidence)

Or there is not enough evidence to conclude that ‘X’ has committed theft (Which does not mean that ‘X’ has not committed theft…only sufficient

evidence is not there)

The testing procedure begins with the assumption that the null hypothesis is true.Thus, until we have further statistical evidence, we will assume:

H0: = 350 (assumed to be TRUE)The next step will be to determine the sampling distribution of the sample mean assuming the true mean is 350.

is normal with 35075/SQRT(25) = 15

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1. Un-standardized test statistic: Is in the guts of the sampling distribution? Depends on what you define as the “guts” of the sampling distribution.If we define the guts as the center 95% of the distribution[this means = 0.05], then the critical values that define the guts will be 1.96 standard deviations of X-Bar on either side of the mean of the sampling distribution [350], orUCV = 350 + 1.96*15 = 350 + 29.4 = 379.4LCV = 350 – 1.96*15 = 350 – 29.4 = 320.6

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2. Standardized test statistic: Since we defined the “guts” of the sampling distribution to be the center 95% [ = 0.05],

If the Z-Score for the sample mean is greater than 1.96, we know that will be in the reject region on the right side or

If the Z-Score for the sample mean is less than -1.97, we know that will be in the reject region on the left side. Z = ( - )/ = (370.16 – 350)/15 = 1.344Is this Z-Score in the guts of the sampling distribution???

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3. The p-value approach (which is generally used with a computer and statistical software): Increase the “Rejection Region” until it “captures” the sample mean.For this example, since is to the right of the mean, calculateP( > 370.16) = P(Z > 1.344) = 0.0901Since this is a two tailed test, you must double this area for the p-value.

p-value = 2*(0.0901) = 0.1802Since we defined the guts as the center 95% [ = 0.05], the reject region is the other 5%. Since our sample mean, , is in the 18.02% region, it cannot be in our 5% rejection region [ = 0.05].

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Un-standardized Test Statistic:Since LCV (320.6) < (370.16) < UCV (379.4), we reject the null hypothesis at a 5% level of significance.

Standardized Test Statistic:Since -Z/2(-1.96) < Z(1.344) < Z/2 (1.96), we fail to reject the null hypothesis at a 5% level of significance.

P-value:Since p-value (0.1802) > 0.05 [], we fail to reject the hull hypothesis at a 5% level of significance.

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Discussions with colleagues and experts about a problem, its origin and objectives in seeking a solution

Examination of data and record for possible trends, peculiarities

Review of similar studies


Exploratory personal investigation/ observation

Logical deduction from the existing theory Continuity of research Intuition and personal experince


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Conceptual clarity Should be clear and precise

Specific Should be specific and limited in scope

Consistent Should be consistent with the objectives of research

Testable Should be capable of being tested

Expectancy Should state the expected relationship between the variables


Simplicity Should be stated as far as possible in simple terms

Objectivity Should not include value judgments, relative terms or any moral preaching

Theoretical relevance

Should be consistent with a substantial body of established or known facts or existing theory

Availability of techniques

Statistical methods should be available for testing the proposed hypothesis


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Technology

16 hypothesis testing