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Unit 2

Hypothesis Testing

Shahaida P

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Hypothesis

Assumptions and suppositions to beproved or disproved

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Characteristics of hypothesis

Clear and precise

Capab

le of being tested

State relationship between variables

Hypothesis should be amenable totesting within a reasonable time

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Null hypothesis

Ho

Ho: =

Ho=

100 Example: there is no difference

between low conservative and highconservative people in there willingness

to try an innovation

Customers in Delhi and Mumbai preferthe same brand

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Alternative hypothesis H1 H

1

: { H1

H1: u H1 H1: e H1 Example: there is difference between

low conservative and high conservativepeople in there willingness to try aninnovation

Customers in Delhi and Mumbai do not

refer the same brand

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Examples:

Automobile A as well as automobile Bperforms in all the conditions I.e. urban,semi-urban, and rural roads.

There is significant positive relationship

between intelligence quotient and jobperformance.

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Type I and Type II error

Rejecting a null hypothesis when it istrue is called a type I error (alpha)

Value is called level of significance-Pvalue

Accepting a null hypothesis when it is

false is called a type II error (beta)

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Statistical Decisions

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H0 (true)

H0 (false)

Accept H0

Reject H0

Correctdecision

Type I error

Type II errorCorrect

decision

Decision

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Two tailed and one tailed test

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Two-Tailed Test of Significance

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18-13

One-Tailed Test of Significance

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18-14

Probability of Making a Type I

Error

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18-15

Probability of Making A Type I Error

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Factors Affecting Probability ofCommitting a FError

True value of parameter

Alpha level selected

One or two-tailed test used

Sample standard deviation

Sample size

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18-17

Statistical Testing Procedures

Obtain criticaltest value

Interpret thetest

Stages

Choosestatistical test

State nullhypothesis

Selectlevel ofsignificance

Computedifference

value

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18-18

Tests of Significance

NonparametricParametric

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18-19

Assumptions for Using Parametric Tests

Independent observations

Normal distribution

Equal variances

Interval or ratio scales

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How To Select A Test

How many samples are involved?

If two or more samples are involved,are the individual cases independent or related?

Is the measurement scalenominal, ordinal, interval, or ratio?

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Recommended Statistical Techniques

Two-Sample Tests____________________________________________

k-Sample Tests____________________________________________

Measurement

Scale One-Sample Case Related Samples

Independent

Samples Related Samples

Independent

Samples

Nominal Binomialx2one-sample test

McNemar Fisher exact testx2two-samples

test

Cochran Q x2

forksamples

Ordinal Kolmogorov-Smirnov

one-sample test

Runs test

Sign test

Wilcoxon

matched-pairs

test

Median test

Mann-Whitney U

Kolmogorov-

SmirnovWald-Wolfowitz

Friedman two-

way ANOVA

Median

extension

Kruskal-Wallis

one-way ANOVA

Interval and

Ratio

t-test

Ztest

t-test for paired

samples

t-test

Ztest

Repeated-

measures ANOVA

One-way

ANOVA

n-way ANOVA

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Parametric Tests

t-testZ-test

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Non Parametric Tests

Chi square test

N

ominaldata