Hypothesis N Testing.ppt (1)

8/2/2019 Hypothesis N Testing.ppt (1)

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Specialization Project

MMS Semester-IV


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Topics

How to Select the Test

Steps for Hypothesis Testing


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Hypothesis

A hypothesis is a proposition that is empiricallytestable.

Its an empirical statement concerned with avariables.


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How To Select Test

Step 1: Which type of data do you have?

When you are determining which type of data you have, remember that

you are looking at the Dependent Variable, or in other words, the

variable that measures the difference (or the relationship for

correlations).

For example, if you are

looking at the difference between men and women in how well they

scored on the SATs, their score on the SAT is the dependent variablebecause it is the one that you are measuring in order to determine if

there is a difference.


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How To Select Test


Nominal Data: Numbers or words that are used merely as labels.

Some examples of nominal data are types of religion (Christian,

Catholic, Jewish, etc.). Note that these cannot be ranked in any logical

order.

Ordinal Data: Numbers (or words, but usually numbers) that can be

rank ordered or scaled. Some examples of ordinal data are the placefinished in a race (1st, 2nd, 3rd, etc.), degrees of happiness (sad, neutral,

happy).

.


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How To Select Test


Numeric Data: Numbers that can be rank ordered or scaled, that do

express a degree of magnitude, that have consistent intervals. Some

examples of numeric data are test scores, time, and height. Note that

with the numeric data of time, 40 minutes is twice as much as 20

minutes, and that the amount of time between 20 to 40 minutes is the

same amount of time as the amount of time between 40 and 60 minutes.


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How To Select Test

Step 2: What are you looking for?

Differences: If you are trying to determine if one group is different, greaterthan, or less than another group. For example, are men taller than women?

Correlations : If you are trying to determine if there is a relationshipbetween one variable and another. For example, does alcohol consumption

increase as unemployment rates increase?

Regressions : If you are trying to determine if one variable can accurately

predict another variable. For example, can the amount of rainfall predict theamount of mud slides?

Note : for Correlation and Regression one need not to take step 3 and 4.


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How To Select Test

Step 3: Between Groups or Within Groups? (aka IndependentGroups or Correlated Groups)

Between (aka Independent) Groups: When each participant is in only one of

the groups. For example, when comparing men and women, a man would not bein both groups. Thus, you are testing two (or more) different groups of people.

Within (aka Correlated) Groups: When each participant is in all of the groups.

For example, giving exams to a group of people on three separate occasions and

comparing their scores on the three different exams (here the three groupswould be the three test scores). Thus, you are comparing the same group of

people at three different times.


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How To Select Test

Step 4: One Group, Two Groups, or More than Two Groups?

Remember that you are looking at the Independent Variable when you are

determining how many groups your variable has.

One Group: If you are comparing the distribution of one group of people to

a hypothetical or actual population distribution. For example, comparing the

ethnic distribution of the Claremont Colleges with the ethnic distribution of

the USA.


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How To Select Test


Two Groups:

For between (aka independent) groups: If you are comparing one group of

people to another. For example, comparing men and women.

For within (aka correlated) groups: If you are comparing the same group of

peoples test scores on two separate occasions.


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How To Select Test


More than Two Groups:

For between (aka independent) groups: If you are comparingmore than two groups. For example, comparing students from

Delhi, Bangalore, Chennai and Punjab University .

For within (aka correlated) groups: If you are comparing thesame group ofpeoples test scores on more than two occasions.


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How To Select Test


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Step 1: Set null and alternative hypothesis

Step 2: Determine the appropriate statistical test

Step 3: Set the level of significance

Step 4: Set the decision rule

Step 5: Collect the sample data

Step 6: Analyse the data

Step 7: Arrive at a statistical conclusion and

business implication

Seven Steps of Hypothesis Testing


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Hypothesis Testing

Null Hypothesis: The null hypothesis, denoted by H0, is

usually the hypothesis that sample observations result purely

from chance.

Alternative Hypothesis: The alternative hypothesis, denoted

by H1 or Ha, is the hypothesis that sample observations are

influenced by some non-random cause.


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Measurement Scale One Sample Case

Nominal Binomial

Chi square one-sample test

Ordinal Kolmogrov-Smirnov one sample test

Runs test

Interval and Ratio t-test

z- test

One Sample Case


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Measurement

Scale

Related

Samples

Independent Samples Related

Samples

Nominal Mc Nemar Fisher exact test

Chi square two-sample test

Cochran Q

Ordinal Sign Test

Wilcoxon

matched pairs

test

Median test

Mann- Whitney U

Kolmogrov-Smirnov

Wald- Wolfowitz

Friedman

Two-way

ANOVA

Interval and

Ratio

t-test for paired

samples

t-test

z- test

Repeated-

measuresANOVA

Two Sample Tests


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Measurement Scale One Sample Case

Nominal Chi square for k samples

Ordinal Median Extension

Kruskal-Wallis one-way ANOVA

Interval and Ratio One-way ANOVA

n-way ANOVA

k-Sample Tests


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Set the Level of Significance

Level of Significance is denoted by .

It is also known as size of rejection area or the size of the

critical region.

The levels of significance which are generally applied by the

researchers are 0.01,0.05,0.10.


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Set the Decision Rule

Critical region, is the area under the normal curve, divided

into two mutually exclusive regions.

These regions are termed as acceptance region when the nullhypothesis is accepted, and the rejection region when the null

hypothesis is rejected.

If the computed value of the test statistics falls in the

acceptance region, the null hypothesis is accepted or otherwise

it is rejected.


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Acceptance and Rejection Regions for Null

Hypothesis

Rejection region, /2 (H0 is rejected)

Acceptance region (1-)

(H0 is accepted)

Critical values

-z +z/2 /2


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Collect the Sample Data

In this stage sampling, data are collected and appropriate

sample statistics are computed.

It is advisable to decide on the stages of hypothesis testing and

then collect the data.


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Analyse the Data

In this stage the researcher compute the test statistic.

This involves the selection of an appropriate probability

distribution for a particular test.

The most commonly used test are t test, z test, F test and chi

square test.


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Statistical Conclusion and Business Implication

In this stage the researcher draw a statistical conclusion. It is a

decision to accept or reject the hypothesis.

This depends on whether the computed test statistics falls in the

acceptance region or the rejection region.

If we test a hypothesis at 5% level of significance and the observed

set of the results have a probability of less than 5% it means that the

difference between sample statistical and hypothesized population

parameter as significant . In this situation researcher rejects null

hypothesis and accepts the alternate hypothesis.

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Hypothesis N Testing.ppt (1)