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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
Step 1: Which type of data do you have?
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
Step 1: Which type of data do you have?
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
Step 4: One Group, Two Groups, or More than Two Groups?
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
Step 4: One Group, Two Groups, or More than Two Groups?
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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