Post on 19-Feb-2018
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HYPOTHESIS TESTING
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What is Hypothesis?
Is a statement about a population developedfor the purpose of testing.
In most cases the population is too large that
it is not feasible to study all items in thepopulation.
We can, therefore, test a statement todetermine whether the sample does or does
not support the statement concerning thepopulation.
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SIGNIFICANCE
When we make quantitative judgments, orhypotheses, about situations, we are either right
or wrong.
However, if we are wrong we may not be far
from the real figure or that is our judgment isnot significantly different. Thus our hypotheses
may be acceptable.
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Example
contractor says that it will take ! months toconstruct a house for a client. The house is
finished in ! months and " week. The
completion time is not ! months however it is
not significantly different.
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STATISTICAL SIGNIFICANCE
Significance is typically designated with words such assignificance, statistical significance, or
probability.
The latter word is the source of the letter that
represents significance, the letter p.
The p value identifies the lielihood that a particular
outcome may have occurred by chance.
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Example: ! group A may score an
average of "# on a scale of depression while group B
scores $% on the same scale.
If a Ttest determines that group ! differs from group& at a p ' .(% level of significance, it may be
concluded that there is a % in %(( probability that the
resulting difference happened by chance, and a )) in
%(( probability that the discrepancy in scores is areliable finding.
The smaller the value the greater confidence the
researcher has that his or her findings are valid.
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Null Hypotheses
The first step is to state the hypothesis being tested. Itis called the null hypothesis, designated *+o
There is usually a not or a no term in the null
hypothesis, meaning that there is no change.
-or eample, the null hypothesis is that the number ofmiles driven on the steel/belted tire is not different
from 0(,(((.
Therefore, Ho: = 60,000.
We either re1ect or fail to re1ect the null hypothesis.
The null hypothesis is a statement that is not re1ected
unless our sample data provide convincing evidence
that it is false.
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Alte!ate Hypotheses
The alternate hypothesis describes what you will
conclude if you re1ect the null hypothesis. It iswritten as +2.. It is also called the researchhypothesis.
The alternate hypothesis is accepted if the sampledata provide us with enough statistical evidence that
the null hypothesis is false.
! recent article indicated that the mean age of 3.S.
commercial aircraft is %4 years.
The null hypothesis represents the current or reportedcondition.
+o5 6 ' %4.
The alternate hypothesis is that the statement is not
true5 +%5 6 7%4.
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The t " Test Po#e$ue
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#ndependent $ %amples t Tests
&aired %amples t Tests
'ne %ample t Tests
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I!$epe!$e!t " Samples tTests
8ompares the means of two different samples.
The two samples share some variable of interest in
common.
&usiness analyst may want to find out the differencebetween the ependiture patterns of the two different
geographical regions.
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Example:
The trade show &ureau conducted a survey todetermine why people go to trade shows.
The respondents were ased to rate a series of a
reasons on a scale from % to 4.
% ' little importance
4 ' great importance
9ne of the reasons suggested was general curiosity.
The following responses for 4( people from the
computers:electronics industry and 4( people from
food: beverage industry were recorded.
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Determine whether there is a signifcantdierence between people in these twoindustries on this question
Computers/Electronics
" ( " ) (
) ) ( * )
) ) " ( (
) ( ) ( )
" ( ) ( "( * ( ) )
( " * " *
) + ) ) (
) ) ( ( )
* ) ) ( )
Food/Beverage
" ) ) ( "
* + ( * )
) ( ( ( (
* ) ) ) )
" " ) ) (
( * * * *
( ) " " "
( " ( ( +
( " " ( )
* ) ) ) (
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Ni%e Case
In a pretest data on ;ie were obtained from $4respondents. These data were given in the S
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Paie$ Samples t & Test
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Health Spa
! health spa in a town advertises a combined fitnessand diet programme where it guarantees that
participants who are overweight will definitely loose
a significant amount of weight if they scrupulously
follow the course. The weights of all participants in the programme are
recorded each time they come to the spa.
The authorities are somewhat scepitical of the
advertising claim so they select at random%" of the
regular participants and they recorded weights in
ilograms before and after 0 months in the
programme.
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'i(ai!e Hea$a#hes
>igraine headaches are not uncommon. They beginwith blurred vision either in one or both eyes and
then are often followed by severe headaches.
There are medicines available but their efficiency is
often ?uestioned. Studies have indicated thatmigraine is caused by stress, drining too much
coffee, or consuming too much sugar.
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! study was made on %( volunteer patients whowere nown to be migraine sufferers.
These patients were first ased to record over a si
month period the number of migraine headachesthey eperienced. This was then calculated into theaverage number per month.
Then they were ased to stop coffee for " months
and record again the number of migraine attacsthey eperienced. This again was reduced tomonthly basis.
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O!e Sample t & test
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O!e Sample t & test
It is designed to test whether the mean of adistribution differs significantly from some present
value.
@id the performance of a particular class differ
significantly from the professorAs goal of an B=CaverageD
Lower Tail Test Upper Tail Test
+o5 6 E 6o +o5 6 F 6o+%5 6 G 6o +%5 6 H 6o
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Waiti!( Time Case
The &an manager has to develop a new system toreduce the time customers spend waiting for teller
service during pea hours.
The manager hopes the new system will reduce
waiting times from the current ) to %( minutes toless than 0 minutes.
Suppose the manager wishes to use the random
sample of %(( waiting times to support the claim
that the mean waiting time under the new system is
shorter than si minutes.
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Example
! soft drin company produces = liters bottles of oneof its popular drins. The ?uality control department
is responsible for verifying that each bottle contains
eactly two liters of soft drins.
@ata in S
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ANO)A
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ANO)A
nalysis of variance or '- is a technique oftesting hypothesis about the significant
differences in several population means.
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Tea#hi!( 'etho$s
Imagine a professor was interested in how differentteaching methods affected students knowledge.
He noticed that some professors were aloof and
arrogant in their teaching style and humiliated
anyone who asked them a question, while otherswere encouraging and supporting of questions and
comments.
The professor took three statistics courses and taught
the same material.
For one group of students he wandered around with
a large cane and beat anyone who asked draft
questions or got questions wrong (punish).
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In the second group he used his normal teachingstyles, which is to encourage students to discuss
things that they find difficult and to give anyone
working hard a nice sweet reward (reward).
The final group he remained indifferent to andneither punished or nor rewarded students efforts
(indifferent).
As the dependent measure he took students exam
marks.
Use ANOVA to test whether the three teaching styles
are significantly different.
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Foei(! Ta*el
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Thanks