comparing two populations (seminar 5)
TRANSCRIPT
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Assoc. Prof. Dr. Nagarajah Lee
Open University Malaysia
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Example 1 : SurveyExample 1 : Survey
The researcher would like to test
students is significantly differentrom e ema e.
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Describing the samplesDescribing the samples
Can we conclude that the mean EQ score of the
What is the suitable test to check for this?
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Purpose To compare differences between two populations
Commonly Used Two Sample Test in Behavioral Science and Medical Research
Number ofDependent Variable
Number of cate ories
measurement ofdependentvariables
Interval/Ratio
One One
Nominal Ordinal
One
for comparing
Unit of analysis
Two or More
Proportion Median or Mean Rank
Mean
Requirement Frequency per cellMore than 5
Chi-
Test
Wilc
o
rank
Inde
Test
Paire
d
Fish
Test
Frequency per cellLess than 5
Relatedsample
Unrelatedsample
Mann
Test
Related Sample Unrelated Sample
Statist ical t est
quare
on
Sign
est
pen
den
tT-
TT
est
rsEx
act
Whitn
eyU
Example Testing whether the there is any difference
in percentage of low birth weight amongsmoking and non-smoking mothers
Testing whether there is any differencein the median values or mean ranks
between two groups
Testing whether there is any difference in the
mean values between two groups
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NORMALITY ASSUMPTION CHECKNORMALITY ASSUMPTION CHECK
NORMALITY:
Ho: The data comes from a normally distributed populationH1: The data does not come from a normally distributed population
Result: Since the p-value > .05, the null hypothesis is not rejected.
Conclusion: The assumption of normality holds.
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TESTING A POPULATION MEANTESTING A POPULATION MEAN
Hypothesis:
Ho: There is no difference in the mean EQ score between
male and female MEd students.
H1: There is a signif icant dif ference in the mean EQ score
between male and female MEd students.
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Analyze >> Compare means >>Independent t-test
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TEST FOR A SIGNIFICANT DIFFERENCE IN MEANTEST FOR A SIGNIFICANT DIFFERENCE IN MEAN
Result: Since the p-value > 0.05, the null hypothesis is NOT rejected.
Conclusion: There is not enough evidence to conclude that there is a
significant difference in the mean EQ scores between male and female MEdstudents.
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Example 2 : MedicalExample 2 : Medical
A st u d y w as ca r r i ed o u t t o d et er m i n e w h e th e r
pa r t i cu la r d r ug . The depend en t va r iab le is t hen u m b er o f t r i a l s r e q u i r ed t o m ast er a g iv enas .
A g roup o f 28 sub j ect s w ere random ly assigned.assigned t o t h e exp e r im en t a l g r oup w ere g i vent he d ru g , and t hose assigned t o t he con t ro l
g r oup w ere g i ven p lacebo. A f te r a g i ven pe r i odo f t i m e, t h e n u m b er s o f t r i al s t o m ast er t h et ask w e re reco rded .
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Experimental Group Cont rol Group
17 14
15
5
14
10
1
12
1
2
16
11
14
8
DATA SET
13
15
16
10
2
12
178
19
112
15
4
12
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Describing the samplesDescribing the samples
Can we conclude that the response time of thetreatment and control groups are significantlydifferent?
What is the suitable test to check for this?
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Purpose To compare differences between two populations
Commonly Used Two Sample Test in Medical Research
Number ofDependent Variable
measurement ofdependentvariables
Interval/Ratio
One One
Nominal Ordinal
One
Number of categoriesfor comparing
Unit of analysis
Two or More
Proportion Median or Mean Rank
Mean
Requirement Frequency per cellMore than 5
Chi-
Test
Wilc
o
rank
Inde
Test
Paire
d
Fish
Test
Frequency per cellLess than 5
Relatedsample
Unrelatedsample
Mann
Test
Related Sample Unrelated Sample
Statist ical t est
quare
on
Sign
est
pen
den
tT-
TT
est
rsEx
act
Whitn
eyU
Example Testing whether the there is any difference
in percentage of low birth weight amongsmoking and non-smoking mothers
Testing whether there is any differencein the median values or mean ranks
between two groups
Testing whether there is any difference in the
mean values between two groups
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NORMALITY ASSUMPTION CHECKNORMALITY ASSUMPTION CHECK
H0 : The data comes from a normally distributed population.
H1 : The data does not come from a normally distributed.
Refer to Shapiro-Wilk statistic, the significance level issmaller than .05, so reject H0.
Conclusion : The data does not come from a normallydistributed population.
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Purpose To compare differences between two populations
Commonly Used Two Sample Test in Medical Research
Number ofDependent Variable
measurement ofdependentvariables
Interval/Ratio
One One
Nominal Ordinal
One
Number of categoriesfor comparing
Unit of analysis
Two or More
Proportion Median or Mean Rank
Mean
Requirement Frequency per cellMore than 5
Chi-
Test
Wilco
rank
Inde
Test
Paire
d
Fish
Test
Frequency per cellLess than 5
Relatedsample
Unrelatedsample
Mann
Test
Related Sample Unrelated Sample
Statist ical t est
quare
on
Sign
est
pen
den
tT-
TT
est
rsEx
act
Whitn
eyU
Example Testing whether the there is any difference
in percentage of low birth weight amongsmoking and non-smoking mothers
Testing whether there is any differencein the median values or mean ranks
between two groups
Testing whether there is any difference in the
mean values between two groups
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TESTING A POPULATION MEANTESTING A POPULATION MEAN
H0 : The drug has no effect on the number of trials.
H1 : The drug has an effect on the number of.
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Analyze >> Non-parametric tests
>> 2- Independent test
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ResultsResults
Result: Since the p-value < 0.05, the null hypothesis is rejected.
Conclusion: There is enough evidence to conclude that the drug has an
effect on the number of trials needed to master the task
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Example 3Example 3
A r esear ch e r w o u l d l i k e t o t est w h e th e r t h e r e i s
any d i f f e rence in pa t i en t s hea r t beat w henn u t r i en t A is g i v en i n t h r ee m eal s d u r i n g t h e
( t r e at m en t Y) .
A random sam p le o f 12 pa t i en t s w as chosen .Th e t w o t r e at m en t s w er e ad m i n ist er e d o n t w o
succeed in g occasions and pa t ien t s hear t bea tp er m i n u t e w er e r eco r d e d.
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Heartbeat per minuteHeartbeat per minute
1 62 54
2 55 63
3 80 1094 66 75
5 84 80
6 88 827 90 77
8 52 89
9 63 6610 58 71
11 73 69
12 67 81
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Purpose To compare differences between two populations
Commonly Used Two Sample Test in Medical Research
Number ofDependent Variable
Number of cate ories
measurement ofdependentvariables
Interval/Ratio
One One
Nominal Ordinal
One
for comparing
Unit of analysis
Two or More
Proportion Median or Mean Rank
Mean
Requirement Frequency per cellMore than 5
Chi-
Test
Wilco
rank
Inde
Test
Paire
d
Fish
Test
Frequency per cellLess than 5
Relatedsample
Unrelatedsample
Mann
Test
Related Sample Unrelated Sample
Statist ical t est
quare
on
Sign
est
pen
den
tT-
TT
est
rsEx
act
Whitn
eyU
Example Testing whether the there is any difference
in percentage of low birth weight amongsmoking and non-smoking mothers
Testing whether there is any differencein the median values or mean ranks
between two groups
Testing whether there is any difference in the
mean values between two groups
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Test of Normalit yTest of Normalit y
0
population.
distributed population.
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OUTPUT
-level is greater than .05, so do not reject H0.
Conclusion : The data comes from a normallydistributed population.
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Pai r ed t t estPai r ed t t est
H0 : There is no significant difference in the heartbeatrate between patients given nutrient A in 3 mealsduring the day and patients given nutrient A in onemeal.
H1 : There is a significant difference in the heartbeat
during the day and patients given nutrient A in onemeal.
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Resu l ts
From the table, the significance value is 0.165 (2-tailed). The
si nificance level is reater than 0.05 so do not re ect H .
Conclusion : There is no significant difference in theheartbeat rate between patients given nutrient A in 3 meals
during the day and patients given nutrient A in one meal.
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Example 4Example 4
response time is influenced by taking a particulardrug. The dependent variable is the number of trialsrequ re o mas er a g ven as .
A group of 28 subjects were randomly assigned to.
to the experimental group were given the drug, andthose assigned to the control group were given
p ace o. ter a g ven per o o t me, t e num ers otrials to master the task were recorded andcate orized as less than 10 times or 10 times andabove.
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Groups * TRIAL_C Crosstabulation
TRIAL_C
4 9 13
30.8% 69.2% 100.0%
Count% within Groups
experimental groupGroups
10 times
or more Total
46.7% 53.3% 100.0%
11 17 28
39.3% 60.7% 100.0%
% within Groups
Count
% within Groups
Total
Can we conclude that the response time of thetreatment and control groups are significantlydifferent?
What is the suitable test to check for this?
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Purpose To compare differences between two populations
Commonly Used Two Sample Test in Medical Research
Number ofDependent Variable
Number of cate ories
measurement ofdependentvariables
Interval/Ratio
One One
Nominal Ordinal
One
for comparing
Unit of analysis
Two or More
Proportion Median or Mean Rank
Mean
Requirement Frequency per cellMore than 5
Chi-
Test
Wilc
o
rank
Inde
Test
Paired
Fish
Test
Frequency per cellLess than 5
Relatedsample
Unrelatedsample
Mann
Test
Related Sample Unrelated Sample
Statist ical t est
quare
on
Sign
est
pen
den
tT-
TT
est
rsEx
act
Whitn
eyU
Example Testing whether the there is any difference
in percentage of low birth weight amongsmoking and non-smoking mothers
Testing whether there is any differencein the median values or mean ranks
between two groups
Testing whether there is any difference in the
mean values between two groups
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Ch iChi-- Sq u ar e TestSq u ar e Test
H0 : Treatment with the drug has no effect on the.
H1
: Treatment with the drug has an effect on the.
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Analyze >> Descriptive Statistics >> Cross Tab
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OutputOutput
Groups * TRIAL_C Crosstabulation
less than
10 times
10 times
or more
TRIAL_C
Total
30.8% 69.2% 100.0%
7 8 1546.7% 53.3% 100.0%
11 17 28
oun
% within Groups
Count% within Groups
Count
exper men a group
control group
roups
Total
. . .
Chi-S uare Tests
.738b 1 .390
.222 1 .638
.745 1 .388
Pearson Chi-Square
Continuity Correctiona
Likelihood Ratio
Value df
Asymp. Sig.
(2-sided)
Exact Sig.
(2-sided)
Exact Sig.
(1-sided)
.460 .320.712 1 .399
28
Fisher's Exact Test
Linear-by-Linear
Association
N of Valid Cases
Computed only for a 2x2 tablea.
0 cells (.0%) have expected count less than 5. The minimum expected count is
5.11.
b.
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nce one o e ce s as ess en o serva ons,to interpret the output from the Ch-Square test,consider the -value re orted b the Fishers ExactTest
From the table, the p-value is 0.460(2-tailed). Thesignificance level is greater than 0.05, so DO NOTreject H0.
onc us on : rea men w e rug as no e econ the trials needed to master the task
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