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t test-origint test-origin
Founder WS GossetFounder WS Gosset
Wrote under the pseudonym “Student”Wrote under the pseudonym “Student”
Mostly worked in tea (t) timeMostly worked in tea (t) time
? Hence known as Student's ? Hence known as Student's t t test. test.
Preferable when the n < 60Preferable when the n < 60
Certainly if n Certainly if n << 30 30
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Is there a difference?Is there a difference?
between you…means,
who is meaner?
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Statistical AnalysisStatistical Analysis
controlgroupmean
treatmentgroupmean
Is there a difference?
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What doesWhat does differencedifference mean?mean?
mediumvariability
highvariability
lowvariability
The mean differenceis the same for all
three cases
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What doesWhat does differencedifference mean?mean?
mediumvariability
highvariability
lowvariability
Which one showsthe greatestdifference?
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What doesWhat does differencedifference mean?mean?
a statistical difference is a function of the a statistical difference is a function of the difference between meansdifference between means relative to the relative to the variabilityvariabilitya small difference between means with a small difference between means with large variability could be due to large variability could be due to chancechancelike a like a signal-to-noisesignal-to-noise ratio ratio
lowvariability
Which one showsthe greatestdifference?
Slide downloaded from the Internet
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So we estimateSo we estimate
lowvariability
signal
noise
difference between group means
variability of groups=
XT - XC
SE(XT - XC)=
= t-value
_ _
_ _
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Probability - pProbability - pWith t we check the probability With t we check the probability
Reject or do not reject Null hypothesisReject or do not reject Null hypothesis
You reject if p < 0.05 or still lessYou reject if p < 0.05 or still less
Difference between means (groups) is Difference between means (groups) is more & more significant if p is less & lessmore & more significant if p is less & less
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TypesTypes
One sample One sample compare with populationcompare with population
UnpairedUnpairedcompare with controlcompare with control
PairedPairedsame subjects: pre-postsame subjects: pre-post
Z-test Z-test large samples >60large samples >60
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Test directionTest direction
One tailed t testOne tailed t test
Two tailed testTwo tailed test
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Mean systolic BP in nephritis is significantly Mean systolic BP in nephritis is significantly higher than of normal personhigher than of normal person
100 110 120 130 140
0.050.05
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Mean systolic BP in nephritis is significantly Mean systolic BP in nephritis is significantly different from that of normal person different from that of normal person
0.025 0.025
100 110 120 130 140
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AssumptionsAssumptions
Normal distributionNormal distribution
Equal varianceEqual variance
Random samplingRandom sampling
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Otherwise prop-up dataOtherwise prop-up data
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SolutionsSolutions
Normalize the data – log conversionNormalize the data – log conversion
Use other testsUse other tests
- Welch test- Welch test
- Cochrane’s modified t test- Cochrane’s modified t test
Use non-parametric testUse non-parametric test
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Limitations - generalLimitations - general
Fails to gauge magnitude of difference Fails to gauge magnitude of difference
between two meansbetween two means
(solution- do CI)(solution- do CI)
Only compares 2 groupsOnly compares 2 groups
(solution- if> than 2 groups – ANOVA)(solution- if> than 2 groups – ANOVA)
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Limitations – paired t testLimitations – paired t test
Doesn’t control a No. of other variables Doesn’t control a No. of other variables in a simple pre-post designin a simple pre-post design
In many studies pre-test not possibleIn many studies pre-test not possible
- mortality - mortality studiesstudies
With-in subject variation is introduced With-in subject variation is introduced twicetwice
- e.g. in pain - e.g. in pain ratings ratings
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Hope! now your view on Hope! now your view on statistics statistics
should have changed…should have changed… It is It is nothing but nothing but
TruthTruth1 – 1 – TruthTruth22
SE (T1 – T2)