t-test t-test M.Prasad NaiduM.Prasad Naidu
MSc Medical Biochemistry, MSc Medical Biochemistry, Ph.D,.Ph.D,.
t test-origint test-originFounder WS GossetFounder WS GossetWrote 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 < 60Certainly if n Certainly if n << 30 30
Is there a difference?Is there a difference?
between you…means,
who is meaner?
Statistical AnalysisStatistical Analysis
controlgroupmean
treatmentgroupmean
Is there a difference?Slide downloaded from the Internet
What doesWhat does differencedifference mean?mean?medium
variability
highvariability
lowvariability
The mean differenceis the same for all
three cases
Slide downloaded from the Internet
What doesWhat does differencedifference mean?mean?
mediumvariability
highvariability
lowvariability
Which one showsthe greatestdifference?
Slide downloaded from the Internet
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
So we estimateSo we estimate
lowvariability
signalnoise
difference between group meansvariability of groups=
XT - XC
SE(XT - XC)=
= t-value
_ __ _
Slide downloaded from the Internet
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 hypothesisYou reject if p < 0.05 or still lessYou reject if p < 0.05 or still lessDifference between means (groups) is Difference between means (groups) is more & more significant if p is less & lessmore & more significant if p is less & less
TypesTypesOne sample One sample
compare with populationcompare with populationUnpairedUnpaired
compare with controlcompare with controlPairedPaired
same subjects: pre-postsame subjects: pre-postZ-test Z-test
large samples >60large samples >60
Test directionTest direction
One tailed t testOne tailed t test
Two tailed testTwo tailed test
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
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
Slide downloaded from the Internet
AssumptionsAssumptionsNormal distributionNormal distribution
Equal varianceEqual variance
Random samplingRandom sampling
Otherwise prop-up dataOtherwise prop-up data
SolutionsSolutions
Normalize the data – log conversionNormalize the data – log conversionUse 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
Limitations - generalLimitations - generalFails 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)
Limitations – paired t testLimitations – paired t testDoesn’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 designIn 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
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)
THANK YOUTHANK YOU