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

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?

mediumvariability

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?

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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

So we estimateSo we estimate

lowvariability

signal

noise

difference between group means

variability 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 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

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

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

AssumptionsAssumptions

Normal distributionNormal distribution

Equal varianceEqual variance

Random samplingRandom sampling

Otherwise prop-up dataOtherwise prop-up data

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

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)

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

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)