t test-origin

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t test-origin

• Founder WS Gosset
• Wrote under the pseudonym Student
• Mostly worked in tea (t) time
• ? Hence known as Student's t test.
• Preferable when the n lt 60
• Certainly if n lt 30

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Is there a difference?
between youmeans, who is meaner?
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Statistical Analysis
control group mean
treatment group mean
Is there a difference?
Slide downloaded from the Internet
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What does difference mean?
The mean difference is the same for all three
cases
medium variability
high variability
low variability
Slide downloaded from the Internet
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What does difference mean?
medium variability
high variability
Which one shows the greatest difference?
low variability
Slide downloaded from the Internet
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What does difference mean?

• a statistical difference is a function of the
  difference between means relative to the
  variability
• a small difference between means with large
  variability could be due to chance
• like a signal-to-noise ratio

Which one shows the greatest difference?
low variability
Slide downloaded from the Internet
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So we estimate
signal
difference between group means

noise
variability of groups
_
_
XT - XC
_
_

SE(XT - XC)

t-value
low variability
Slide downloaded from the Internet
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Probability - p

• With t we check the probability
• Reject or do not reject Null hypothesis
• You reject if p lt 0.05 or still less
• Difference between means (groups) is more more
  significant if p is less less

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Types

• One sample
• compare with population
• Unpaired
• compare with control
• Paired
• same subjects pre-post
• Z-test
• large samples gt60

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Test direction

• One tailed t test
• Two tailed test

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Mean systolic BP in nephritis is significantly
higher than of normal person
0.05
100 110 120 130 140
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Mean systolic BP in nephritis is significantly
different from that of normal person
0.025
0.025
100 110 120 130 140
Slide downloaded from the Internet
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Assumptions

• Normal distribution
• Equal variance
• Random sampling

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Otherwise prop-up data
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Solutions

• Normalize the data log conversion
• Use other tests
• - Welch test
• - Cochranes modified t test
• Use non-parametric test

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Limitations - general

• Fails to gauge magnitude of difference
• between two means
• (solution- do CI)
• Only compares 2 groups
• (solution- ifgt than 2 groups ANOVA)

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Limitations paired t test

• Doesnt control a No. of other variables in a
  simple pre-post design
• In many studies pre-test not possible
• - mortality studies
• With-in subject variation is introduced twice
• - e.g. in pain ratings

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• Hope! now your view on statistics
• should have changed It is nothing but
• Truth1 Truth2
• SE (T1 T2)