Transcript Null hypothesis

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 < 60
Certainly if n < 30
Is there a difference?
between you…means,
who is meaner?
Statistical Analysis
control
group
mean
treatment
group
mean
Is there a difference?
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What does difference mean?
medium
variability
The mean difference
is the same for all
three cases
high
variability
low
variability
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What does difference mean?
medium
variability
high
variability
low
variability
Which one shows
the greatest
difference?
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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
low
variability
Which one shows
the greatest
difference?
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So we estimate
signal
noise
=
=
=
difference between group means
variability of groups
_ _
XT - XC
_ _
SE(XT - XC)
t-value
low
variability
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Probability - p
With t we check the probability
Reject or do not reject Null hypothesis
You reject if p < 0.05 or still less
Difference between means (groups) is
more & more significant if p is less &
less
Types
One sample
compare with population
Unpaired
compare with control
Paired
same subjects: pre-post
Z-test
large samples >60
Test direction
One tailed t test
Two tailed test
Mean systolic BP in nephritis is significantly
higher than of normal person
100
110
120
130
140
Mean systolic BP in nephritis is significantly
different from that of normal person
0.025
0.025
100
110
120
130
140
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Assumptions
Normal distribution
Equal variance
Random sampling
Otherwise prop-up data
Solutions
Normalize the data – log conversion
Use other tests
- Welch test
- Cochrane’s modified t test
Use non-parametric test
Limitations - general
Fails to gauge magnitude of difference
between two means
(solution- do CI)
Only compares 2 groups
(solution- if> than 2 groups – ANOVA)
Limitations – paired t test
Doesn’t 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
Hope! now your view on
statistics
should have changed… It is
nothing but
Truth1 – Truth2
SE (T1 – T2)