Title: T-test
1t-test
- M.Prasad Naidu
- MSc Medical Biochemistry, Ph.D,.
2t 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
3Is there a difference?
between youmeans, who is meaner?
4Statistical Analysis
control group mean
treatment group mean
Is there a difference?
Slide downloaded from the Internet
5What does difference mean?
The mean difference is the same for all three
cases
medium variability
high variability
low variability
Slide downloaded from the Internet
6What does difference mean?
medium variability
high variability
Which one shows the greatest difference?
low variability
Slide downloaded from the Internet
7What 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
8So 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
9Probability - 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 -
10Types
- One sample
- compare with population
- Unpaired
- compare with control
- Paired
- same subjects pre-post
- Z-test
- large samples gt60
11Test direction
- One tailed t test
- Two tailed test
12Mean systolic BP in nephritis is significantly
higher than of normal person
0.05
100 110 120 130 140
13 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
14Assumptions
- Normal distribution
- Equal variance
- Random sampling
15Otherwise prop-up data
16Solutions
- Normalize the data log conversion
- Use other tests
- - Welch test
- - Cochranes modified t test
- Use non-parametric test
17Limitations - general
- Fails to gauge magnitude of difference
- between two means
- (solution- do CI)
- Only compares 2 groups
- (solution- ifgt than 2 groups ANOVA)
18Limitations 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
19- Hope! now your view on statistics
- should have changed It is nothing but
- Truth1 Truth2
- SE (T1 T2)
20THANK YOU