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? Slide downloaded from the Internet

What does difference mean? medium variability high variability low variability The mean difference is the same for all three cases Slide downloaded from the Internet

What does difference mean? medium variability high variability low variability Which one shows the greatest difference? Slide downloaded from the Internet

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? Slide downloaded from the Internet

So we estimate low variability signal noise difference between group means variability of groups = X T - X C SE(X T - X C ) = = t-value __ __ Slide downloaded from the Internet

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

Mean systolic BP in nephritis is significantly different from that of normal person Mean systolic BP in nephritis is significantly different from that of normal person Slide downloaded from the Internet

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 Truth 1 – Truth 2 SE (T 1 – T 2 )