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## T - test

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**t-test**M.Prasad Naidu MSc Medical Biochemistry, Ph.D,.**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 doesdifferencemean?**The mean difference is the same for all three cases medium variability high variability low variability Slide downloaded from the Internet**What doesdifferencemean?**medium variability high variability Which one shows the greatest difference? low variability Slide downloaded from the Internet**What doesdifferencemean?**• a statistical difference is a function of the difference between meansrelative 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**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**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 0.05 100 110 120 130 140**Mean systolic BP in nephritis is significantly**different from that of normal person 0.025 0.025 100 110 120 130 140 Slide downloaded from the Internet**Assumptions**• Normal distribution • Equal variance • Random sampling**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)

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