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1. Dr. S. Parthasarathy MD., DA., DNB, MD (Acu), Dip. Diab. DCA, Dip. Software statistics PhD (physio) Mahatma Gandhi medical college and research institute , puducherry – India Statistics made easy

2. Statistics -- data and ‘t’ test Don't worry

3. Data Type Examples • Interval 1, 2, 3, 4 • Constant interval, no zero point • Eg. Temperature airway pressure • Ordinal 1st, 3rd • Ranked eg, ASA, APGAR

4. Data Type Examples • Nominal scale • No numerical • but by quality • eg. Pseudocholinesterase types

5. Data Type Examples • Categorical—(binary) -- Male/female, alive/dead Yes/No • Categorical—(multiple) Red, green, blue

6. Parametric & • Nonparametric

7. Randomization • It prevents selection bias • insures against accidental bias. • It produces comparable groups,

8. Methods of randomization 1. Simple Randomization 2. Block Randomization 3. Stratified Randomization 4. Unequal Randomization

9. Select some Randomization to avoid bias

10. Central tendency 1.Mean • Age • 23 , 25 , 24, 23 , 23 • 23 + 25 + 24+ 23 + 23 = 23.6 5

11. 2.Mode • 23 , 25 , 24, 23 , 23 • Most frequent • 23

12. 3. Median 23 , 25 , 24, 23 , 23 Arrange in ascending order 23,23,23,24, 25. middle Mode is 23

13. Distribution of data • Healthy adults PaO2 • Eg. • 96 to 99 • Follow a bell shaped curve • Gaussian distribution

14. Normal distribution

15. Action of ephedrine • Alpha blocked persons • hypotension -12, -14,-10,-11 • Others • Hypertension • +12,+12,+10,+11 • Mean of all it is zero

16. Action of ephedrine • Conclusion • Ephedrine has no effect on BP ?? • See the curve , it is normal distribution?? • Naked eye

17. Deviation • 33,34,35,36,37 • Mean 35 • 25, 30, 35, 40, 45 • Mean 35

18. Variance • 33,34,35,36,37 • -2, -1, 0, +1, +2 • (Square all values above ) • 4+1+0+1+4 = 2 5 Mean square deviation = Variance

19. Std. deviation • Root mean square deviation • 68% of the data fall within 1 SD of the mean • 95% fall within 2 SD of the mean value. VARIANCE = SD2 • 95 %confidence interval = 1.96 SD

20. Std. deviation • PaCO2 • SD = 2.5 • Mean= 44 • 31.5 to 46.5 = 68 % • 39 to 49 = 95 %

21. Std error • Std deviation values • Sometimes like this • TFA = 495 ± 286 minutes • SE = SD / √ n • = 286 / √ 100 • = 286 / 10 = 28.6

22. Z value • Z = value – mean ---------------- SD • 1.96

23. Probability • P < 0.05 • The event occurs less frequently than once in twenty times • Probability of 5% • Probability of 1% = P < 0.01

24. Type of errors • Conclusion : • difference exists when there is nothing • Type 1 or Alpha error • How often can we be wrong?? • 5 % or less • α = 0.05 • Reject the null hypothesis when it is true

25. Type of errors • Type 2 • β error • Find out no difference when there is • Power of a test • Accept the null hypothesis when it is false • Sample size adequate to prevent errors

26. BP 120 ± 15 error = 6 • How to calculate sample size ?? • Error value d = 6 mm, • SD=15 mm Hg • Z alpha=1.96 • n > zα2 +SD2 d 2 1.96 2 + 15 2 = 24.01 • 62

27. Ponv = 60 % d = 10% of 60 % = 6 • n > Zα2 * P * Q • ----------------- • d 2 • 256.6

28. Sampling • Conclusion of a study : • Dose of thiopentone is high in Pondicherry • ???? • Chronic alcoholism ??

29. Appropriate statistics • Descriptive analysis • Our most general statistical goal is to describe our data set. • Put graphs , plots , • Mean ± SD • Is it looking for the naked eye??

30. Null hypothesis • states that there is no difference between two groups of data • H0 : μx= μy • PONV – perinorm Vs control • Reject the null hypothesis and prove the drug efficacy

31. t test or student t test • Gosset • Employer - Guinness brewing company • Not allowed • So student • Z value but for limited samples it increases

32. t test or student t test • Used to compare the means of two independent groups. • Usually normally distributed samples • Infinite – z value -- 1.96 is OK • But n = 20, then 2.05 is Z value • t distribution • n= 20, p <0.05,z =2.05

33. Paired t test • Same sample different values • 30 patients – baseline BP • Give propofol measure change in BP • Compare means to reject the null hypothesis • Apply t test (Paired t test) • Propofol decreased BP

34. Unpaired t test • Different samples • Eg. • 30 tonsilectomy – placebo • 30 tonsilectomy – ondansetron • Age, weight of patients compare means to accept null hypothesis • Means are similar

35. One and two tailed • Two tailed – • If you are using a significance level of 0.05, a two-tailed test allots half of your alpha to testing the statistical significance in one direction and half of your alpha to testing statistical significance in the other direction. .

36. This means that .025 is in each tail of the distribution of your test statistic. When using a two-tailed test, regardless of the direction of the relationship you hypothesize, you are testing for the possibility of the relationship in both directions • Two tailed image !!

37. Two tailed image !!

38. One tailed • significance level of .05, a one-tailed test allots all of your alpha to testing the statistical significance in the one direction of interest.  • Eg. • Propofol, ketamine on BP

39. One tailed

40. One sample and two sample t test • One sample means • Type of sample is same • Eg. • enalapril on potassium values in hypertensives

41. Two sample t test • Two different samples • Eg • Enalapril reduces BP • Diabetics and nondiabeticshow different

42. Nonparametric t test • Nonparametric data • Based on ranking • Non numerical ordinal • Also used if data deviate from normal distribution

43. Mann –Whitney U test • Unpaired samples • Assess ranks • For nonparametric data • Wilcoxon test • Paired samples • Assess ranks • For nonparametric data

44. ANOVA • Two sets of data • t test is ok • Eg. • Spinal bupi + fentanylVs Spinal bupi • H0 : μx= μy =μn= μz • But three or more what to do?? • Spinal bupi • Vs Spinal bupi + fentanyl (10 μg) • Vs Spinal bupi + fentanyl (25 μg)

45. Analysis of variance (ANOVA) • F = between group variance /within group variance • 5 % DEVIATION FOR THREE OR MORE GROUPS MAY BE SOME 20 % • t test with bonferroni correction is acceptable

46. ANOVA -Parametric data • 1.One way analysis of variance • 2.Repeated measures (paired )ANOVA

47. Nonparametric data • Kruskal Wallis • Two groups • Friedman test • Repeated measures

48. Proportions • Eg. • Post op pain relief after spinal clonidine • Group 1 (clonidine) • 8 out of 25 received ketoroloc as rescue analgesia • Group 2 (control) • 15 out of 25 received ketoroloc as rescue analgesia