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# Basic Statistics

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1. Basic Statistics

2. “I always find that statistics are hard to swallow and impossible to digest. The only one I can remember is that if all the people who go to sleep in church were laid end to end they would be a lot more comfortable.” [Mrs Robert A Taft]

3. “Data! Data! Data!”he cried impatiently.“I can’t make bricks without clay” [Sherlock Holmes]

4. Qualitative a) Nominal data (dead/alive, blood group O,A,B,AB) b) Ordered categorical/ranked data (mild/moderate/severe)

5. Quantitative a) Numerical discrete (no. of deaths in a hospital per year) b) Numerical continuous (age, weight, blood pressure)

6. Presenting data • Graphs • Summary statistics • Tables

7. Graphical methods Piechart Barchart Histogram Scattergram

8. Pie chart

9. Bar chart

10. Histogram

11. Boxplot

12. Error bar plot

13. Scattergram

14. Graph Example

15. Graph

16. Solution

17. Summary statistics Qualitative data • Percentages • Numbers

18. Secondary prevention of coronary heart disease

19. Summarizing data example I

20. Summary StatisticsQuantitative data • Non-normal median range inter-quartile range • Normal mean standard deviation variance

21. Boxplot

22. Summary StatisticsNormal data Approximately 95% of observations lie between the mean plus or minus 2 standard deviations

23. Histogram

24. Histogram of IgM values

25. How to test for Normality • Mean = Median • (mean-2sd, mean+2sd) reasonable range • -1 < skewness < 1 • -1 < kurtosis < 1 • Histogram shows symmetric bell shape

26. Checking for Normality

27. Secondary prevention of coronary heart disease [* Median (range)]

28. Summary statistics example II

29. Natural log transformation • Can transform +vely skewed data to ‘Normal’ data • Use transformed data in analysis • Resulting mean value transformed back (using ex) to give geometric mean • Present geometric mean and range

30. Effect of loge transformation [Geometric mean = e 2.2 = 9.0]

31. Secondary prevention of coronary heart disease [* Median (range), # Geometric mean (range)]

32. Confidence Interval “ The estimated mean difference in systolic blood pressure between 100 diabetic and 100 non-diabetic men was 6.0 mmHg with 95% confidence interval (1.1mmHg, 10.9mmHg)”

33. Confidence Interval • Contains information about the (im)precision of the estimated effect size • Presents a range of values, on the basis of the sample data, in which the population value for such an effect size may lie

34. Confidence Interval95% CI for mean = mean +/- 1.96 SEM90% CI for mean = mean +/- 1.64 SEMSEM = sd / sqrt(n)

35. Confidence Interval • The 95% CI is a range of values which we are 95% confident covers the true population mean • There is a 5% chance that the ‘true’ mean lies outside the 95% CI

36. Error bar plot

37. Confidence Interval Example

38. Significance/hypothesis tests Measure strength of evidence provided by the data for or against some proposition of interest Eg. Is the survival rate after X better than after Y?

39. Significance/hypothesis tests Null hypothesis: “Effects of X and Y are the same” Alternative hypothesis: “Effects of X and Y are different”

40. Significance/hypothesis tests One-sided : “X is better than Y” Two-sided: “ X and Y have different effects”

41. P-value P is the probability of how true is the null hypothesis

42. P-value P <= 0.05 • null hypothesis is not true • there is a difference between X and Y • result is statistically significant

43. P-value P > 0.05 • null hypothesis may be true • there is probably no difference between X and Y • result is not statistically significant

44. P-value Power of study • probability of rejecting null hypothesis when false • increased by increasing sample size • increased if true difference between treatments is large

45. P-value Statistical significance does not imply clinical significance

46. A statistician is a person whose lifetime ambition is to be wrong 5% of the time

47. Types of significance tests Chi-square test: “28 out of 70 smokers have a cough compared with 5 out of 50 non-smokers - is there a significant difference?” [28/70 = 40% compared with 5/50=10%]

48. Chi-square test result “P=0.001” There is a significant relationship between smoking and cough

49. Types of significance tests Two-sample t-test: “Is there a difference in the 24 hour energy expenditure between groups of lean and obese women?”

50. Types of significance tests Mann-Whitney U-test: “Is there a difference in the nausea score between chemo patients receiving an active anti-emetic treatment and those receiving placebo?”