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# 9.testing of hypothesis

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### 9.testing of hypothesis

1. 1. Testing ofHypothesisD.A. Asir John Samuel, BSc (Psy),MPT (Neuro Paed), MAc, DYScEd, C/BLS, FAGE
2. 2. Hypothesis• Hypothesis is defined as the statement regarding parameter (characteristic of a population) Dr.Asir John Samuel (PT), Lecturer, ACP 2
3. 3. Test of significance• A statistical procedure by which one can conclude, if the observed results from the sample is due to chance (sampling variation) or not Dr.Asir John Samuel (PT), Lecturer, ACP 3
4. 4. A B1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 Dr.Asir John Samuel (PT), Lecturer, ACP 4
5. 5. Null hypothesis (H0)• A hypothesis which states that the observed result is due to chance• Researcher anticipate “no difference” or “no relationship” Dr.Asir John Samuel (PT), Lecturer, ACP 5
6. 6. Alternate hypothesis (HA)• A hypothesis which states that the observed results is not due to chance (research hypothesis)• Statement predict that a difference or relationship b/w groups will be demonstrated Dr.Asir John Samuel (PT), Lecturer, ACP 6
7. 7. Testing of hypothesis1. Evaluate data2. Review assumption3. State hypothesis4. Presume null hypothesis5. Select test statistics6. Determine distribution of test statistics7. State decision rule Dr.Asir John Samuel (PT), Lecturer, ACP 7
8. 8. Testing of hypothesis8. Calculate test statistics9. What is the probability that the data conform10. Make statistical decision11. If p>0.05, then reject (HA)12. If p<0.05, then accept (HA) Dr.Asir John Samuel (PT), Lecturer, ACP 8
9. 9. Testing of Hypothesis Presume null hypothesis What is the probability that data conform top>0.05 null hypothesis P<0.05 Retain H0 reject H0 Dr.Asir John Samuel (PT), Lecturer, ACP 9
10. 10. p-value• Probability of getting a minimal difference of what has observed is due to chance• Probability that the difference of at least as large as those found in the data would have occurred by chance Dr.Asir John Samuel (PT), Lecturer, ACP 10
11. 11. p value in decision• P value very large- Probability to get the observed result due to chance• P value very small- Small probability to get the observed result not due to chance Dr.Asir John Samuel (PT), Lecturer, ACP 11
12. 12. Decision for 5% LOS• Probability of rejecting true null hypothesis• If p-value <0.05, then data favours alternate hypothesis• If p-value ≥0.05, then data favours null hypothesis Dr.Asir John Samuel (PT), Lecturer, ACP 12
13. 13. Type I & II errors Possible states of Null Hypothesis Possible True Falseactions on Accept Correct Type II Null Action errorHypothesis Reject Type I Correct error Action Prob (Type I error) – α (LoS) Prob (Type II error) – β 1-β – power of test Dr.Asir John Samuel (PT), Lecturer, ACP 13
14. 14. LOS and Power• Prob (type I error) = α• Prob (type II error) = β• α – LOS• 1- β – power of the study Dr.Asir John Samuel (PT), Lecturer, ACP 14
15. 15. Test of Hypothesis• Parametric test• Non-parametric test Dr.Asir John Samuel (PT), Lecturer, ACP 15
16. 16. Parametric & non-parametric test• Paired t-test • Wilcoxon Signed Rank T• Repeated measure • Friedman test ANOVA• Independent t-test • Mann-Whitney U test• One way ANOVA • Krushal Wallis test• Pearson correlation • Spearman Rank coefficient correlation coefficient Dr.Asir John Samuel (PT), Lecturer, ACP 16
17. 17. Paired t-test• Two measures taken on the same subject or naturally occurring pairs of observation or two individually matched samples• Variable of interest is quantitative Dr.Asir John Samuel (PT), Lecturer, ACP 17
18. 18. Assumption• The difference b/w pairs in the population is independent and normally or approximately normally distributed Dr.Asir John Samuel (PT), Lecturer, ACP 18
19. 19. Wilcoxon Signed Rank test• Used for paired data• The sample is random• The variable of interest is continuous• The measurement scale is at least interval• Based on the rank of difference of each paired values Dr.Asir John Samuel (PT), Lecturer, ACP 19
20. 20. Repeated measures ANOVA• Measurements of the same variable are made on each subject on more than two different occasion• The different occasions may be different point of time or different conditions or different treatments Dr.Asir John Samuel (PT), Lecturer, ACP 20
21. 21. Assumptions• Observations are independent• Differences should follow normal distribution• Sphericity-differences have approximately same variances Dr.Asir John Samuel (PT), Lecturer, ACP 21
22. 22. Fried Man test• Data is measured in ordinal scale• The subjects are repeatedly observed under 3 or more conditions• The measurement scale is at least ordinal (qualitative)• The variable of interest is continuous Dr.Asir John Samuel (PT), Lecturer, ACP 22
23. 23. Independent t-test• Compare the means of two independent random samples from two population• Variable of interest is quantitative Dr.Asir John Samuel (PT), Lecturer, ACP 23
24. 24. Assumptions• The population from which the sample were obtained must be normally or approximately normally distributed• The variances of the population must be equal Dr.Asir John Samuel (PT), Lecturer, ACP 24
25. 25. Mann Whitney-U test• Two independent samples have been drawn from population with equal medians• Samples are selected independently and at random• Population differ only with respect to their median• Variable of interval is continuous Dr.Asir John Samuel (PT), Lecturer, ACP 25
26. 26. Mann Whitney-U test• Measurement scale is at least ordinal (qualitative)• Based on ranks of the observations Dr.Asir John Samuel (PT), Lecturer, ACP 26
27. 27. ANOVA• Extension of independent t-test to compare the means of more than two groups• F = b/w group variation/within group variation• F ratio• Post hoc test (which mean is different) Dr.Asir John Samuel (PT), Lecturer, ACP 27
28. 28. Assumptions• Observations are independent and randomly selected• Each group data follows normal distribution• All groups are equally variable (homogeneity of variance) Dr.Asir John Samuel (PT), Lecturer, ACP 28
29. 29. Why not t-test?• Tedious• Time consuming• Confusing• Potentially misleading – Type I error is more Dr.Asir John Samuel (PT), Lecturer, ACP 29
30. 30. Kruskal Wallis H test• Used for comparison of more than 2 groups• Extension of Mann-Whitney U test• Used for comparing medians of more than 2 groups Dr.Asir John Samuel (PT), Lecturer, ACP 30
31. 31. Assumptions• Samples are independent and randomly selected• Measurement scale is at least ordinal• Variable of interest is continuous• Population differ only with respect to their medians Dr.Asir John Samuel (PT), Lecturer, ACP 31
32. 32. Chi-square Test (x2)• Variables of interest are categorical (quantitative)• To determine whether observed difference in proportion b/w the study groups are statistically significant• To test association of 2 variables Dr.Asir John Samuel (PT), Lecturer, ACP 32
33. 33. Chi-square Test-Assumption• Randomly drawn sample• Data must be reported in number• Observed frequency should not be too small• When observed frequency is too small and corresponding expected frequency is less than 5 (<5) – Fischer Exact test Dr.Asir John Samuel (PT), Lecturer, ACP 33
34. 34. Relationship• Correlation• Regression Dr.Asir John Samuel (PT), Lecturer, ACP 34
35. 35. Correlation• Method of analysis to use when studying the possible association b/w two continuous variables• E.g.- Birth wt and gestational period- Anatomical dead space and ht- Plasma volume and body weight Dr.Asir John Samuel (PT), Lecturer, ACP 35
36. 36. Correlation• Scatter diagram• Linear correlation• Non-linear correlation Dr.Asir John Samuel (PT), Lecturer, ACP 36
37. 37. Properties• Scatter diagrams are used to demonstrate the linear relationship b/w two quantitative variables• Pearson’s correlation coefficient is denoted by r• r measures the strength of linear relationship b/w two continuous variable (say x and y) Dr.Asir John Samuel (PT), Lecturer, ACP 37
38. 38. Properties• The sign of the correlation coefficient tells us the direction of linear relationship• The size (magnitude) of the correlation coefficient r tells us the strength of a linear relationship Dr.Asir John Samuel (PT), Lecturer, ACP 38
39. 39. Properties• Better the points on the scatter diagram approximate a straight line, the greater is the magnitude r• Coefficient ranges from -1 ≤ r ≤ 1 Dr.Asir John Samuel (PT), Lecturer, ACP 39
40. 40. Interpretation• r = 1, two variables have a perfect +ve linear relationship• r = -1, two variables have a perfect -ve linear relationship• r = 0, there is no linear relationship b/w two variables Dr.Asir John Samuel (PT), Lecturer, ACP 40
41. 41. Assumption• Observations are independent• Relationship b/w two variables are linear• Both variables should be normal distributed Dr.Asir John Samuel (PT), Lecturer, ACP 41
42. 42. Caution• Correlation coefficient only gives us an indication about the strength of a linear relationship• Two variables may have a strong curvilinear relationship but they could have a weak value for r Dr.Asir John Samuel (PT), Lecturer, ACP 42
43. 43. Judging the strength – Porteney & Watkins criteria• 0.00-0.25 – little or no relationship• 0.26-0.50 – fair degree of relationship• 0.51-0.75 – moderate to good degree of relationship• 0.76-1.00 – good to excellent relationship Dr.Asir John Samuel (PT), Lecturer, ACP 43
44. 44. Scatter diagram• Each pair of variables is represented in scatter diagram by a dot located at the point (x,y) Dr.Asir John Samuel (PT), Lecturer, ACP 44
45. 45. Scatter diagram - Merits• Simple method• Easy to understand• Uninfluenced• First step Dr.Asir John Samuel (PT), Lecturer, ACP 45
46. 46. Scatter diagram - Demerits• Does not establish exact degree of correlation• Qualitative method• Not suitable for large sample Dr.Asir John Samuel (PT), Lecturer, ACP 46
47. 47. Spearman’s Rank correlation• Non-parametric measure of correlation between the two variables (at least ordinal)• Ranges from -1 to +1Eg:- Pain score of age- IQ and TV watched /wk- Age and EEG output values Dr.Asir John Samuel (PT), Lecturer, ACP 47
48. 48. Situation• Relationship b/w two variables is non-linear• Variables measured are at least ordinal• One of the variables not following normal distribution• Based on the difference in rank between each variable Dr.Asir John Samuel (PT), Lecturer, ACP 48
49. 49. Assumption• Observation are independent• Samples are randomly selected• The measurement scale is at least ordinal Dr.Asir John Samuel (PT), Lecturer, ACP 49
50. 50. Regression• Expresses the linear relationship in the form of an equation• In other words a prediction equation for estimating the values of one variable given the valve of the other, y = a + bx Dr.Asir John Samuel (PT), Lecturer, ACP 50
51. 51. Regression - eg• Wt (y) and ht (x)• Birth wt (y) and gestation period (x)• Dead space (y) and height (x)x and y are continuousy-dependent variablex-independent variable Dr.Asir John Samuel (PT), Lecturer, ACP 51
52. 52. Regression line• Shows how are variable changes on average with another• It can be used to find out what one variable is likely to be (predict) when we know the other provided the prediction is within the limits of data range Dr.Asir John Samuel (PT), Lecturer, ACP 52
53. 53. Regression analysis• Derives a prediction equation for estimating the value of one variable (dependent) given the value of the second variable (independent) y = a + bx Dr.Asir John Samuel (PT), Lecturer, ACP 53
54. 54. Assumption• Randomly selection• Linear relationship between variables• The response variable should have a normal distribution• The variability of y should be the same for each value of the predictor value Dr.Asir John Samuel (PT), Lecturer, ACP 54
55. 55. Multiple regression• One dependent variable and multiple independent variable• Derives a prediction equation for estimating the value of one variable (dependent) given the variable of the other variable (independent) Dr.Asir John Samuel (PT), Lecturer, ACP 55
56. 56. Multiple regression• The dependent variable is continuous and follows normal distribution• Independent variable can be quantitative as well as qualitative Dr.Asir John Samuel (PT), Lecturer, ACP 56