TESTS OF SIGNIFICANCE.pptx

TEST OF SIGNIFICANCE

1. TESTS OF SIGNIFICANCE MODERATOR: PRESENTER: MR.ARUN GOPI DR.ANCHU R NATH LECTURER IN bioSTATISTICS FIRST YEAR PG RESIDENT DEPT. OF COMMUNITY MEDICINE

2. PLAN OF PRESENTATION : HISTORY INTRODUCTION HYPOTHESIS TESTING NULL HYPOTHESIS & ALTERNATIVE HYPOTHESIS TYPE I & TYPE II ERROR P VALUE PARAMETRIC TEST NON-PARAMETRIC TEST SUMMARY REFERENCES 09-06-2023 2

3. HISTORY The term Statistical significance was coined by the Ronald Fisher (1890-1962) Father of Modern Statistics. Student t-test : William Sealy Gosset 09-06-2023 3

4. INTRODUCTION 09-06-2023 4

5. HYPOTHESIS TESTING During investigation, there is assumption and presumption, which subsequently in study must be proved or disproved. To test the statistical hypothesis about the population parameter or true value of universe. Two Hypothesis are made to draw the inference from the sample value: A null hypothesis or hypothesis of no difference (H ) Alternative hypothesis of significant difference (H 1 ) 09-06-2023 5

6. CHARACTERISTICS OF HYPOTHESIS: Hypothesis should be clear and precise. It should be capable of being tested. It should state relationship between variables. It must be specific and stated as simple as possible. 09-06-2023 6

7. There is no difference between the statistic of a sample and parameter of population or between statistics of two samples. The observed difference is entirely due to sampling error, i.e., it has occurred purely by chance. Example : There is no difference between the incidence of measles between vaccinated and non-vaccinated children. NULL HYPOTHESIS 09-06-2023 7

8. ALTERNATIVE HYPOTHESIS Sample result is different, that is greater or smaller than the hypothetical value of population. Example: weight gain or loss due to new feeding regimen. Test of significance is performed to accept the null hypothesis or to reject it and accept the alternative hypothesis. 09-06-2023 8

9. INTERPRETING THE RESULT OF HYPOTHESIS: The null Hypothesis is true – our test accepts it because the result falls within the Zone of acceptance at 5% level of significance. The null hypothesis is false- test rejects it because the estimate falls in the area of rejection. 09-06-2023 9

10. ZONE OF ACCEPTANCE: If the result of a sample falls in the plain area i.e. within the mean + 1.96 standard error (SE), the null hypothesis is accepted. ZONE OF REJECTION : If the result of a sample falls in the shaded area, i.e beyond mean + 1.96 SE , it is significantly different from the universe value. So null hypothesis is rejected and alternative hypothesis is accepted. 09-06-2023 10

11. TYPE I AND TYPE II ERROR When a null hypothesis is tested , there may be four possible outcomes : Type I error – rejecting the null hypothesis when null hypothesis is true. It is called Type II error – accepting null hypothesis when null hypothesis is false . It is called   09-06-2023 11

12. P – VALUE : It is the probability of obtaining a result equal to or more extreme than what was actually observed. First introduced by Karl Pearson in his Pearson’s Chi squared test Choice of cut-off value: Arbitrary cut off 0.05 (5% chance of a false positive conclusion) If p < 0.05 , statistically significant – Reject H0 , Accept H1 If p > 0.05 , statistically not significant – Accept H0 , Reject H1 09-06-2023 12

13. P-value Interpretation : A p-value measures the strength of evidence against a hypothesis. If the p- value is small , then either the null hypothesis is false or we got a very unlikely sample. If the p-value is large , then there is a weak evidence against null hypothesis , as a result its accepted 09-06-2023 13

14. Test of Significance ??? A formal procedure for comparing observed data with a claim(also called a hypothesis) whose truth we want to assess. A significance test uses data to evaluate a hypothesis by comparing sample point estimates of parameters to values predicted by the hypothesis. .. 09-06-2023 14

15. Why Test of Significance??? Have the observation changed with time / intervention? Do two or more groups observations differ from each other? Is there an association between different observations? 09-06-2023 15

16. Stages in performing a Test of Significance: A research question A null hypothesis (H0) suitable to the problem is set up. An alternate hypothesis is defined if necessary. A suitable statistical test , using a relevant formula is calculated. Then the p value is found out, corresponding to the calculated value of test. If the p value is < 0.05, null hypothesis is rejected. 09-06-2023 16

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18. TEST OF SIGNIFICANCE PARAMETRIC TEST NON-PARAMETRIC TEST Independent t test Paired t test ANOVA Repeated Measure ANOVA Pearson’s Correlation Test Mann –Whitney U test Wilcoxon signed rank test Kruskal Wallis test Friedman’s test Spearman Correlation test Chi square test 09-06-2023 18

19. PARAMETRIC TEST Student’s t – Test: Developed by Prof. W.S. Gossett in 1908, who published statistical papers under the pen name of ‘Student’. T-test Independent t-test Paired t-test 09-06-2023 19

20. Indication for the test: When samples are small. Population variance are not known. Assumptions made in the use of t-test Samples are randomly selected. Data utilized is Quantitative. Variable follow normal distribution. Samples size lower than 30. 09-06-2023 20

21. INDEPENDENT T TEST We compare the means of two different samples. Degree of Freedom : number of values in the final calculation of a statistics that are free to vary. degree of freedom = sample size   - 1)   t =   09-06-2023 21

22. Example: The marks of boys and girls are given: Is there any significant difference between marks of boys and girls? Firstly , we will calculate mean, SD, DOF Boys Girls Girls N1=9 df = 9-1 = 8 X1= 9.778 S1 = 4.1164 N2 = 10 df = 10-1 = 9 X2= 15.1 S2 = 4.2805 t = = = - 2.758 -2.758 < 2.652 So we have to accept null hypothesis. i.e , there is no statistical significant difference between the marks of boys and girls.   Marks :Boys Girls 12 21 14 18 10 14 8 20 16 11 5 19 3 8 9 12 11 13 15 09-06-2023 22

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24. PAIRED T-TEST We compare the means of two related or same group at two different time. m = mean of difference between each pair of values s = SD of difference between each pair of values n = sample size Example: BP of 8 patients before and after an antihypertensive drug are recorded: Is there any significant difference between BP reading before and after?   09-06-2023 24

25. Firstly, we find the mean, SD of difference between each pair of values. Mean (m) = = 465 = 58.125 8 8   Before After d(= Before-After) 180 140 40 200 145 55 230 150 80 240 155 85 170 120 50 190 130 60 200 140 60 165 130 35 = 465 Before After d(= Before-After) 180 140 40 200 145 55 230 150 80 240 155 85 170 120 50 190 130 60 200 140 60 165 130 35 09-06-2023 25

26. H0: there is no significant difference between BP before & after the drug H1: there is significant difference Let the alpha value is 0.05 , DOF = 8-1 = 7 t value = 2.36 = 9.38 9.38 > 2.36 So, we have to reject null hypothesis. i.e. there is significant difference between BP reading before & after drug.   09-06-2023 26

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28. ANOVA (Analysis of Variance) Given by Sir Ronald Fischer Principle aim of statistical model is to explain the variation in measurements. Test of significance for more than 2 groups independent of each other. Assumptions for ANOVA Sample population follow normal distribution. Samples are selected randomly and independently. Each group have common variance. 09-06-2023 28

29. Test statistics for ANOVA is F-test ANOVA ONE WAY ANOVA TWO WAY ANOVA One way ANOVA Two way ANOVA One factor or independent variable more than one factor or independent variable Compares 3 or more levels of one compares the effect of factor multiple levels of 2 factors 09-06-2023 29

30. ANOVA = Variance between groups Variance within groups Variance between > Variance within Reject H0 Variance between < or = Variance within Fail to Reject H0 1 1 Example : We want to see if three different studying methods can lead to different mean exam scores or not. To test this , we select 30 students and randomly assign 10 each to use a different studying method. 09-06-2023 30

31. Sno Method A Method B Method C 1. 10 8 9 2. 9 9 8 3. 8 10 7 4. 7.5 8 10 5. 8.5 8.5 9 6. 9 7 8 7. 10 9.5 7 8. 8 9 10 9. 8 7 9 10. 9 10 8 8.7 8.6 8.5 Overall mean = 8.6 Between group variation = 10*(8.7-8.6)^2 + 10*(8.6-8.6)^2 + 10*(8.5-8.6)^2 = 0.2 Within group variation = Method A = (10-8.7) 2 + (9-8.7) 2 + (8-8.7) 2 + (7.5-8.7) 2 + (8.5-8.7) 2 + (9-8.7) 2 + (10-8.7) 2 + (8-8.7) 2 = 6.6 Method B = 10.9 Method C = 10.5 Within group variation = 6.6 +10.9+10.5=28 Variance between = 0.2 = 0.0071 < Variance within groups 28 Accepting the null hypothesis   1 09-06-2023 31

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33. REPEATED MEASURE ANOVA Statistically significant differences between three or more dependent samples. For example, if a sample is drawn of people who have knee surgery, These people are interviewed for pain perception before surgery , 1 week and 2 weeks after surgery. 09-06-2023 33

34. Example : Therapy after a slipped disc has an influence on patient’s perception of pain. Measuring the pain perception before, in the middle and at the end of therapy. H1: there is a significant difference among the dependent groups H0:there are no significant difference among the dependent groups 09-06-2023 34

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36. PEARSON’s CORRELATION TEST Test to compare the linear relationship between two quantitatively measured or continuous variables. Eg : Height and weight , temperature and pulse The extent of relationship measured by Pearson’s correlation coefficient ‘ r ’. & – variable samples & mean of values in x & y samples. Assumptions made in calculation of ‘r’ Subjects selected for study with pair of X & Y value are chosen randomly. Both X & Y variables are continuous & follow normal distribution.     09-06-2023 36

37. r = +1 r= -1 r=0 09-06-2023 37

38. Each point in the graph represents a single persons paired measurement of height & weight. r = +0.38 ---- positive correlation. 09-06-2023 38

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40. NON PARAMETRIC TEST MANN-WHITNEY U TEST Determine whether two independent samples have been drawn from the same population. Analyses the degree of separation ( or the amount of overlap) between Experimental & Control groups. n 1 n 2 : sample sizes R1 and R2 are sum of ranks assigned to group I & II To be statistically significant obtained U has to be equal or less than critical value. - R1 or R2   09-06-2023 40

41. EXAMPLE : A researcher, while conducting studies on the Biomass of various trees, wished to determine if there was a difference in the biomass of male and female Juniper trees. So, he randomly selected 6 tress of each gender from the field. He dries them to constant moisture, chips them, and then weighs them to the nearest kg . H : There is no difference between the biomass of male and female Juniper trees H 1 : There is a difference between the biomass of male and female Juniper trees n1= 6 , n2 =6 R1 =23 ,R2 =55 U calculated = min ( 34 ,   2 ) = 2 U critical  = 5 U calculated   < U critical  . Hence, we can reject the null hypothesis. 09-06-2023 41

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43. WILCOXON SIGNED RANK TEST Used to compare two related samples , matched samples or repeated measurements. Assumptions: Data are paired & come from same population. Each paired is chosen randomly & independently. To be statistically significant , obtained W has to be equal or less than critical value. Example: In order to investigate whether adults report verbally presented material more accurately from their right than from their left ear , a dichotic listening test was carried out. The data were found to be positively skewed. 09-06-2023 43

44. Participant Lt ear Rt ear Difference (d) 1 25 32 -7 2 29 30 -1 3 10 8 2 4 31 32 -1 5 27 20 -7 6 24 32 -8 7 26 27 -1 8 29 30 -1 9 30 32 2 10 32 32 11 20 30 -10 12 5 32 -27 To the rank the difference: Lowest difference = -1 (1+2+3+4=10/4 = 2.5) next lowest difference = 2( 5+6=11/2 = 5.5) Adding the scores with + sign = 13 - sign = 53 Smaller value W = 13 N is the number of differences( omitting 0 difference) N = 12 -1 = 11 Critical value ( N=11 , p = 0.05 ) = 14 Calculated value 13 < critical value 14 There is a difference between the number of words recalled from the Rt ear & number of words recalled from Lt ear. 09-06-2023 44

45. Category Pre test Post Test Z P Knowledge 21 (4-30) 48 (12-54) 6.56 0.001 Practice 11.2 (2-22) 22 (8- 33) 8.99 0.001 P value <0.05 , there is a statistically significant difference in the knowledge of pre test & post test of rabies & its prevention. 09-06-2023 45

46. KRUSKAL WALLIS TEST Used to compare three or more independent groups. We use sum of the rank of k samples to compare the distribution. The test statistic for the Kruskal Wallis test ( denoted as H) is defined as: samples drawn from the same population To test the T i  = rank sum for the ith sample i = 1, 2,…,k of population medians among groups 09-06-2023 46

47. EXAMPLE: In a manufacturing unit, 4 teams of operators were randomly selected and sent to 4 different facilities for machining techniques training. After the training, the supervisor conducted the exam and recorded the test scores. At 95% confidence level does the scores are same in all four facilities? H : The distribution of operator scores are same. H 1 : The scores may vary in four facilities H calculated = 9.77 > H critical = 7.81   H ence, we reject the null hypotheses So, there is enough evidence to conclude that difference in test scores exists for four teaching methods at different facilities. 09-06-2023 47

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49. FRIEDMAN’s TEST Non –parametric measure to repeated ANOVA To test for differences between groups (three or more paired groups) of the dependent variable.  Assumptions: Samples are not normally distributed One group that is measured on three or more different occasions. Group is a random sample from the population. 09-06-2023 49

50. EXAMPLE: Department of Public health and safety monitors whether the measures taken to clean up drinking water were effective. Trihalomethanes (THMs) in 12 counties drinking water compared before cleanup, 1 week later, and 2 weeks after cleanup. H  = the cleanup system had no effect on the THMs H1= the cleanup system effected the THMs Significance level α=0.05 Q calculated = 20.16 > Q critical = 6.5 hence reject the null hypotheses. So, it is concluded that the cleanup system effected the THMs of drinking water. 09-06-2023 50

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52. SPEARMAN’s CORRELATION TEST Assess the relationship between two variables. Rho ρ – non-parametric measure of statistical dependence between two variables. d – difference between ranks of each observation.   09-06-2023 52

53. Example: 5 college students having following ranks in maths & science subjects. Is there an association between Science & Maths rank? = -0.5 There is negative correlation between the Science & maths subject rankings   09-06-2023 53

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55. CHI – SQUARE TEST (X 2 ) TEST An important continuous probability distribution Applied for smaller & larger samples Prerequisites for Chi-square test: The sample must be a random sample. None of the observed values must be zero. Data should be qualitative categorical. 09-06-2023 55

56. Steps in calculating (X 2 ) value. Make a contingency table mentioning the frequencies in all cells. Determine the expected value (E) in each cell. Calculate the difference between observed and expected values in each cell (O-E) E= row total x column total Grand total 09-06-2023 56

57. Calculate X2 value for each cell Sum up X 2 value of each table to get X 2 value of table Find out the p value from table. If p > 0.05 - difference is not significant – null hypothesis accepted If p <0.05 - difference is significant – null hypothesis rejected. X2 of each cell = (O-E) 2 E 09-06-2023 57

58. EXAMPLE: Attack rate among vaccinated & unvaccinated children against measles. Group Attacked Not- Attacked Total Vaccinated ( obs ) 10 90 100 Unvaccinated ( obs ) 26 74 100 Total 36 164 200 Prove protective value of vaccination by X 2 test at 5% level of significance. Group Attacked Not- Attacked Total Vaccinated (Exp) 18 82 100 Unvaccinated (exp) 18 82 100 Total 36 164 200 X2 =Ʃ (O-E) 2 E = 8.67 Calculated value (8.67) > table value (3.84) for p value 0.05. Null hypothesis is rejected. Vaccination is protective. 09-06-2023 58

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60. SUMMARY PARAMETRIC TEST NON-PARAMETRIC TEST Independent measures, 2 groups INDEPENDENT T TEST MANN-WHITNEY TEST Independent measures, > 2 groups ANOVA KRUSKAL WALLIS TEST Repeated measures, 2 dependent groups PAIRED T TEST WILCOXON SIGNED RANK TEST Repeated measures, > 2 dependent groups REPEATED MEASURE ANOVA FRIEDMAN TEST Correlation test PEARSON SPEARMAN 09-06-2023 60

61. SELECTION OF THE STATISTICAL TEST OBJECTIVE / STUDY DESIGN TYPE OF OUTCOME NATURE OF OUTCOME Cohort Case control Cross-sectional Clinical trial Qualitative Quantitative Normal or not 09-06-2023 61

62. REFERENCES Kadri A M. IAPSM’s Textbook of Community Medicine ,2nd ed. New Delhi: Jaypee brothers medical publishers (P) Ltd; 2021. Chapter 11 , Research methodology and biostatistics ; p . 186 -190. K Park .Park’s Textbook of Preventive and Social Medicine , 27th ed.Jabalpur , M/s Banarasidas Bhanot : 2022 Chapter 21,Health information and basic medical statistics, page no: 978-981. Bratati Banerjee.Mahajans methods in Biostatistics for medical students and research workers ,9 th edition , New Delhi :Jaypee brothers medical publishers (P) Ltd:2018.Chapter 8,SamplingVariability and Significance ,p.183-247. Mohammadi S, Rastmanesh R, Jahangir F, Amiri Z, Djafarian K, Mohsenpour MA, et al. Melatonin Supplementation and Anthropometric Indices: A Randomized Double-Blind Controlled Clinical Trial. Biomed Res Int. 2021 Aug 10;2021:3502325. Fathnezhad-Kazemi A, Aslani A, Hajian S. Association between Perceived Social Support and Health-Promoting lifestyle in Pregnant Women: A Cross-Sectional Study. J Caring Sci. 2021 May 24;10(2):96–102. 09-06-2023 62

63. 6 .Adane T, Getaneh Z, Asrie F. Red Blood Cell Parameters and Their Correlation with Renal Function Tests Among Diabetes Mellitus Patients: A Comparative Cross-Sectional Study. Diabetes Metab Syndr Obes . 2020 Oct 23;13:3937–46. 7. Non Parametric Hypothesis Test [Internet]. [cited 2023 Jun 7]. Available from: https://sixsigmastudyguide.com/1-sample-sign-non-parametric-hypothesis-test/ 8 . Mohebi S, Parham M, Sharifirad G, Gharlipour Z, Mohammadbeigi A, Rajati F. Relationship between perceived social support and self-care behavior in type 2 diabetics: A cross-sectional study. J Educ Health Promot . 2018 Apr 3;7:48. 9 .Aenumulapalli A, Kulkarni MM, Gandotra AR. Prevalence of Flexible Flat Foot in Adults: A Cross-sectional Study. J Clin Diagn Res. 2017 Jun;11(6):AC17–20. 09-06-2023 63

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