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### Z test

1. 1. Dr. Muhammedirfan H. MominAssistant ProfessorCommunity Medicine DepartmentGovernment Medical College, Surat. DR IRFAN MOMIN
2. 2. INTRODUCTION The use of any statistical method for analyzing data is based on the objectives of the study, the hypothesis to be tested and type of available statistical data which is to be analyzed to answer the research questionsDR IRFAN MOMIN
3. 3. Statistical Tests How to tell if something (or somethings) is different from something else DR IRFAN MOMIN
4. 4. TYPES OF DATA It can be -Primary or Secondary -Qualitative or QuantitativeDR IRFAN MOMIN
5. 5. • Primary data is that which is collected by the researcher to address the current research. • Secondary data refers to data gathered by others or from other studies like official records, publications, documents etc. • Qualitative data refers to data having counting of the individuals for the same characteristic and not by measurement. • Quantitative data refers to data having magnitude and the characteristic is measured either on an interval or on a ratio scale.DR IRFAN MOMIN
6. 6. Qualitative ( Sex, Religion)• Data types Quantitative Continuous Discrete (measurable) (countable) Age No. of. Children Hb No. of CasesDR IRFAN MOMIN
7. 7. SAMPLE DATA SET Pt. No. Hb. Pt. No. Hb. Pt. No. Hb. 1 12.0 11 11.2 21 14.9 2 11.9 12 13.6 22 12.2 3 11.5 13 10.8 23 12.2 4 14.2 14 12.3 24 11.4 5 12.3 15 12.3 25 10.7 6 13.0 16 15.7 26 12.7 7 10.5 17 12.6 27 11.8 8 12.8 18 9.1 28 15.1 9 13.5 19 12.9 29 13.4 10 11.2 20 14.6 30 13.1DR IRFAN MOMIN
8. 8. TABLE FREQUENCY DISTRIBUTION OF 30 ADULT MALE PATIENTS BY Hb Hb (g/dl) No. of patients 9.0 – 9.9 1 10.0 – 10.9 3 11.0 – 11.9 6 12.0 – 12.9 10 13.0 – 13.9 5 14.0 – 14.9 3 15.0 – 15.9 2 Total 30DR IRFAN MOMIN
9. 9. DR IRFAN MOMIN
10. 10. Table 1 Risk factors for Myocardial Infarction for patients (n=57) admitted to the Kilpauk Medical College Hospital, Chennai, Jan- Sep 1998 Risk factor MI Patients No % Hypertension 24 42.1 Smoking 20 35.1 Diabetes 13 22.8 CAD 9 15.8 Hyperlipedemia 2 3.5 None 8 14.0 DR IRFAN MOMIN
11. 11. Steps in Test of Hypothesis1. Determine the appropriate test2. Establish the level of significance3. Formulate the statistical hypothesis4. Calculate the test statistic5. Compare computed test statistic against a tabled/critical value DR IRFAN MOMIN
12. 12. 1. Determine Appropriate Test• Z Test for the Mean• (Standard error of difference between two means)• Z Test for the Proportion• (Standard error of difference between two proportions) DR IRFAN MOMIN
13. 13. 2. Establish Level of Significance p is a predetermined value The convention  p = .05  p = .01  p = .001 DR IRFAN MOMIN
14. 14. NORMAL DISTRIBUTIONDR IRFAN MOMIN
15. 15. NORMAL DISTRIBUTIONDR IRFAN MOMIN
16. 16. DR IRFAN MOMIN
17. 17. DR IRFAN MOMIN
18. 18. DR IRFAN MOMIN
19. 19. A sampling distribution for H0 showing the region of rejection for = .05 in a 2-tailed z-test.2-tailed regions Fig 10.4 (Heiman DR IRFAN MOMIN
20. 20. A sampling distribution for H0 showing the region of rejection for = .05 in a 1-tailed z-test.1-tailed region, above mean Fig 10.7 (Heiman DR IRFAN MOMIN
21. 21. A sampling distribution for H0 showing the region of rejection for = .05 in a 1-tailed z-test where a decrease in the mean is predicted.1-tailed region, below mean Fig 10.8 (Heiman DR IRFAN MOMIN
22. 22. DR IRFAN MOMIN
23. 23. If P < 0.05, the observed difference is ‘SIGNIFICANT (Statistically)’ P< 0.01, sometimes termed as ‘Highly Significant’DR IRFAN MOMIN
24. 24. INTERPRETATION OF SIGNIFICANCESIGNIFICANT Does not necessarily mean that the observed difference is REAL or IMPORTANT. Only that it is unlikely (< 5%) to be due to chance.DR IRFAN MOMIN
25. 25. INTERPRETATION OF NON - SIGNIFICANCENON - SIGNIFICANT Does not necessarily mean that there is no real difference; it means only that the observed difference could easily be due to chance (Probability of at least 5%)DR IRFAN MOMIN
26. 26. 3. Determine The Hypothesis:Whether There is an Associationor Not Write down the NULL HYPOTHESIS and ALTERNATIVE HYPOTHESIS and set the LEVEL OF SIGNIFICANCE. Ho : The two variables are independent Ha : The two variables are associated We will set the level of significance at 0.05. DR IRFAN MOMIN
27. 27. For Example Some null hypotheses may be:  ‘there is no relationship between the height of the land and the vegetation cover’.  ‘there is no difference in the location of superstores and small grocers shops’  ‘there is no connection between the size of farm and the type of farm’ DR IRFAN MOMIN
28. 28. TEST FOR PROPORTIONSDR IRFAN MOMIN
29. 29. STANDARD ERROR OF DIFFERENCEBETWEEN TWO PROPORTIONS P1 - P2 Z = ------------------ SE (P1 - P2) DR IRFAN MOMIN
30. 30. STANDARD ERROR OF DIFFERENCEBETWEEN TWO PROPORTIONSSE (P1 - P2) = P1Q1 + P2Q2 n1 n2 DR IRFAN MOMIN
31. 31. EXAMPLEIf swine flu mortality in one sample of 100 is 20% and in another sample of 100 it is 30%. Is the difference in mortality rate is significant?P1= 20 q1 = 80 n1 = 100P2= 30 q2 = 70 n2 = 100 P1 - P2 Z = ------------------ SE (P1 - P2) DR IRFAN MOMIN
32. 32. STANDARD ERROR OF DIFFERENCEBETWEEN TWO PROPORTIONSSE (P1 - P2) = 20x80 + 30x70 100 100 DR IRFAN MOMIN
33. 33. STANDARD ERROR OF DIFFERENCEBETWEEN TWO PROPORTIONSSE (P1 - P2) = 37 = 6.08 DR IRFAN MOMIN
34. 34. EXAMPLEIf swine flu mortality in one sample of 100 is 20% and in another sample of 100 it is 30%. Is the difference in mortality rate is significant?P1= 20 q1 = 80 n1 = 100P2= 30 q2 = 70 n2 = 100 P1 - P2 Z = ------------------ SE (P1 - P2) DR IRFAN MOMIN
35. 35. EXAMPLEIf swine flu mortality in one sample of 100 is 20% and in another sample of 100 it is 30%. Is the difference in mortality rate is significant?P1= 20 q1 = 80 n1 = 100P2= 30 q2 = 70 n2 = 100 20-30 Z = --------- = -1.64 6.08 DR IRFAN MOMIN
36. 36. Z value and probability z 1.96 2.58 p 0.05 0.01 DR IRFAN MOMIN
37. 37.  Obtained z value (1.64) is less than critical z value (1.96) , so P >0.05, hence difference is insignificant at 95 % confidence limits. DR IRFAN MOMIN
38. 38. STANDARD ERROR OF DIFFERENCEBETWEEN TWO MEANS X1 - X2 Z = ------------------ SE (X1 - X2) DR IRFAN MOMIN
39. 39. STANDARD ERROR OF DIFFERENCEBETWEEN TWO MEANSSE (X1 - X2) = SD12 + SD22 n1 n2 DR IRFAN MOMIN
40. 40. EXAMPLEIn a nutritional study, 100 children were given usual diet and 100 were given vitamin A and D tablets. After 6 months, average weight of group A was 29kg with SD of 1.8kg and average weight of group B was 30kg with SD of 2kg. Is the difference is significant?SD1= 1.8 n1 = 100SD2= 2 n2 = 100 X1 - X2 Z = ------------------ SE (X1 - X2) DR IRFAN MOMIN
41. 41. STANDARD ERROR OF DIFFERENCEBETWEEN TWO MEANSSE (X1 - X2) = SD12 + SD22 n1 n2 DR IRFAN MOMIN
42. 42. STANDARD ERROR OF DIFFERENCEBETWEEN TWO MEANSSE (X1 - X2) = (1.8)2 + (2)2 100 100 DR IRFAN MOMIN
43. 43. STANDARD ERROR OF DIFFERENCEBETWEEN TWO MEANSSE (X1 - X2) = (1.8)2 + (2)2 100 100 DR IRFAN MOMIN
44. 44. STANDARD ERROR OF DIFFERENCEBETWEEN TWO MEANSSE (X1 - X2) = 3.24+4 100 DR IRFAN MOMIN
45. 45. STANDARD ERROR OF DIFFERENCEBETWEEN TWO MEANSSE (X1 - X2) = 0.0724 =0.27 DR IRFAN MOMIN
46. 46. EXAMPLEIn a nutritional study, 100 children were given usual diet and 100 were given vitamin A and D tablets. After 6 months, average weight of group A was 29kg with SD of 1.8kg and average weight of group B was 30kg with SD of 2kg. Is the difference is significant?SD1= 1.8 n1 = 100SD2= 2 n2 = 100 X1 - X2 Z = ------------------ SE (X1 - X2) DR IRFAN MOMIN
47. 47. EXAMPLEIn a nutritional study, 100 children were given usual diet and 100 were given vitamin A and D tablets. After 6 months, average weight of group A was 29kg with SD of 1.8kg and average weight of group B was 30kg with SD of 2kg. Is the difference is significant?SD1= 1.8 n1 = 100SD2= 2 n2 = 100 29 - 30 Z = ---------------- = -3.7 0.27 DR IRFAN MOMIN
48. 48. A sampling distribution for H0 showing the region of rejection for = .05 in a 2-tailed z-test.2-tailed regions Fig 10.4 (Heiman DR IRFAN MOMIN
49. 49. Z value and probability z 1.96 2.58 p 0.05 0.01 DR IRFAN MOMIN
50. 50.  As obtained value of z (-3.7) is higher than critical value (-1.96 or -2.58), the observed difference is highly significant, vitamins played a role in weight gain . DR IRFAN MOMIN
51. 51. THANK YOUdrmhmomin@yahoo.co.inMobile: +91-9426845307 DR IRFAN MOMIN