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RESITATION

RESITATION. - ONE SAMPLE HYPOTHESIS TESTS - TWO SAMPLE HYPOTHESIS TESTS (INDEPENDENT AND DEPENDENT SAMPLES). June 7, 2012.

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RESITATION

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  1. RESITATION - ONE SAMPLE HYPOTHESIS TESTS - TWO SAMPLE HYPOTHESIS TESTS (INDEPENDENT AND DEPENDENT SAMPLES) June 7, 2012

  2. Example: A researcher believes that mean hemoglobin value is 12 in the population. He selected 64 adults from population randomly to verify this idea and identified hemoglobin mean as 11.2. According to these findings, is population hemoglobin mean different from 12? • Since • The variable hemoglobin is continuous • The sample size is 64 • Hemoglobin is normally distributed • There is only one group One sample t test is used

  3. Sample results: Population mean: 12 Hypothesis: H0: = 12 Ha:  12 Test statistic: Since the population variance is unknown, our test statistic is t Level of significance: =0.05

  4. t(/2,n-1)= t(0.025,64-1)≈2.00 tcal > ttable Reject H0 Population mean is different from 12.

  5. Example: To test the median level of energy intake of 2 year old children as 1280 kcal reported in another study, energy intakes of 10 children are calculated.Energy intakes of 10 children are as follows:

  6. Since • The variable concerning energy intake is continuous • The sample size is not greater than 10 • Energy intake is not normally distributed • There is only one group Sign test

  7. H0: The population median is 1280. HA: The population median is not 1280. + - + + - - - - + - Number of (-) signs = 6 and number of (+) signs = 4 For k=4 and n=10 From the sign test table p=0.377

  8. Since p > 0.05 we accept H0 We conclude that the median energy intake level in 2 year old children is 1280 kcal.

  9. Example: The dean of the faculty wants to know whether the smoking ratio among the Phase I students is 0.25 or not. For this purpose, 50 student is selected and 18 of them said they were smoking. According to this results, can we say that this ratio is different from 0.25 at the 0.05 level of significance? • One sample z test for proportion / one sample chi-square test p=18/50=0.36 H0: P=0.25 HA: P0.25 Critical z values are 1.96 1.80<1.96 Accept H0. Smoking ratio among the Phase I student is 0.25.

  10. We can solve this problem with one sample chi square test at the same time.

  11. SPSS Output

  12. Example: In a heart study the systolic blood pressure was measured for 24 men aged 20 and for 30 men aged 40. Do these data show sufficient evidence to conclude that the older men have a higher systolic blood pressure, at the 0.05 level of significance? • Since • The variable concerning systolic blood pressure is continuous • The sample size of each group is greater than 10 • Systolic blood pressure values in each group is normally distributed • There are two groups and they are independent Independent samples t-test is used

  13. GROUP N Mean Std. Deviation 20- year-old 24 122,8333 16,7790 40- year-old 30 133,6667 17,3013 160 150 140 Mean  1 SD SBP 130 120 110 100 N = 24 30 20- year-old 40- year-old GROUP

  14. (1)H0:1=2 Ha: 1<2 (2) Testing the equality of variances H0:21= 22 Ha: 21 22 Accept H0. Variances are equal.

  15. t(52,0.05)=1.675 < p<0.05, Reject H0. (4) (5) The older men have higher systolic blood pressure (3)

  16. SPSS Output

  17. Example: Cryosurgery is a commonly used therapy for treatment of cervical intraepithelial neoplasia (CIN). The procedure is associated with pain and uterine cramping. Within 10 min of completing the cryosurgical procedure, the intensity of pain and cramping were assessed on a 100-mm visual analog scale (VAS), in which 0 represent no pain or cramping and 100 represent the most severe pain and cramping. The purpose of study was to compare the perceptions of both pain and cramping in women undergoing the procedure with and without paracervical block.

  18. 5 women were selected randomly in each groups and their scores are as follows:

  19. Since • The variable concerning pain/cramping score is continuous • The sample size is less than 10 • There are two groups and they are independent Mann Whitney U test

  20. R1= 1+2+3+4.5+10 = 20.5 From the table, critical value is 21 19.5 < 21 accept H0 We conclude that the median pain/ cramping scores are same in two groups.

  21. SPSS Output

  22. Example: We want to know if children in two geographic areas differ with respect to the proportion who are anemic. A sample of one-year-old children seen in a certain group of county health departments during a year was selected from each of the geographic areas composing the departments’ clientele. The followig information regarding anemia was revealed. The difference between two population proportion

  23. Reject H0 We concluded that the proportion of anemia is different in two geographic areas.

  24. CHD Smoking Total + - 10 Yes 30 40 46 4 50 No Total 14 76 90 Example: A study wasconducted to analyze the relation between coronary heart disease (CHD) and smoking. 40 patients with CHD and 50 control subjects were randomly selected from the records and smoking habits of these subjects were examined. Observed values are as follows:

  25. CHD Smoking Total + - 33.8 6.2 10 40 30 Yes 7.8 42.2 46 4 50 No Total 14 76 90 Observed and expected frequencies

  26. df = (r-1)(c-1)=(2-1)(2-1)=1 2(1,0.05)=3.841 reject H0 2=4. 95 > Conclusion: There is a relation between CHD and smoking.

  27. SPSS Output

  28. Example: A study was conducted to see if a new therapeutic procedure is more effective than the standard treatment in improving the digital dexterity of certain handicapped persons. Twenty-four pairs of twins were used in the study, one of the twins was randomly assigned to receive the new treatment, while the other received the standard therapy. At the end of the experimental period each individual was given a digital dexterity test with scores as follows.

  29. Since • The variable concerning digital dexterity test scores is continuous • The sample size is greater than 10 • digital dexterity test score is normally distributed • There are two groups and they are dependent Paired sample t-test

  30. H0: d = 0 New Standard Difference 49 54 -5 56 42 14 Ha: d> 0 70 63 7 83 77 6 83 83 0 68 51 17 84 82 2 63 54 9 67 62 5 79 71 8 88 82 6 48 50 -2 52 41 11 73 67 6 52 57 -5 73 70 3 78 72 6 64 62 2 71 64 7 42 44 -2 Since, rejectH0. 51 44 7 56 42 14 40 35 5 81 73 8 Total 129 Mean 65,46 60,08 5,38 SD 14,38 14,46 5,65 t(23,0.05)=1.714 We conclude that the new treatment is effective.

  31. SPSS Output

  32. Example: To test whether the weight-reducing diet is effective 9 persons were selected. These persons stayed on a diet for two months and their weights were measured before and after diet. The following are the weights in kg: • Since • The variable concerning weight is continous. • The sample size is less than 10 • There are two groups and they are dependent Wilcoxon signed ranks test

  33. T = 1.5 reject H0 , p<0.05 T = 1.5 < T(n=9,a =0.05) = 6 We conclude that the diet is effective.

  34. Example: 35 patients were evaluated for arrhythmia with two different medical devices. Is there any statistically significant difference between the diagnose of two devices? The significance test for the difference between two dependent population / McNemar test

  35. H0: P1=P2 Ha: P1 P2 Critical z value is ±1.96 Reject H0

  36. McNemar test approach: 2(1,0.05)=3.841<5.1 p<0.05; rejectH0.

  37. SPSS Output

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