# 33821 - 1 Two-samples tests 2 X Dr Mona Hassan Ahmed Prof...

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2 Two-samples tests, X 2 Dr. Mona Hassan Ahmed Prof. of Biostatistics HIPH, Alexandria University
3 Z-test   (two independent proportions) P1= proportion in the first group P2= proportion in the second group n1= first sample size n2= second sample size 2 2 2 1 1 1 2 1 n ) P (1 P n ) P (1 P P P Z - + - - =

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4 Critical z = 1.96 at 5% level of significance 2.58 at 1% level of significance
5 Researchers wished to know if urban and rural adult residents of a developing country differ with respect to prevalence of a certain eye disease. A survey revealed the following information Residence Eye disease Total Yes No Rural 24 276 300 Urban 15 485 500 Test at 5% level of significance, the difference in the prevalence of eye disease in the 2 groups Example

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6 P1 = 24/300 = 0.08 p2 = 15/500 = 0.03 87 . 2 500 ) 03 . 0 1 ( 03 . 0 300 ) 08 . 0 1 ( 08 . 0 03 . 0 08 . 0 Z = - + - - = 2.87 > Z* The difference is statistically significant Answer
7 t-Test (two independent means) 2 2 1 2 2 1 n p S n p S x x t + - = 1 X = mean of the first group 2 X = mean of the second group S 2 p = pooled variance

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8 2 n n 1)S (n 1)S (n P S 2 1 2 2 2 1 2 1 2 - + - + - = Critical t from table is detected at degree of freedom = n 1 + n 2 - 2 level of significance 1% or 5%
9 Sample of size 25 was selected from healthy population, their mean SBP =125 mm Hg with SD of 10 mm Hg . Another sample of size 17 was selected from the population of diabetics, their mean SBP was 132 mmHg, with SD of 12 mm Hg . Test whether there is a significant difference in mean SBP of diabetics and healthy individual at 1% level of significance Example

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10 17 n 25 n 2 1 = = 132 X 125 X 2 1 = = S 1 = 12 S 2 =11 6 . 117 2 17 25
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33821 - 1 Two-samples tests 2 X Dr Mona Hassan Ahmed Prof...

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