Analyze Statistic by Using SPSS 5 th Day 1Fadwa Flemban .. 57 .. 114 .. 117 .. 234 .. .. .. 36 12 .. 332 .. 332 12 .. 365 .. 2Fadwa Flemban 3 Non Parametric Tests t . t . 4Fadwa Flemban Non Parametric Tests Fadwa Flemban5 Non Parametric Tests One-Sample The Binomial Test Example: random sample was withdrawn for a number of children's weights and were as follows: 35, 25, 15, 20, 30, 24, 35, 15, 25, 30, 32, 33, 34, 16, 19, 20, 31, 10. Required test the hypothesis average weight of the child over than 25 kilos at the confidence interval 99%? Fadwa Flemban6 Mathematically solution Fadwa Flemban7 H 0 := 25 H 1: > 25 Use a = 0.01 Compute for the z statistic. = = 0 from observations the sign= (It means s = 8, n = 18-2 = 16 ). Compute for the critical region. At a = 0.01, we reject H 0 if z>z 0.01 (z>+2.33). Thus, we don't reject the null hypothesis and conclude that the average weight of the child equal 25 kilos. Analyze Nonparametric Tests Binomial Fadwa Flemban8 Solution by SPSS Fadwa Flemban9 The result: p-value (1-tailed) = 0.815/2= 0.41 a = >0.01 don't reject H 0 The result: p-value (1-tailed) = 0.815/2= 0.41 a = >0.01 don't reject H 0 Non Parametric Tests Two-Independent Samples The Man-Whitney test Fadwa Flemban10 Example: To compare the ratios of intelligence between the two schools A and B, selected a random sample of students from these schools, intelligence test was conducted and the results were: A B test the hypothesis that the students in the school A are smarter than the students in the school B at the level 0.05? Fadwa Flemban11 Mathematically solution rankschoolObs. 15A A A A 21 20A A 20 4A 18 20A 24 15A 22 22A 25 20A A 20 rankschoolObs. 4B18 9.5B20 2B17 15B22 6.5B B B21 1B16 4B18 9.5B20 Rank all observations in increasing order from smallest to largest. Assign the smallest observation the rank 1. If some observations have tied values, assign the rank that is the average of the ranks they would have been assigned if there were no ties. Rank all observations in increasing order from smallest to largest. Assign the smallest observation the rank 1. If some observations have tied values, assign the rank that is the average of the ranks they would have been assigned if there were no ties. Mathematically solution 1.H : 1=2,H1 : 1>2 2.W=( )=171.5 Fadwa Flemban12 Compute for the critical region. At a = 0.05, we reject H 0 if z>z 0.05 (z>+1.65), from above 2.21 > 1.65 Thus, we reject the null hypothesis and conclude that the students in the school A are smarter than the students in the school B at the level 0.05 Solution by SPSS Analyze Nonparametric Tests 2 Independent Samples Fadwa Flemban13 Fadwa Flemban14 Output: Fadwa Flemban15 p-value: (1-tailed) = a = 0.05, 0.014z 0.05 (z>+1.65). Thus, we reject the null hypothesis and conclude that the person A gives the degrees larger than the person B. Fadwa Flemban17 Solution by SPSS Analyze Nonparametric Tests 2 Related Samples Fadwa Flemban18 Fadwa Flemban19 Fadwa Flemban20 Output: The result: p-value= 0.05 Dont reject H There is no difference between the mean of samples. Non Parametric Tests K-Related Samples The Freidman test Assume we have this data: Examine if there is difference in the methods of treatment at the confidence interval 99%? Fadwa Flemban28 T3T2T1Num Solution by SPSS Fadwa Flemban29 H : there is no difference between the methods of treatments. H1 : there is difference between the methods of treatments. Solution by SPSS Analyze Nonparametric Tests k Related Samples Fadwa Flemban30 Fadwa Flemban31 By default : the confidence interval is 99% Output : Fadwa Flemban32 p-value = a = 0.01, 0.004