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Ada assignment

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Anurag Bohra
Anurag Bohra

1. The document describes tests performed to analyze survey data on perceptions of a hypothetical car (Nano). Kolmogorov-Smirnov tests found some variables were not normally distributed. 2. Levene's tests found variances were equal (homogeneous) for variables testing the relationship between occupation and value for money, and occupation and current vehicle owned. 3. ANOVA tests found perceived value for money did not differ by occupation, but current vehicle owned did differ significantly by occupation.

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1. Run Test: Ho : The sequence of observations is random. H1 : The sequence of observations is not random. If significance value(p) > .05 , we fail to reject Ho i.e. the sequence of observations is random. Hence the hypothesis that the sample is drawn in a random order is accepted.
2.Kolmogorov-Smirnov Test This test is used for testing whether the sample drawn has normal distribution. Ho: The population of random variable is normally distributed. H1: The population of random variable is not normally distributed. One-Sample Kolmogorov-Smirnov Test
would you want sex to buy a NANO? N 35 35 a,,b Normal Parameters Mean 1.40 1.37 Std. Deviation .497 .490 Most Extreme Differences Absolute .390 .404 Positive .390 .404 Negative -.286 -.272 Kolmogorov-Smirnov Z 2.304 2.392 Asymp. Sig. (2-tailed) .000 .000 One-Sample Kolmogorov-Smirnov Test how do you plan to finance the Rate the design car? Space of the car?
N 35 35 35 a,,b Normal Parameters Mean 1.83 3.23 3.74 Std. Deviation 1.098 1.497 1.221 Most Extreme Differences Absolute .375 .167 .241 Positive .375 .132 .152 Negative -.225 -.167 -.241 Kolmogorov-Smirnov Z 2.217 .990 1.423 Asymp. Sig. (2-tailed) .000 .280 .035 One-Sample Kolmogorov-Smirnov Test Rate the safety of the car? Fuel effeciency N 35 35 a,,b Normal Parameters Mean 4.17 4.37 Std. Deviation .954 .646 Most Extreme Differences Absolute .257 .292 Positive .193 .260 Negative -.257 -.292 Kolmogorov-Smirnov Z 1.522 1.728 Asymp. Sig. (2-tailed) .019 .005 a. Test distribution is Normal. b. Calculated from data. One-Sample Kolmogorov-Smirnov Test Considering the increase in traffic and pollution is it Value for money a boon or curse N 35 35 a,,b Normal Parameters Mean 3.29 1.34 Std. Deviation 1.100 .482 Most Extreme Differences Absolute .202 .419 Positive .202 .419 Negative -.142 -.257 Kolmogorov-Smirnov Z 1.198 2.478
Asymp. Sig. (2-tailed) .113 .000 a. Test distribution is Normal. b. Calculated from data. As we can see from the above test result, the significance level of the variables sex,would you buy nano,model preferred,Financeplan,Design,Safety,Fuelefficiency,View on pollution <.05, so we fail to accept Ho which shows that the population of this variable is not normally distributed. For all other variables as the significance level is greater than .05, so the population of these variables is normally distributed. For all the variables which have passed the KS Test, we are going to test it for homogeneity by performing the Levenes Test. 3.Levene Test- This test is used for testing the homogeneity of the variable. Ho: The population of variable is homogeneous (variances are equal) H1: The population of variable is not homogeneous (variances are not equal) We take Value for Money as andependent variable and Occupation as a independent variable. Performing the Levene Test, we get the following result. Test of Homogeneity of Variances Value Value for money Levene Statistic df1 df2 Sig. .352 3 31 .788 Levene's test is used to assess Variance homogeneity, which is a precondition for parametric tests such as the t-test and ANOVA. The test can be used with two or more samples. With two samples, it provides the test of variance homogeneity for the t-test. With more samples, it provides the test for ANOVA.
If the significance from this test is less than 0.05, then variances are significantly different and parametric tests cannot be used (and a non-parametric test will probably have to be used). As significance value is greater than .05, we do accept the null hypothesis. The population of variable is homogeneous. Since this variables variance is not significantly different, we are going to perform the parametric test on it. As the number of samples are more than two,we perform ANOVA test,the result of which is as follows: ANOVA Value Value for money Sum of Squares df Mean Square F Sig. Between Groups 4.082 3 1.361 1.138 .349 Within Groups 37.061 31 1.196 Total 41.143 34 Here: Ho: Nanos Value for money perceived is same across all occupations H1: Nanos Value for money perceived is different for different occupations As the Significance value is 0.379>0.05,we need to accept the null hypothesis,i.e. theNanos value for money perceived does not significantly differ across the different types of occupations. We,now, take Occupation as an dependent variable and Vehicle currently owned as a independent variable. Performing the Levene Test, we get the following result. Test of Homogeneity of Variances occupation Levene Statistic df1 df2 Sig. .211 2 32 .811 Since Significance is 0.811>0.05. As significance value is greater than .05, we do accept the null hypothesis. The population of variable is homogeneous. Since this variables variance is not significantly different, we are going to perform the parametric test on it.
ANOVA occupation Sum of Squares df Mean Square F Sig. Between Groups 8.771 2 4.386 8.066 .001 Within Groups 17.400 32 .544 Total 26.171 34 Here: Ho: There are no significant differences between the groups'(occupation) mean scores for the type of vehicle owned. H1:There are significant differences between the groups'(occupation) mean scores for the type of vehicle owned. As the Significance value is 0.001<0.05,we need to reject the null hypothesis, i.eThere are significant differences between the groups'(occupation) mean scores for the type of vehicle owned. Thus the type of vehicle owned varies significantly across the different types of populations. For those variables which fail to pass the required assumptions, non parametric test such as Kruskal-Wallis Test(Anova) or Mann Whitney Test (2 sample) is performed on it. Lets consider the variables which have failed the Assumptions of parametric tests . Independent variable :Sex Dependent Variable : Perceived safety of the car Ho: Safety of the car is perceived not differently across the two genders. H1: : Safety of the car isperceived differently across the two genders. Since variable sex results into a 2 samples and both the variables failed to qualify the assumptions of the Parametric tests,we apply Mann Whitney test on them. Results are as follows: Ranks sex N Mean Rank Sum of Ranks Safety Rate the safety of the 1 male 21 18.95 398.00 car? 2 female 14 16.57 232.00 Total 35 b Test Statistics Safety Rate the safety of the car?
Mann-Whitney U 127.000 Wilcoxon W 232.000 Z -.728 Asymp. Sig. (2-tailed) .467 a Exact Sig. [2*(1-tailed Sig.)] .516 a. Not corrected for ties. b. Grouping Variable: sex As we can see,the significance value is 0.467> 0.05 ,thus have to accept the null hypothesis. Thus,Safety of the car is perceived similarly across the two genders. Similarly we can consider all the parameters which had failed the parametric test assumptions against Gender variable. The results are as follows: Ranks sex N Mean Rank Sum of Ranks View Considering the 1 male 21 17.83 374.50 increase in traffic and 2 female 14 18.25 255.50 pollution is it a boon or curse Total 35 Fuel Fueleffeciency 1 male 21 15.93 334.50 2 female 14 21.11 295.50 Total 35 Safety Rate the safety of the 1 male 21 18.95 398.00 car? 2 female 14 16.57 232.00 Total 35 Design Rate the design of 1 male 21 17.95 377.00 the car? 2 female 14 18.07 253.00 Total 35 Model which model would 1 male 21 18.33 385.00 you prefer? 2 female 14 17.50 245.00 Total 35 Buy would you want to buy a 1 male 21 18.17 381.50 NANO? 2 female 14 17.75 248.50 Total 35 Finance how do you plan to 1 male 21 20.24 425.00 finance the car? 2 female 14 14.64 205.00 Total 35
As we can for none of the variables the significance variable is <0.05 ,thus ,for all the variables the the values do not differ according to gender or no distinction can be made in the variables on the basis of gender.

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Ada assignment

  • 1. 1. Run Test: Ho : The sequence of observations is random. H1 : The sequence of observations is not random. If significance value(p) > .05 , we fail to reject Ho i.e. the sequence of observations is random. Hence the hypothesis that the sample is drawn in a random order is accepted.
  • 2. 2.Kolmogorov-Smirnov Test This test is used for testing whether the sample drawn has normal distribution. Ho: The population of random variable is normally distributed. H1: The population of random variable is not normally distributed. One-Sample Kolmogorov-Smirnov Test
  • 3. would you want sex to buy a NANO? N 35 35 a,,b Normal Parameters Mean 1.40 1.37 Std. Deviation .497 .490 Most Extreme Differences Absolute .390 .404 Positive .390 .404 Negative -.286 -.272 Kolmogorov-Smirnov Z 2.304 2.392 Asymp. Sig. (2-tailed) .000 .000 One-Sample Kolmogorov-Smirnov Test how do you plan to finance the Rate the design car? Space of the car?
  • 4. N 35 35 35 a,,b Normal Parameters Mean 1.83 3.23 3.74 Std. Deviation 1.098 1.497 1.221 Most Extreme Differences Absolute .375 .167 .241 Positive .375 .132 .152 Negative -.225 -.167 -.241 Kolmogorov-Smirnov Z 2.217 .990 1.423 Asymp. Sig. (2-tailed) .000 .280 .035 One-Sample Kolmogorov-Smirnov Test Rate the safety of the car? Fuel effeciency N 35 35 a,,b Normal Parameters Mean 4.17 4.37 Std. Deviation .954 .646 Most Extreme Differences Absolute .257 .292 Positive .193 .260 Negative -.257 -.292 Kolmogorov-Smirnov Z 1.522 1.728 Asymp. Sig. (2-tailed) .019 .005 a. Test distribution is Normal. b. Calculated from data. One-Sample Kolmogorov-Smirnov Test Considering the increase in traffic and pollution is it Value for money a boon or curse N 35 35 a,,b Normal Parameters Mean 3.29 1.34 Std. Deviation 1.100 .482 Most Extreme Differences Absolute .202 .419 Positive .202 .419 Negative -.142 -.257 Kolmogorov-Smirnov Z 1.198 2.478
  • 5. Asymp. Sig. (2-tailed) .113 .000 a. Test distribution is Normal. b. Calculated from data. As we can see from the above test result, the significance level of the variables sex,would you buy nano,model preferred,Financeplan,Design,Safety,Fuelefficiency,View on pollution <.05, so we fail to accept Ho which shows that the population of this variable is not normally distributed. For all other variables as the significance level is greater than .05, so the population of these variables is normally distributed. For all the variables which have passed the KS Test, we are going to test it for homogeneity by performing the Levenes Test. 3.Levene Test- This test is used for testing the homogeneity of the variable. Ho: The population of variable is homogeneous (variances are equal) H1: The population of variable is not homogeneous (variances are not equal) We take Value for Money as andependent variable and Occupation as a independent variable. Performing the Levene Test, we get the following result. Test of Homogeneity of Variances Value Value for money Levene Statistic df1 df2 Sig. .352 3 31 .788 Levene's test is used to assess Variance homogeneity, which is a precondition for parametric tests such as the t-test and ANOVA. The test can be used with two or more samples. With two samples, it provides the test of variance homogeneity for the t-test. With more samples, it provides the test for ANOVA.
  • 6. If the significance from this test is less than 0.05, then variances are significantly different and parametric tests cannot be used (and a non-parametric test will probably have to be used). As significance value is greater than .05, we do accept the null hypothesis. The population of variable is homogeneous. Since this variables variance is not significantly different, we are going to perform the parametric test on it. As the number of samples are more than two,we perform ANOVA test,the result of which is as follows: ANOVA Value Value for money Sum of Squares df Mean Square F Sig. Between Groups 4.082 3 1.361 1.138 .349 Within Groups 37.061 31 1.196 Total 41.143 34 Here: Ho: Nanos Value for money perceived is same across all occupations H1: Nanos Value for money perceived is different for different occupations As the Significance value is 0.379>0.05,we need to accept the null hypothesis,i.e. theNanos value for money perceived does not significantly differ across the different types of occupations. We,now, take Occupation as an dependent variable and Vehicle currently owned as a independent variable. Performing the Levene Test, we get the following result. Test of Homogeneity of Variances occupation Levene Statistic df1 df2 Sig. .211 2 32 .811 Since Significance is 0.811>0.05. As significance value is greater than .05, we do accept the null hypothesis. The population of variable is homogeneous. Since this variables variance is not significantly different, we are going to perform the parametric test on it.
  • 7. ANOVA occupation Sum of Squares df Mean Square F Sig. Between Groups 8.771 2 4.386 8.066 .001 Within Groups 17.400 32 .544 Total 26.171 34 Here: Ho: There are no significant differences between the groups'(occupation) mean scores for the type of vehicle owned. H1:There are significant differences between the groups'(occupation) mean scores for the type of vehicle owned. As the Significance value is 0.001<0.05,we need to reject the null hypothesis, i.eThere are significant differences between the groups'(occupation) mean scores for the type of vehicle owned. Thus the type of vehicle owned varies significantly across the different types of populations. For those variables which fail to pass the required assumptions, non parametric test such as Kruskal-Wallis Test(Anova) or Mann Whitney Test (2 sample) is performed on it. Lets consider the variables which have failed the Assumptions of parametric tests . Independent variable :Sex Dependent Variable : Perceived safety of the car Ho: Safety of the car is perceived not differently across the two genders. H1: : Safety of the car isperceived differently across the two genders. Since variable sex results into a 2 samples and both the variables failed to qualify the assumptions of the Parametric tests,we apply Mann Whitney test on them. Results are as follows: Ranks sex N Mean Rank Sum of Ranks Safety Rate the safety of the 1 male 21 18.95 398.00 car? 2 female 14 16.57 232.00 Total 35 b Test Statistics Safety Rate the safety of the car?
  • 8. Mann-Whitney U 127.000 Wilcoxon W 232.000 Z -.728 Asymp. Sig. (2-tailed) .467 a Exact Sig. [2*(1-tailed Sig.)] .516 a. Not corrected for ties. b. Grouping Variable: sex As we can see,the significance value is 0.467> 0.05 ,thus have to accept the null hypothesis. Thus,Safety of the car is perceived similarly across the two genders. Similarly we can consider all the parameters which had failed the parametric test assumptions against Gender variable. The results are as follows: Ranks sex N Mean Rank Sum of Ranks View Considering the 1 male 21 17.83 374.50 increase in traffic and 2 female 14 18.25 255.50 pollution is it a boon or curse Total 35 Fuel Fueleffeciency 1 male 21 15.93 334.50 2 female 14 21.11 295.50 Total 35 Safety Rate the safety of the 1 male 21 18.95 398.00 car? 2 female 14 16.57 232.00 Total 35 Design Rate the design of 1 male 21 17.95 377.00 the car? 2 female 14 18.07 253.00 Total 35 Model which model would 1 male 21 18.33 385.00 you prefer? 2 female 14 17.50 245.00 Total 35 Buy would you want to buy a 1 male 21 18.17 381.50 NANO? 2 female 14 17.75 248.50 Total 35 Finance how do you plan to 1 male 21 20.24 425.00 finance the car? 2 female 14 14.64 205.00 Total 35
  • 9. As we can for none of the variables the significance variable is <0.05 ,thus ,for all the variables the the values do not differ according to gender or no distinction can be made in the variables on the basis of gender.