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. Hencethe 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 normaldistribution.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,,bNormal Parameters Mean 1.40 1.37 Std. Deviation .497 .490Most 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,,bNormal Parameters Mean 1.83 3.23 3.74 Std. Deviation 1.098 1.497 1.221Most 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,,bNormal Parameters Mean 4.17 4.37 Std. Deviation .954 .646Most Extreme Differences Absolute .257 .292 Positive .193 .260 Negative -.257 -.292 Kolmogorov-Smirnov Z 1.522 1.728 Asymp. Sig. (2-tailed) .019 .005a. 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,,bNormal Parameters Mean 3.29 1.34 Std. Deviation 1.100 .482Most Extreme Differences Absolute .202 .419 Positive .202 .419 Negative -.142 -.257 Kolmogorov-Smirnov Z 1.198 2.478
Asymp. Sig. (2-tailed) .113 .000a. 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 buynano”,”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 thesevariables is normally distributed.For all the variables which have passed the KS Test, we are going to test it for homogeneity byperforming the Levene’s 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 VariancesValue Value for money Levene Statistic df1 df2 Sig. .352 3 31 .788Levenes test is used to assess Variance homogeneity, which is a precondition for parametrictests such as the t-test and ANOVA. The test can be used with two or more samples. With twosamples, it provides the test of variance homogeneity for the t-test. With more samples, it providesthe test for ANOVA.
If the significance from this test is less than 0.05, then variances are significantly different andparametric 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 ofvariable is homogeneous. Since this variable’s variance is not significantly different, we are goingto perform the parametric test on it.As the number of samples are more than two,we perform ANOVA test,the result of which is asfollows: ANOVAValue Value for money Sum of Squares df Mean Square F Sig.Between Groups 4.082 3 1.361 1.138 .349Within Groups 37.061 31 1.196Total 41.143 34Here: Ho: Nano’s Value for money perceived is same across all occupations H1: Nano’s Value for money perceived is different for different occupationsAs the Significance value is 0.379>0.05,we need to accept the null hypothesis,i.e. theNano’s valuefor 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 aindependent variable.Performing the Levene Test, we get the following result. Test of Homogeneity of Variancesoccupation Levene Statistic df1 df2 Sig. .211 2 32 .811Since Significance is 0.811>0.05. As significance value is greater than .05, we do accept the nullhypothesis. The population of variable is homogeneous. Since this variable’s variance is notsignificantly different, we are going to perform the parametric test on it.
ANOVAoccupation Sum of Squares df Mean Square F Sig.Between Groups 8.771 2 4.386 8.066 .001Within Groups 17.400 32 .544Total 26.171 34Here: Ho: There are no significant differences between the groups(occupation) meanscores for the type of vehicle owned. H1:There are significant differences between the groups(occupation) mean scores for thetype of vehicle owned.As the Significance value is 0.001<0.05,we need to reject the null hypothesis, i.eThere aresignificant differences between the groups(occupation) mean scores for the type of vehicleowned.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 asKruskal-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 :SexDependent Variable : Perceived safety of the carHo: 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 assumptionsof the Parametric tests,we apply Mann Whitney test on them.Results are as follows: Ranks sex N Mean Rank Sum of RanksSafety Rate the safety of the 1 male 21 18.95 398.00car? 2 female 14 16.57 232.00 Total 35 b Test Statistics Safety Rate the safety of the car?
Mann-Whitney U 127.000Wilcoxon W 232.000Z -.728Asymp. Sig. (2-tailed) .467 aExact Sig. [2*(1-tailed Sig.)] .516a. Not corrected for ties.b. Grouping Variable: sexAs 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 assumptionsagainst Gender variable.The results are as follows: Ranks sex N Mean Rank Sum of RanksView Considering the 1 male 21 17.83 374.50increase in traffic and 2 female 14 18.25 255.50pollution is it a boon or curse Total 35Fuel Fueleffeciency 1 male 21 15.93 334.50 2 female 14 21.11 295.50 Total 35Safety Rate the safety of the 1 male 21 18.95 398.00car? 2 female 14 16.57 232.00 Total 35Design Rate the design of 1 male 21 17.95 377.00the car? 2 female 14 18.07 253.00 Total 35Model which model would 1 male 21 18.33 385.00you prefer? 2 female 14 17.50 245.00 Total 35Buy would you want to buy a 1 male 21 18.17 381.50NANO? 2 female 14 17.75 248.50 Total 35Finance how do you plan to 1 male 21 20.24 425.00finance 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 thethe values do not differ according to gender or no distinction can be made in the variables on thebasis of gender.