# Understanding and Exploring Assumptions

Document Type:Coursework

Subject Area:Statistics

### Document 1

These assumptions have to be met for the particular tests to be used otherwise the tests cannot be used. The various types of assumptions covered in Field (2013) include: I. Activity and Linearity II. Normality of something or the other III. Independence IV. P-P Plots for variable Day3 from DownloadFestival. sav dataset Question 4 Comparison of the simple histograms and the respective p-p plots for normal distribution. From the above illustrations (question 2 and question 3), there is a clear distinction between the three variables (Day1, Day2, and Day3) in terms of data representation as normal distribution is concerned as portrayed by the histograms and p-p plots of the respective variables. Out of the three variables, Day1 is the closest to the normal distribution since it is evident from both the simple histogram and the p-p plots since the bell shape exists which normally represents normal distribution ("Using SPSS in Research," 2013, p.

It is also evident from the p-p plot that variable Day1 has a closer normal distribution since all the data points and the ideal line of the curve are very close. sav data set and Frequency command Statistics Hygiene (Day 1 of Download Festival) Hygiene (Day 2 of Download Festival) Hygiene (Day 3 of Download Festival) N Valid 810 264 123 Missing 0 546 687 Mean 1. 9765 Median 1. 7600 Mode 2. 44a Std. Deviation. 41 Percentiles 25 1. 5500 a. Multiple modes exist. The smallest value is shown The sample size for Day1 is 810 with no missing data. It seems that the intended sample size is 810 since Day2 and Day3 have missing values of 546 and 687 respectively. 520 and 0. Day1 has the highest median of 1. Day2 and Day3 median are 0. 79 and 0. 76 respectively. 41, for Day2 is 0. 822 and for Day3 is 0.

The same variables have standard errors of 1. 299 and 0. 433 respectively whereby the negative means that the distribution has more data points at the tails or ends while the negative kurtosis indicates a flat, light-tailed distribution. For example; For Day1 z-scores = 1. 047 This value for Day1 (0. 047) shows that there is no significance since (the scores are not all skewed) p>5. As for Day2 and Day3, the z-scores (7. 3 and 4. 961 Std. Error of Skewness. 241 Kurtosis -1. 946 Std. Error of Kurtosis. Histogram for Numeracy The sample size is 100 with all the variables having the sample of 100 (no missing data). The maximum, minimum and range values of the variables are as follows; Variable Exam Maximum-99 Minimum-15 Range-84 Variable Lecture Maximum-100 Minimum-8 Range-92 Variable Computer Maximum-73 Minimum-27 Range-46 Variable Numeracy Maximum-14 Minimum-1 Range-13 The mean for the four variables are as follows; Computer-50.

71, Exam-58. 10, Lecture-59. 765 and Numeracy-4. From the statistics shown, the distribution of variable Computer should have a lot of data points clustered near the middle center (mean) and this is evident from the histogram. (Argyrous, 1997, p. 65)The highest point (mode) is to the right but it is close to the mean. Its actual distribution fits the bell shape. The same applies to the variable Lecture. 292 Median 38. 00 Mode 34b 48b 48. 5b 4 Std. Deviation 12. 067 Variance 158. 0 206 Percentiles 25 31. 00 a. University = Duncetown University b. Multiple modes exist. The smallest value is shown University= Sussex Statistics Percentage on SPSS exam Computer literacy Percentage of lectures attended Numeracy N Valid 50 50 50 50 Missing 0 0 0 0 Mean 76. 337 Kurtosis -. 260 Std. Error of Kurtosis. 662 Range 43 46 87. 5 13 Minimum 56 27 12. From the statistics again, it is evident that Sussex University has the same mean and median (54.

00) while Duncetown University has a median of 49 and a mode of 48. The kurtosis values for all the variables for Duncetown University are negative showing that the distributions are heavy-tailed distributions. Question 7 Using SPSSExam. sav dataset The Levene’s test is used to test the null hypothesis that there exists no difference between the variances in the different groups (Brace, Kemp, & Snelgar, 2016, p. 97 Upper Bound 52. 55 5% Trimmed Mean 50. 12 Median 49. 00 Variance 65. 094 Std. Deviation 8. 505 Minimum 27 Maximum 73 Range 46 Interquartile Range 9 Skewness -. 337 Kurtosis 1. 662 Percentage of lectures attended Duncetown University Mean 56. 3619 95% Confidence Interval for Mean Lower Bound 49. 8 Skewness -. 337 Kurtosis -. 662 Sussex University Mean 63. 6827 95% Confidence Interval for Mean Lower Bound 57. 879 Upper Bound 68. 337 Kurtosis -. 662 Test of Homogeneity of Variance Levene Statistic df1 df2 Sig. Computer literacy Based on Mean.

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