Malik_BUSI820_Assignment3

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School of Business, Liberty University Faizan Malik Quantitative Analysis- Descriptive Statistics, Ordinal Scale and Dichotomous Variable Assignment Author Note: Faizan Malik I have no known conflict of interest to disclose. Correspondence concerning this article should be addressed to Faizan Malik: Fmalik@Liberty.edu

BUSI820 Assignment 3 Table of Contents Quantitative Analysis- Descriptive Statistics, Ordinal Scale and Dichotomous Variable 3 Skewness 3 Stem-and-Leaf Plot 5 Nominal Variables 6 Boxplots 7 References 9 2

BUSI820 Assignment 3 4.1.For the variables with five or more ordered levels, compute the skewness. Describe the results. Which variables in the dataset are approximately normally distributed/scale? Which ones are ordered but not normal? Figure 1 Descriptive Statistics N Mean Skewness Statistic Statisti c Statistic Std. Error positive evaluation, institution 50 3.38 .059 .337 positive eval, social life 50 3.10 .031 .337 positive evaluation, major 49 3.27 -.115 .340 positive evaluation, facilities 50 2.76 -.136 .337 age group 50 1.96 .074 .337 Valid N (listwise) 49 3

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BUSI820 Assignment 3 4.1.a. The variables that exist with five or more ordered levels are positive evaluation/institution, positive evaluation/social life, positive evaluation/major, positive evaluation/facilities, and age group. 4.1.b. Positive evaluation institution and social life, and age group have skewness near 0, indicating a normal distribution. Positive evaluation major and facilities both carry a negative skewness, indicating asymmetry of data and potential outliers in the data set. 4.1.c. Variables closest to zero will be considered normally distributed or scaled, which would be positive eval/social life (0.31), sex at birth (0.83), age group (.074), and positive eval/institution (.059). 4.1.d. The variable positive evaluation/major is ordered but not normal, it has many ordered levels but is extremely skewed. Brys et al. (2003) makes note that, “Asymmetry of a univariate continuous distribution is commonly described as skewness. The well- known classical skewness coefficient is based on the first three moments of the data set, and hence it is strongly affected by the presence of one or more outliers” (Brys et al., 2003). 4

BUSI820 Assignment 3 4.2.Do a stem-and-leaf plot for the same-sex parent’s height split by sex at birth. Discuss the plots. Figure 2 Stem-and-Leaf Plots same sex parent's height Stem-and-Leaf Plot for sbirth= males Frequency Stem & Leaf .00 6 . 4.00 6 . 4455 2.00 6 . 67 5.00 6 . 88888 1.00 7 . 1 6.00 7 . 223333 7.00 7 . 4444555 1.00 7 . 6 Stem width: 10.00 Each leaf: 1 case(s) same sex parent's height Stem-and-Leaf Plot for sbirth= females Frequency Stem & Leaf 1.00 Extremes (=<58.0) 1.00 59 . 0 3.00 60 . 000 .00 61 . 7.00 62 . 0000000 5.00 63 . 00000 1.00 64 . 0 2.00 65 . 00 4.00 66 . 0000 Stem width: 1.00 Each leaf: 1 case(s) 4.2.a Stem and leaf plots are most often used to “provide macro-level visual distribution and a micro-level view of the individual data points,” by illustrating how frequently certain values or scores occur. In stem and leaf plots, the stem indicates the first digit of a value and the leaf is the second and collectively shows the frequency of each value. Figure 2 illustrates that 11 same-sex parents have heights between 64 and 68 inches, and 15 same-sex parents have heights above 70 inches. 5

BUSI820 Assignment 3 4.3.Which variables are nominal? Run Frequencies for the nominal variables and other variables with fewer than five levels. Comment on the results. Figure 3 Frequency Table sex at birth Frequency Percent Valid Percent Cumulative Percent Valid males 26 52.0 52.0 52.0 females 24 48.0 48.0 100.0 Total 50 100.0 100.0 marital status Frequency Percent Valid Percent Cumulative Percent Valid single 20 40.0 40.8 40.8 married 18 36.0 36.7 77.6 divorced 11 22.0 22.4 100.0 Total 49 98.0 100.0 Missing System 1 2.0 Total 50 100.0 does subject have children Frequency Percent Valid Percent Cumulative Percent Valid no 24 48.0 48.0 48.0 yes 26 52.0 52.0 100.0 Total 50 100.0 100.0 television shows-sitcoms Frequency Percent Valid Percent Cumulative Percent Valid no 18 36.0 36.0 36.0 yes 32 64.0 64.0 100.0 Total 50 100.0 100.0 television shows-movies Frequency Percent Valid Percent Cumulative Percent Valid no 32 64.0 64.0 64.0 yes 18 36.0 36.0 100.0 4.3.a From the results, the variables sex at birth, marital status, does the subject have children, television show-sitcoms, and television shows- movies are nominal, or have variables that “are just names and thus are not ordered” (Morgan et al., 2020). 6

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BUSI820 Assignment 3 4.4.Do boxplots for student height and for hours of study. Compare the two plots. Figure 4 Case Processing Summary Cases Valid Missing Total N Percent N Percent N Percent student height in inches 50 100.0% 0 0.0% 50 100.0% hours of study per week 50 100.0% 0 0.0% 50 100.0% 7

BUSI820 Assignment 3 4.4.a Box plots are utilized to visually represent statistical measures to show the distribution of results and provide other general information about data. Figure 4 illustrates scores for student height and hours of study per week, with neither variable having any outliers or missing data. The box plot for student height indicates the data is symmetrically distributed, ordered from largest to smallest, and has no significant skewness. Hours of study per week, however, indicate that the lower half of the data set is relatively smaller than the upper half or a positively skewed distribution. 8

BUSI820 Assignment 3 References Brath, R., & Banissi, E. (2017, May). Stem & leaf plots extended for text visualizations. In 2017 14th International Conference on Computer Graphics, Imaging and Visualization (pp. 99-104). IEEE. Brys, G., Hubert, M., & Struyf, A. (2003). A comparison of some new measures of skewness. In Developments in robust statistics: international conference on robust statistics 2001 (pp. 98-113). Physica-Verlag HD. Morgan, G., Leech, N., Gloeckner, G., Barrett, K. (2020). IBM SPSS for Introductory Statistics (5th Ed.). New York, NY 9

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