BUSI820DB2

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School of Business, Liberty University Faizan Malik Week 2 Discussion 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 D2.3.1 If you have categorical, ordered data (such as low income, middle income, high income) what type of measurement would you have? Why? D2.3.1a Data that is categorical and ordered, such as those relating to income levels, would be considered to be an ordinal measurement, as it contain greater than three ordered level in which the difference between pairs is unequal (Morgan et al., 2020). Morgan et al. (2020) goes on to explain that, due to the imbalance between pairs, the data within ordinal measurements contain some degree of distortion (Morgan et al., 2020). D2.3.2. (a) Compare and contrast nominal, dichotomous, ordinal, and normal variables. (b) In social science research, why isn’t it important to distinguish between interval and ratio variables? D2.3.2a Nominal, dichotomous, ordinal, and, and normal variables all utilized within statistical analysis, each having some degree of categories and/or order. Nominal variables contain numbers that represent categories, but they carry no implied order or value, whereas dichotomous variables will only have two categories that may or may not have an implied order (Morgan et al., 2020). Ordinal and normal variables, however, are both ordered from low to high with ordinal variables focusing on differences of pairs being equal and normal variables focusing on scores being equally distributed (Morgan et al., 2020). D2.3.2b Although interval and ratio variables both have ordered levels with quantifiable differences, ratio variables differ in that they carry a true zero point (Morgan et al., 2020). In the context of social science research, many studies are centered around non- quantifiable variables such as human emotion. As such, an absolute or true zero becomes non-sensical, as having zero emotions would not be included within such a study. Rather, social studies may benefit from the use of inferential statistics, which “a variety of statistical significance tests that investigators can use to make inferences about their sample data” (Allua & Thompson, 2008).

D2.3.3. What percent of the area under the standard normal curve is within one standard deviation of (above or below) the mean? What does this tell you about scores that are more than one standard deviation away from the mean? D2.3.3.a There is an area of approximately 34% both above and below the mean, which means approximately 32% would be more than one standard deviation away from the mean. D2.3.4. (a) How do z scores relate to the normal curve? (b) How would you interpret a z score of –3.0? (c) What percentage of scores is between a z of –2 and a z of +2? Why is this important? D2.3.4.a Z scores refer to the number of standard deviations that a score would be above or below zero and relate to the normal curve, as all normal curves can be converted into standard normal curves by setting the mean as 0 and standard deviation as 1 (Morgan et al., 2020). D2.3.4.b A z-score of 3.0 indicates that the score is three standard deviations below the mean, meaning the score itself is rare or can be considered an outlier. D2.3.4.c Approximately 95% of all scores will fall between a -2 and 2 z-score, as one standard deviation will entail approximately 68% of scores. Given most scores will fall into this range, it allows researchers to detect outliers and other disruptions to their study. Abdi (2007) also explains that “scores from different distributions can be standardized in order to provide a way of comparing them that includes consideration of their respective distributions” (Abdi, 2007). D2.3.5. Why should you not use a frequency polygon if you have nominal data? What would be better to use to display nominal data? D2.3.5c Given nominal data exists in the absence of any inherent order, displaying such data via a frequency polygon would imply a false sequence. A better option would be to utilize frequency distribution or bar chart (Morgan et al., 2020). References Abdi, H. (2007). Z-scores. Encyclopedia of measurement and statistics , 3 , 1055-1058. Allua, S., & Thompson, C. B. (2009). Inferential statistics. Air Medical Journal , 28 (4), 168-171. Morgan, G., Leech, N., Gloeckner, G., Barrett, K. (2020). IBM SPSS for Introductory Statistics (5th Ed.). New York, NY

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