BUSI820DB3

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School of Business, Liberty University Faizan Malik Week 3 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 D3.4.1 Using Outputs 4.1a and 4.1b: (a) What is the mean visualization test score? (b) What is the skewness statistic for the math achievement test? What does this tell us? (c) What is the minimum score for the mosaic pattern test? How can that be? D3.4.1.a The mean visualization test score is 5.2433. D3.4.1.b The skewness statistic, which Morgan et al. (2020) explain is used to understand the distribution for a variable, for the math achievement test is .044 (Morgan et al., 2020). Since this falls between -1 and 1, the variable is considered evenly distributed. D3.4.1.c The minimum score for the mosaic pattern test is -4.0, which indicates that the particular test can yield negative scores. In reviewing the codebook, the test scores range between -4 to 16 which indicates at least one individual received the lowest possible score for the mosaic pattern test. D3.4.2.Using Output 4.1b: (a) For which variables that we called scale, is the skewness statistic more than 1.00 or less than –1.00? (b) Why is the answer important? (c) Does this agree with the boxplot for Output 4.2? Explain. D3.4.2.a The competence scale is the only variable that has a skewness that is outside of the range of -1 to 1, with a skewness statistic of -1.634. D3.4.2.b This is significant as it indicates the tail of the score distribution is elongated to the left, with most of the data concentrated on the left side of the distribution, suggesting a substantial imbalance in the distribution that may be a result of errors within the dataset (Morgan et al., 2020). D3.4.2.c This does agree with the boxplot for Output 4.2, as the larger portion of the box (which signifies the majority of the data) is to the left of the median. D3.4.3.Using Output 4.2b: (a) How many participants have missing data? (b) What percent of students have a valid (non-missing) motivation scale or competence scale score? (c) Can you tell

from Outputs 4.1 and 4.2b how many are missing both motivation scale and competence scale scores? Explain. D3.4.3.a There are a total of 4 participants that have missing data. D3.4.3.b A total of 94.7% of participants had valid, non-missing data for both motivation and competence scale scores. D3.4.3.c From Output 4.1b, it is shown that both competence and motivation have a score of 73, a scale of 71, and a population of 75. This indicates that two participants are missing both motivation and competence scores and a total of four participants are missing at least one score. 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). D3.4.4.Using Output 4.4: (a) Can you interpret the means? Explain. (b) How many participants are there altogether? (c) How many have complete data (nothing missing)? (d) What percent are on the fast track? (e) What percent took Algebra 1 in h.s.? D3.4.4.a Output 4.4 is a table of descriptive statistics, which indicates the number of participants with valid data (N) and the mean which dictates where categories each of the participants belongs to. D3.4.4.b There were a total of 75 participants. D3.4.4.c All participants have complete data, as indicated by Valin N (listwise). D3.4.4.d From the dataset, it can be 1 is coded as the regular track and 0 for the fast track. With the mean of students on the regular track at 0.55, we can infer that 45% of students are on the fast track. D3.4.4.e From the dataset, 79% of participants took Algebra 1 in high school. D3.4.5.Using Output 4.5: (a) 9.6% of what group are Asian-Americans? (b) What percent of students have visualization 2 scores of 6? (c) What percent had such scores of 6 or less? D3.4.5.a Based on Output 4.5, 9.6% are the percentage of participants with valid data and that identify as Asian- American. D3.4.5.b Of the participants, 5.3% received a score of 6 on the visualization retest. D3.4.5.c Using the cumulative percent, 70.7% of participants scored 6 or less on the visualization retest. Cumulative percent provides a summary of the distribution of a variable within a dataset and allows researchers to understand the proportion of values that fall below or equal to a specific threshold or percentile, thus allowing researchers to communicate the spread and characteristics of the data (Shaharudin, & Ahmad, 2017). References

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 Shaharudin, S. M., & Ahmad, N. (2017). Choice of cumulative percentage in principal component analysis for regionalization of peninsular Malaysia based on the rainfall amount. In Modeling, Design and Simulation of Systems: 17th Asia Simulation Conference, AsiaSim 2017, Melaka, Malaysia, August 27–29, 2017, Proceedings, Part II 17 (pp. 216-224). Springer Singapore.

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