This individual assignment requires you to apply statistical knowledge and skills learned from BEO5539 lectures between week 6 and 7. Please note the following: (a)...

This individual assignment requires you to apply statistical knowledge and skills learned from BEO5539 lectures between week 6 and 7. Please note the following:

1. 
   

   (a) YouwillundertakeANOVA(AnalysisOfVAriance),correlationanalysisandKruskal-Wallis test for this assignment. The model can be based on a theory, several theories, your experience, and/or ideas from research article(s). Suggest you consider model that is of interest to you or one that is related to your profession or you have knowledge about.

   
   

Victoria Graduate School of Business BEO5539 BUSINESS STATISTICS ASSIGNMENT 2 (INDIVIDUAL ASSIGNMENT) – 20% This individual assignment requires you to apply statistical knowledge and skills learned from BEO5539 lectures between week 6 and 7. Please note the following: (a) You will undertake ANOVA (Analysis Of VAriance), correlation analysis and Kruskal-Wallis test for this assignment. The model can be based on a theory, several theories, your experience, and/or ideas from research article(s). Suggest you consider model that is of interest to you or one that is related to your profession or you have knowledge about. (b) Table 1 – Variables for Assignment 2 Variables* Remarks Database Dependent variable This variable must be interval or ratio scale data. The World Bank. Refer to point e(i) Factor A This variable must be an ordinal data with at least 3 categories. Refer to point e(ii) Factor B This variable must be an ordinal data with at least 3 categories. Refer to point e(ii) Note: In this assignment, your sample is used to make inferences about the population means. *You must not use GDP, IQ score and Happiness score as any of your variables in this individual assignment because these variables are being used in the tutorial example. (c) Following are equations and conceptual diagrams relating to one-way ANOVA, two-way ANOVA and bivariate correlation in this assignment: (i) One-way ANOVA Y ij =μ+ τ i +ϵ ij where Y ij = Dependent variable μ = grand mean. τ i = treatment effect of Factor A. ϵ ij = error terms. Note: ϵ ij is not reflected in Figure 1. (ii) Two-way ANOVA Y ij =μ+ τ i + + α + ϵ ij where Y ij = Dependent variable μ = grand mean. τ i = treatment effect of Factor A. = treatment effect of Factor B. α = Interaction between Factor A and B. ϵ ij = error terms. Note: ϵ ij is not reflected in Figure 2. Figure 2 – Two-way ANOVA Figure 1 – One-way ANOVA (iii) Bivariate Correlation Figure 3 – Bivariate correlation between Dependent variable and Factor A (d) Real data must be used in this assignment. You should not use the tutorial’s practice data set for your assignment. (i) Accessed The World Bank database via this weblink http://data.worldbank.org/indicator to download your Dependent Variable (Yij ). (ii) Accessed the following websites to consider and search for Factor A and Factor B http://hdr.undp.org/en/data https://photius.com/rankings/ (iii) Please refer to Excel file ‘Assignment 2 supplementary info.xlsx’ for country information. (e) For statistical analysis involving any hypothesis test in this assignment, you are required to do the following for each hypothesis test:  Formulate the null and alternative hypotheses.  State your statistical decision using significant value (?) of 5%.  State your conclusion in context. Note: Hypothesis testing must be undertaken one at a time, do not consolidate a series of hypothesis tests even if the hypothesis statements appeared to be similar. (f) This assignment is due in week 9. Please submit your assignment in Word document via VU Collaborate together with a completed and signed assessment declaration form and your SPSS data file in ‘sav’ format. http://data.worldbank.org/indicator http://hdr.undp.org/en/data https://photius.com/rankings/ Assignment tasks: (1) Provide an introduction section on the context of your assignment, sample size, the dependent variables and factors (including their units of measurement). Identify the source and period of the data used in this assignment. (2) Assume normality in data distribution for one-way ANOVA [task 2(i)]; two-way ANOVA [task 2(ii)]; and bivariate correlation [task 2(iii)]). No. Variable Requirements: 2(i) ● Dependent variable ● Factor A (1) Conduct a one-way ANOVA to test the null hypothesis that the dependent variable means are the same for all categories in Factor A amongst the population of countries. Please perform hypothesis tests for homogeneity of variances, main effect and post-hoc analysis. (2) Find Tukey or Games-Howell confidence intervals for the mean difference between pair of Factor A’s categories. Is there any statistically significant mean difference between pair of categories? (Report on these only where the differences are statistically significant.) Each hypothesis test must adhere to the hypothesis testing requirements in point (e), clearly analysed and presented. 2(ii) ● Dependent variable ● Factor A ● Factor B (1) Conduct a 2-way ANOVA to test the null hypothesis that dependent variable means are the same for all categories in Factor A and Factor B amongst the population of countries. Allow for the possibility of an interaction effect between Factor A and Factor B towards the dependent variable. (2) Produce Tukey or Games-Howell confidence intervals for row and column differences. (Report on these only where the differences are statistically significant.) Each hypothesis test must adhere to the hypothesis testing requirements in point (e), clearly analysed and presented. 2 (iii) ● Dependent variable ● Factor A Conduct a Bivariate Correlation analysis on the relationship between Dependent variable and Factor A using an appropriate statistical technique. Hypothesis test must adhere to the hypothesis testing requirements in point (e), clearly analysed and presented. (3) Remove the data normality assumption in Assignment task (2) and run the Kruskal-Wallis test. No. Variable Requirements: 3 ● Dependent variable ● Factor A (1) Conduct a Kruskal-Wallis analysis to test the null hypothesis that the mean ranks for the dependent variable are the same for all categories in Factor A amongst the population of countries. Compare the results between this test and one-way ANOVA [obtained in 2(i)] and determine which is an appropriate test (explain why). Each hypothesis test must adhere to the hypothesis testing requirements in point (e), clearly analysed and presented.