Conducting inferential statistical analysis

Order Description Course: Research Methods Week 5: Collecting and analyzing quantitative data (part II) Useful Guide for uk.bestessays.com Dear writer, please note that what is written in red is a message from myself to you. Also, you need to know that this assignment needs a person who is quite knowledgeable in statistical analysis and research methods. Learning Resources (the required files are attached) 1- OLS Regression Example. 2- The book: a. Collis, J. & Hussey, R. (2013) Business Research: A Practical Guide for Undergraduate and Postgraduate Students. 4th ed. London: Palgrave-MacMillan. i. Chapter 12, ‘Analysing data using inferential statistics’ (pp. 258-296). 3- Youtube: a. https://www.youtube.com/watch?v=LnfPKGhJypU b. https://www.youtube.com/watch?v=nRAAAp1Bgnw c. https://www.youtube.com/watch?v=ECXeUj8I6w8 d. https://www.youtube.com/watch?v=HgfHefwK7VQ e. https://www.youtube.com/watch?v=tlbdkgYz7FM 4- Test Your Knowledge. 5- Inferential Statistical Analysis – Questions. Key Concept Exercise: Review of quantitative research design (this was the assignment we have already submitted to the university) Inferential statistical methods are widely used in research in order to conduct tests of differences for dependent or independent samples, analyse associations between different types of variables and establish relationships using models between dependent and independent variable(s). For this week's Key Concept Exercise you will evaluate examples of inferential statistical analysis by discussing empirical results and the strengths, weakness and suitability of different statistical estimation and hypothesis testing procedures. To prepare for this Key Concept Exercise: ? Read the Required Learning Resources for Week 5. ? It is strongly recommended that you work through the Week 5 Test Your Knowledge Questions and while undertaking your reading. These are located with the Week 5 Learning Resources. To complete this Key Concept Exercise: 1- In approximately 500 words, answer TWO of the FOUR questions in the file provided here on Inferential Statistical Analysis (1- the questions are attached. 2- all questions were answered, not only two). Find my answers below … Question 1 (a) The p-value of each independent variable tests the null hypothesis. If the coefficient is zero the independent variable has no effect on the dependent variable. A low p-value (of less than 0.05) means that the null hypothesis can be rejected. Additionally, this indicates that a parameter with a low p-value is more meaningful since a change in its value leads to a change in the value of the dependent variable (Creswell, 2003). Conversely, a parameter with high p-value is insignificant because a change in the dependent variable is not necessarily associated with it. In the table, the constant variable is significant because it has a p-value of 0.000. It also has a positive coefficient value of 0.015 meaning if its value increases slightly, the REALGDP value will increase significantly. The OIL parameter has a p-value of 0.03 (which is < 0.05). This means it is significant. Furthermore, its coefficient value is -0.037. This means a unit increase in oil prices leads to a small decrease in the REALGDP value. The interest rate has a p-value of 0.032 (which is <0.05). This means it is statistically significant in relation to the GDP growth rate. It has a coefficient value of -0.012, which means that a small increase in the interest rate leads to a big decrease in GDP growth rate value. Inflation rate variable has a p-value of 0.145 (which is > 0.05). This shows its effect on the GDP growth rate value is insignificant. Moreover, its coefficient value of -0.004 means that a big increase in the inflation rate variable leads a minor decrease in GDP growth rate value. The overall fit of the model is indicated by the coefficients of the predictors. From the table, each predictor has a coefficient value greater than one (not equal to zero). The null hypothesis is tested and confirmed that it is acceptable. (b) Yes. The OLS model assumes that the parameters are independent and randomly distributed. This assumption holds for this question. Also, Adj-R2 of 58% means that there is a high correlation between the dependent and the independent variables. Question 2 (a – 1) This hypothesis is correct because from the test statistics table the distribution of productivity values in asymptotic and exact statistical significance levels are not the same. The Asymptotic significance (2-tailed) value is 0 .448 and the Exact asymptotic (2-tailed) value is 0.454. (a – 2) This hypothesis is right because from the test statistics table the distribution of productivity, the values in asymptotic and exact statistical significance levels are not the same. The Asymptotic significance (2-tailed) value is 0 .005 and the Exact asymptotic (2-tailed) value is 0.004. (a – 3) This hypothesis is acceptable because from the test statistics table the distribution of productivity, the values in asymptotic and exact statistical significance levels are not the same. The Asymptotic significance (2-tailed) value is 0.218 and The Exact asymptotic value is 0.221. (b – 1) The Mann-Whitney test has two major assumptions. One is that the samples under study and the observations in each sample are random and independent. The other one is that the observations are ordinal (ranked) or numeric (Creswell, 2003). The first assumption has not been met because the participants were not randomly and independently assigned to each category. They were rather put in groups. The second assumption has been met because each group variable (Sex, Postgrad, and Training) has been ranked in each category, for example, male and female categories have been ranked separately. Question 3 (a) The null hypothesis (H0) being tested for the Chi-Square test is that the three mobile phones are equally popular. (b) Using the Chi-Square table, at two degrees of freedom and a significance level (a) of 0.05, the answer on the chart is 5.99. Therefore, for the null hypothesis to be rejected the calculated Chi-Square value must be must be = 5.99. However, our calculated Chi-Square value is 6.86. This value is greater than 5.99, thus the null hypothesis will be rejected. Using the SPSS output, Asymptotic Significance (2-sided) has a value of 0.032 also known as the p-value. This value is less than the chosen significance value of 0.05. This confirms further that the null hypothesis will be rejected. The value of expected observations is 33.3 and is the same for each category. This indicates that the model in question is an equiprobability model. It also indicates that the mobile phones are equally popular. There are statistically significant differences in the participant’s preference of three mobile devices. The low-range, mid-range, and high range devices have a residual value of -2.3, 11.7, and -9.3 respectively. The values indicate that each mobile device has a different popularity. (c) One assumption of the Chi-Square test is that data in the cells should be counts rather than percentages. The assumption is met in the above example. Another assumption is that the study groups must be independent. This implies a different test must be applied if the categories are related. The assumption is not met in the example because all the participants were given the same test. Question 4 (a) The Wald statistic provides the significance index of each variable in the equation. It also has a Chi-Square distribution. Sex has the highest Wald value of 2.154 while Age has the least Wald value of 0.940. This indicates Sex is more significant than age in the equation. The Exp(B) column indicates the extent to which increasing the corresponding measure by a single unit will influence the odds ratio. It is interpreted based on a change of odds. An Exp(B) value greater than one means that odds of an event occurring increases; if Exp(B) is less than one means an increase in the value of a predictor results in a drop in the odds of the event occurring (Creswell, 2003). For example, experience has an Exp(B) value of 1.159 this indicates that if experience is increased by one unit (one year) the odds ratio becomes one times higher. Therefore, the likelihood of getting a promotion becomes higher as the number of years of experience increases. (b) Yes. This is because Experience has an Exp(B) value greater than one, and greater than Exp(B) value of Age. Thus, the years of experience increase the chances of getting a promotion. References Creswell, J. W. (2003). Research design: qualitative, quantitative, and mixed methods approaches. 2nd ed. Sage Publications. Available online from https://isites.harvard.edu/fs/docs/icb.topic1334586.files/2003_Creswell_A%20Framework%20for%20Design.pdf (Accessed: 10 February 2017). End of my answers. Collaboration: Conducting inferential statistical analysis (this is what I need you to do for me, my dear writer) In your Collaboration you will further discuss statistical analysis with your classmates. In examining the different inferential statistical methods, consider their fundamental characteristics, underlying assumptions, strengths, weakness and suitability for producing generalisations regarding an unbeknown population. To prepare for this Collaboration: 1- Review the required Learning Resources and your Key Concept Exercise from Week 5. To complete this Collaboration (this is what matters here): 1- reply to your classmates’ posts in the Collaboration Forum by: a. Providing constructive critique on your classmates’ submissions by analysing further the fundamental characteristics of the inferential statistical methods. b. Discussing critically the purposes and wider issues when conducting statistical analyses. c. Analysing the suitability of the inferential statistical methods by highlighting their strengths and limitations, with emphasis put on your research plans. Find below the paper of one of my colleagues which I would like you to respond to. My colleague wrote: “Question 3: In the question where a company want to produce three different mobile phones in various ranges of low-range, mid-range and high-range specifications. The Chi-Square test, is a test used for analyzation of association between nominal variables. This test was used to see if the observed responses was in line with the original null hypothesis (H0), which was that there was no dependency on selection of model, and that these ranges would be equally popular. Using this test implies that the researchers presented three models that are mutually exclusive and that the responders could just pick one object. The test statistics shows that there is 0 cells with an expected frequency less than 5, which mean that the analysis method is valid. Further we see that the asymptotic significance (Asymp. Sig.) is at .032 or 3,2% which is lower than the threshold for normal p-value which is 0.05 or 5%. P-value is the percentage probability of the hypothesis to be true. In this case, there is a 3,2% change of experiencing these findings under extreme conditions with the hypothesis being true. As the threshold for significance level is 5%, we can conclude that the hypothesis of that the choice of phone is independent of specifications/model range is untrue. (Ling, 2008) Question 2: In a case where there is non-parametric data and the objective is to test the differences of independence in samples, Mann-Whitney is the prevalent choice of analysis method (Collis & Hussey 2013). This was the chosen test in a case where the question was to find the distribution of productivity between gender, degree and training of employees in a company. The data tables are found as appendix 1. H0.1: The distribution of productivity of male employees is equal to the distribution of productivity of female employees. ? We find in statistics from comparison of gender performance that the p value is 0,454 which is above the threshold of significance value of 0,05. Meaning that the hypothesis of no connection between gender and performance cannot be rejected. H0.2: The distribution of productivity of graduate employees is equal to the distribution of productivity of undergraduate employees. ? We find in statistics from comparison of gender performance that the p value is 0,004 which is below the threshold of significance value of 0,5. Meaning that the hypothesis of no connection between postgrad and performance is rejected. H0.3: The distribution of productivity of trained employees is equal to the distribution of untrained employees. ? We find in statistics from comparison of gender performance that the p value is 0,221 which is above the threshold of significance value of 0,05. Meaning that the hypothesis of no connection between training and performance cannot be rejected. I believe that the reasoning behind choosing Mann-Whitney is valid because of there being one linear value being male/female, under/postgrad and trained/non-trained, and one variable measurement being the number of each. The Variables are non-normal and are mutually exclusive. References: Ling, (2008). Tutorial: Pearson's Chi-square Test for Independence. [online] Ling.upenn.edu. Available at: http://www.ling.upenn.edu/~clight/chisquared.htm [Accessed 11 Feb. 2017]. Collis, J. & Hussey, R. (2013) Business Research: A Practical Guide for Undergraduate and Postgraduate Students. 4th ed. London: Palgrave-MacMillan. Chapter 12, ‘Analysing data using inferential statistics’ (pp. 258-296) Saunders, M., Lewis, P. & Thornhill, A. (2012) Research Methods for Business Students, 6th ed. Pearson Learning Solutions. Chapter 12, ‘Analysing quantitative data’ (pp. 472-543)” End of my colleague’s post.