What is the mathematical reasoning behind how linear contrasts are used for a priori comparison of means after an ANOVA?
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- Males under the age of 25 must pay far higher auto insurance premiums than females in this age group. How does this fact relate to statistical discrimination? Statistical discrimination implies that discrimination can persist indefifinitely, while the taste-for-discrimination model suggests that competition might reduce discrimination in the long run. Explain the difference.The Chi-Square analysis provides researchers with a specific estimate of the overall significance for the relationship between an outcome and a categorical exposure variable when there are more than 2 categories, but in order to assess the individual relationships, researchers should calculate individual risk ratios. True FalseAn MBA student wants to answer the question "How does an MBA major affect the number of job offers received?" He randomly sampled four recent graduates in each of the following three MBA majors [Finance (x1), Marketing(x2) and Management(x3)] and asked each of them to report the number of job offers. He obtains the following results. Sum of square between majors (SSB) = 62.17 Mean of square within majors (MSW) = 2.28 Mean number of job offers received from each MBA major are as follows: Finance major (x1) = 2.25 Marketing major (x2) = 3.25 Management major (x3) = 7.5 Construct the Analysis of Variance (ANOVA) table, and then find the SSW 62.17 20.52 82.69 SST 20.52 62.17 82.69 MSB 31.085 50 2.28 F calculated 15.45 12.20 13.36
- Provide an illustration on how Bayesian analysis is used.True or False: For both AIC and BIC (two statistics we often use to compare model fit), the model with higher values of AIC or BIC is considered a better fit to the data.How might the absence of data screening affect a researcher’s data quality, their interpretations of the data, and thereby their interpretations of their study’s findings?
- A Midwest college admissions committee recently conducted a study to determine the relative debt incurred by students receiving their degrees in four years versus those taking more than four years. Some on the committee speculated a four-year student would likely be attending full time, whereas one taking more than four years could have a part-time job. However, average total debt provides only part of the information. Since the average, or mean, is affected by both large and small values, the committee also needed some way to determine the relative variances for the two groups. Samples of size 20 produced standard deviations of 2,636 for four-year graduates and 1,513 for those taking more than four years. Conduct a test of hypothesis to determine if the standard deviation of the debt for four-year graduates is larger than those taking more than four years. Use a significance level of 0.05.What is the lowest measure of central tendency and is used primarily for nominal data to identify the category with the greatest number of cases?What does less replicates mean in the context of understanding variance of data?
- A researcher has found a strong relationship between level of education and income and concludes that “higher levels of education cause higher income.” What error has been made?When should you use a one-way ANOVA to analyze your data? Distinguish between one–way ANOVA for independent groups and a one–way Repeated Measures ANOVA.A research study was conducted about gender differences in "sexting." The researcher believed that the proportion of girls involved in “sexting” is less than the proportion of boys involved. The data collected in the spring of 2010 among a random sample of middle and high school students in a large school district in the southern United States is summarized in Table. Is the proportion of girls sending sexts less than the proportion of boys "sexting?" Test at a 1% level of significance. Table 2: Frequency of "sexts" sent by gender Gender Males Females Sent "sexts" 183 156 Total number surveyed 2231 2169
