Questions and Answers of Bayesian Statistics An Introduction

Complete each of the following:a. 17 3b. 17(3)c. (17)(3)d. 17/3e. (42)2f. 1113
Explain the limitations of partial and multiple regression analysis.
Calculate and interpret the multiple correlation coefficient (R2).
Find and interpret the least-squares multiple regression equation with partial slopes.
Compute and interpret partial correlation coefficients.
Cite and explain the limitations of elaborating bivariate tables.
Compute and interpret partial gamma.
Recognize and interpret direct, spurious or intervening, and interactive relationships.
Compute and interpret partial measures of association.
Construct and interpret partial tables.
Explain the purpose of multivariate analysis in terms of observing the effect of a control variable.
Test Pearson’s r for significance
Use regression and correlation techniques to analyze and describe a bivariate relationship in terms of the three questions introduced in Chapter 12.
Explain the concepts of total, explained, and unexplained variance.
Find and explain the least-squares regression line and use it to predict values of Y.
Calculate and interpret slope (b), Y intercept (a), and Pearson’s r and r 2.
Interpret a scatter gram.
Test gamma and Spearman’s rho for significance.
Use gamma and Spearman’s rho to analyze and describe a bivariate relationship in terms of the three questions introduced in Chapter 12.
Explain the logic of proportional reduction in error in terms of gamma.
Calculate and interpret gamma and Spearman’s rho.
Compute and interpret measures of association for variables measured at the nominal level.
Investigate a bivariate association by properly calculating percentages for a bivariate table and interpreting the results.
List and explain the three characteristics of a bivariate relationship: existence, strength, and pattern or direction.
Define association in the context of bivariate tables and in terms of changing conditional distributions.
Explain how we can use measures of association to describe and analyze the importance of relationships (vs. their statistical significance).
Explain the limitations of the chi square test and, especially, the difference between statistical significance and importance.
Perform the chi square test using the five-step model and correctly interpret the results.
Explain the logic of hypothesis testing as applied to a bivariate table.
Explain the structure of a bivariate table and the concept of independence as applied to expected and observed frequencies in a bivariate table.
Identify and cite examples of situations in which the chi square test is appropriate.
Explain the difference between the statistical significance and the importance of relationships between variables.
Define and explain the concepts of population variance, total sum of squares, sum of squares between, sum of squares within, mean square estimates, and post hoc tests.
Perform the ANOVA test, using the five-step model as a guide, and correctly interpret the results.
Explain the logic of hypothesis testing as applied to ANOVA.
Identify and cite examples of situations in which ANOVA is appropriate.
List and explain each of the factors (especially sample size) that affect the probability of rejecting the null hypothesis. Explain the differences between statistical significance and importance.
Perform a test of hypothesis for two sample means or two sample proportions following the five-step model and correctly interpret the results.
Explain what an independent random sample is.
Explain the logic of hypothesis testing as applied to the two-sample case.
Identify and cite examples of situations in which the two-sample test of hypothesis is appropriate.
Use the Student’s t distribution to test the significance of a sample mean for a small sample.
Define and explain Type I and Type II errors and relate each to the selection of an alpha level.
Explain the difference between one- and two-tailed tests and specify when each is appropriate.
Test the significance of single-sample means and proportions using the five-step model and correctly interpret the results.
Identify and cite examples of situations in which one-sample tests of hypotheses are appropriate.
Explain what it means to “reject the null hypothesis” or “fail to reject the null hypothesis.”
Define and explain the conceptual elements involved in hypothesis testing, especially the null hypothesis, the sampling distribution, the alpha level, and the test statistic.
Explain the logic of hypothesis testing.
Use the Student’s t distribution to test the significance of a sample mean for a small sample.
Define and explain Type I and Type II errors and relate each to the selection of an alpha level.
Explain the difference between one- and two-tailed tests and specify when each is appropriate.
Test the significance of single-sample means and proportions using the five-step model and correctly interpret the results.
Identify and cite examples of situations in which one-sample tests of hypotheses are appropriate.
Explain what it means to “reject the null hypothesis” or “fail to reject the null hypothesis.”
Define and explain the conceptual elements involved in hypothesis testing, especially the null hypothesis, the sampling distribution, the alpha level, and the test statistic.
Explain the logic of hypothesis testing.
Explain the relationships between confidence level, sample size, and the width of the confidence interval
Construct and interpret confidence intervals for sample means and sample proportions.
Define and explain the concepts of bias and efficiency.
Explain the logic of estimation and the role of the sample, sampling distribution, and the population.
Explain the two theorems presented.
Differentiate between the sampling distribution, the sample, and the population.
Explain and define these key terms: population, sample, parameter, statistic, representative, EPSEM.
Define and explain the basic techniques of random sampling.
Explain the purpose of inferential statistics in terms of generalizing from a sample to a population.
Express areas under the curve in terms of probabilities.
Convert empirical scores to Z scores and use Z scores and the normal curve table (Appendix A) to find areas above, below, and between points on the curve.
Define and explain the concept of the normal curve.
Describe and explain the mathematical characteristics of the standard deviation.
Select an appropriate measure of dispersion and correctly calculate and interpret the statistic.
Compute and explain the index of qualitative variation (IQV), the range (R), the interquartile range (Q), the standard deviation (s), and the variance (s2).
Explain the purpose of measures of dispersion and the information they convey.
Select an appropriate measure of central tendency according to level of measurement and skew.
Explain the mathematical characteristics of the mean.
Calculate, explain, and compare and contrast the mode, median, and mean.
Explain the purposes of measures of central tendency and interpret the information they convey.
Construct and analyze bar and pie charts, histograms, and line graphs.
Construct and analyze frequency distributions for variables at each of the three levels of measurement.
Compute and interpret percentages, proportions, ratios, rates, and percentage change.
Explain the purpose of descriptive statistics in making data comprehensible.
Identify and describe three levels of measurement and cite examples of variables from each.
Distinguish between discrete and continuous variables and cite examples of each.
Distinguish between three applications of statistics and identify situations in which each is appropriate.
Describe the limited but crucial role of statistics in social research.
Apply a three-group discrete mixture model to the baseball average data. A two group mixture, with code as below, gives an LPML (for the original data) of -726.5 , with plots of \(p_{\text {new }}\)
Many evaluations of Poisson mixture models consider aggregated data, for example numbers of consumers making 0,1,2, etc. purchases. Brockett et al. (1996) present such data for purchases of 'salty
A request in the UK parliament (http://www.theyworkforyou.com/wrans/?id=2011-03 \(-07 c .44095\).h) related to 2009 mortality rates (per 100000 population) in Wales according to income decile of
Apply the normal-latent beta model to data on short-term changes in depression ratings (Tarpey and Petkova, 2010). Such changes in depression are unlikely to be due to the pharmacological
In Example 3.1, adapt the code to include a posterior predictive \(p\)-tests to assess skewness and kurtosis in the residuals. For example, the \(p\)-test for skewness would compare a skew measure
In Example 3.2 (student attainment), standardize the SATM-score predictor to provide values \(x_{i}^{s}\). Then replace the conventional prior by a CMP prior at values \(\tilde{x}_{1}=\left(1,
Using data originally from Mullahy (1997) on smoking consumption (cigarettes smoked per day) by \(\mathrm{n}=807\) subjects, assess the suitability of a Poisson regression using a posterior
Using data on Irish education transitions (http://lib.stat.cmu.edu/datasets/irish.ed) compare logit and probit regression using the augmented data method and the dbern.aux function. Take \(P=2\)
Apply the Kuo-Mallick model to predictor selection in the nodal involvement data using a uniform prior on \(k\) between the extremes \(k=0.5\) and \(k=4\). So the variance in the normal prior for
In Example 3.6 use the WinBUGS jump RJMCMC interface to obtain the highest posterior probability model for the Chevrolet asking price data, assuming a prior \(P_{\text {ret }} \sim\)
In Example 3.7, define quantities \(s_{1}=\exp \left(\alpha_{3}+\beta_{33}\right)\) and \(s_{2}=\exp \left(\alpha_{2}+\beta_{32}\right)\), and by monitoring them obtain the probability that
In Example 3.8, compare models 1 and 2 (standard conditional logistic and nested logit) using LPML and DIC criteria, and also predictive classification success: how far predicted choice obtained by
In Example 3.9 (political involvement), compare predictive accuracy, DIC and LPML between the proportional odds logistic model and a model allowing the regression effect to differ by response
Compare the suitability of ordinal logistic and ordinal probit regression for the political involvement data using the posterior predictive criteria\[\operatorname{Pr}\left(z_{\text {rep },
In Example 4.1, estimate a variance transformation model with \(\log \left(\sigma_{i}^{2}\right)=\xi_{0}+\xi_{1} \mu_{i}\), and compare its fit with a constant variance normal linear regression using

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