Chapter 17 Multiple choice questions

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. Before you start, make sure you have the BayesFactor package installed and activated. Download the data file for the multiple-choice questions for Chapter 17 , and open it in R.
The variable q1data contains some synthetic data created using the rnorm function, for 100 samples with a mean of 1 and a standard deviation of 3. Compute a one-sample t-test Bayes factor using the ttestBF function. The resulting Bayes factor:

Suggests some evidence for the alternative hypothesis correct incorrect

Suggests some evidence for the null hypothesis correct incorrect

Suggests overwhelming evidence for the null hypothesis correct incorrect

Cannot distinguish between the null and alternative hypotheses correct incorrect

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. The variable q2data contains another set of 100 values. Calculate a Bayes factor for an independent samples t-test comparing q1data and q2data. The resulting Bayes factor:

Suggests strong evidence for the alternative hypothesis correct incorrect

Suggests some evidence for the null hypothesis correct incorrect

Suggests some evidence for the alternative hypothesis correct incorrect

Cannot distinguish between the null and alternative hypotheses correct incorrect

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. The variable q3data contains two variables (dv1 and dv2) that are correlated with r=0.48. Calculate a Bayes factor for a linear regression between the two variables using the lmBF function. The Bayes factor:

Suggests some evidence for the alternative hypothesis correct incorrect

Suggests some evidence for the null hypothesis correct incorrect

Suggests very strong evidence for the alternative hypothesis correct incorrect

Cannot distinguish between the null and alternative hypotheses correct incorrect

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. The variable q4data is similar in structure to q3data, and produces a Bayes factor of 34. The two variables:

Show a strong positive relationship correct incorrect

Show a strong negative relationship correct incorrect

Are unrelated to each other correct incorrect

There is no way to determine how the variables are related correct incorrect

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. The variable q5data contains data formatted for a one-way ANOVA with three groups (DV1-3). Plot these data to examine them. Then compute a standard ANOVA using aov(alldata ~ group, data = q5data), and a Bayes factor using the anovaBF function. The results reveal:

A significant effect of group, with a Bayes factor >10 correct incorrect

A significant effect of group, but a weak Bayes factor correct incorrect

No significant effect of group, but a large Bayes factor >10 correct incorrect

No significant effect of group, and a weak Bayes factor correct incorrect

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. We can produce plots of the posterior distributions for the t-test in Q1 by entering: plot(posterior(ttestBF(q1data),iterations=1000)). The peak of the sig2 density plot is around:

1 correct incorrect

10 correct incorrect

0.1 correct incorrect

0.3 correct incorrect

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. The dataset puzzles is built into the BayesFactor package, and you can load it into the workspace by entering data(puzzles). It contains data on puzzle completion times (the DV, called RT) for different shapes (IV1, called shape) and colours (IV2, called color) of puzzles (e.g. jigsaws). Run a Bayes factor analysis for a two-way ANOVA with subject ID as a random factor as follows: anovaBF(RT ~ shape*color + ID, whichRandom = "ID", data = puzzles). Which model has the largest Bayes factor?

Shape alone correct incorrect

Colour alone correct incorrect

Shape and colour with an interaction (shape:color) correct incorrect

Shape and colour with no interaction correct incorrect

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. Calculate a Bayes factor for the correlation between the two variables stored in q8data. The result suggests that:

There is a positive relationship correct incorrect

There is a negative relationship correct incorrect

There is insufficient evidence to say if there is a relationship correct incorrect

There is more evidence to support the null hypothesis correct incorrect

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. The within-participant correlation affects the power of repeated measures designs. The data object q9data is a 2 x 10 x 12 array. The first dimension is the two conditions from an experiment. The second dimension represents the correlation between repeated measures (10 levels increasing in magnitude). The third dimension represents observations from 12 subjects. Calculate the Bayes factor for a paired t-test for each level of correlation. As the correlation increases:

Bayes factors decrease correct incorrect

Bayes factors increase correct incorrect

Bayes factors stay approximately constant correct incorrect

Bayes factors change randomly or non-monotonically correct incorrect

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. Suppose that the probability of a man sporting a moustache is 0.1. However, during November lots more people grow moustaches for charity, and the probability of an individual man having a moustache increases to 0.3. Use Bayes rule to calculate the conditional probability that it is November given that you see a man with a moustache. The probability is:

0.03 correct incorrect

0.08 correct incorrect

0.25 correct incorrect

0.36 correct incorrect