Doing Tests of Assumptions

Qn1. Download the file designtime.csv from the course materials. This file describes a study in which designers used Adobe Illustrator or Adobe InDesign to create a benchmark set of classic children’s illustrations. The amount of time they took was recorded, in minutes. How many subjects took part in this study?

Qn2. Create a boxplot of the task time data for each tool. At a glance, which of the following conclusions seems to be most likely?

-Illustrator and InDesign have similar median task times, with similar variances.
- Illustrator has a higher median task time than InDesign, with similar variances.
- Illustrator has a higher median task time than InDesign, with dissimilar variances.
- InDesign has a higher median task time than Illustrator, with similar variances.
- InDesign has a higher median task time than illustrator, with dissimilar variances.

Qn3. Conduct a Shapiro-Wilk test on the time response for each of the tools. To the nearest ten-thousandth (four digits), what is the p-value of this test for illustrator?

Qn4. Conduct a Shapiro-Wilk normality test on the residuals of Time by Tool. To the nearest ten-thousandth (four digits), What is the W value displayed? Hint: use aov to fit a model and then run Shapiro.test on the model residuals.
Qn5. In light of your normality tests, would you conclude the data does or does not violate normality?

-The data does violate normality
-The data does not violate normality

Qn6. Conduct a Brown-Forsythe test of homoscedasticity. To the nearest hundredth (two digits), what is the F statistic for the test? Hint: use the car library and its leveneTest function with center=median.
Qn7. Fit a lognormal distribution to the Time response of each of the design tools. Conduct a Kolmogorov-Smirnov goodness-of-fit test. To the nearest ten-thousandth (four digits), What is the exact p-value of the test for the Illustrator data? Hint: use the MASS library and its fitdistr function with “lognormal” to acquire a fit estimate. The use ks.test with “plnorm” passing the acquired fit values as meanlog and sdlog. Request and exact fit.
Qn8. Create a new column that is the log-transformed Time response. Compute the mean of this log-transformed response for each drawing tool. To the nearest hundredth (to digits), what is the mean of the log-transformed response for InDesign?
Qn9. Conduct an independent-samples t-test on the log-transformed Time response. Use the Welch version for unequal variances. To the nearest hundredth (two digits), what is the t statistic for the test?
Qn10. As an alternative to log-transforming the Time response, leave Time as it is and conduct an exact nonparametric Mann-Whitney U test on it. To the nearest ten-thousandth (four digits), what is the z statistic that results from this test? Hint: use the coin library and its wilcox test function with distribution=”exact”

Doing Independent-Samples T-tests

1. Download the file timeonsite.csv from the course materials. This file describes a website A/B test in which visitors’ time-on-site was measured in two website variations. How many subjects were in this website A/B test?
2. How many subjects were exposed to each variation of the website A and B?
3. To the nearest tenth (one digit), what was the median time on sire for site “B”?
4. To the nearest hundredth (two digits), what was the standard deviation of time on site for site “A”?
5. Conduct an independent-samples t-test on Time by Site. Assume equal variances. To the nearest hundredth (two digits), What is the t-statistic?
6. How many degrees of freedom resulted from the t-test?
7. To the nearest ten-thousandth (four digits), what was the p-value for this test?
8. What is the most proper way to report this t-test result?
9. The results show that, on average, website “A” resulted in almost 13 seconds greater time-on-sire than website “B”, and that this difference was statistically significant. (Note: Assume Time is measured in seconds).
10. By Setting the var. equal parameter to FALSE, a Welch t-test can be run, which does not assume equal variances.