## 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”