1. Chapter 2 Analysis using R

2. Few Tips for R Commands included here CANNOT ALWAYS be copied and pasted directly without alteration. –One major reason is the type of quotations… –R only accepts double-straight vertical quotations( '' '' ), not the standard “word” type of quotations ( “ ” )‏ Also, R is very case sensitive

3. Example 2.3.1 Introduction to the data (pg 21)‏ –“Shortly after…each of a group of 44 students [in meters]…another group of 69 students…width [in feet]” –Will there be a significant difference?

4. Initiate the data To initiate the data that we will use, activate from HSAUR package: R> data(“roomwidth”, package = “HSAUR”)‏

5. Conversion Since some of the units are in meters, and some are in feet, we need to convert R> convert <- ifelse(roomwidth$unit == “feet”, 1, 3.28)‏ –Convert is the variable that we are creating now. –In it, we will store two possible values through the use of an ifelse statement. How to read: “If the column ‘unit’ found in data ‘roomwidth’ (which was previously initiated) reads as “feet”, then convert = 1. However [else], if ‘unit’ does NOT equal feet, then convert = 3.28 3.28 = conversion factor, meters  feet.

6. Summary Statistics Let’s say that we want to bring up general statistics about the data… –Min, quartiles, max, mean, median, standard deviation… Use summary or sd command. tapply(roomwidth$width * convert, roomwidth$unit, summary)‏ –Reads: “Apply the following function to each cell of our data: take the width column, found in data roomwidth, and multiple it by convert (a vector with two possible values depending on the value of width). Then, depending on the column ‘unit” found in data roomwidth, display the summary statistics about it.”

7. Output (R)‏

8. SD Statistic Since the standard deviation is not included in the displayed statistics for some reason, a unique comment must be added. The command reads the same as before, except the “sd” function is applied. tapply(roomwidth$width * convert, roomwidth$unit, sd)‏

9. Graphical Analysis (Input)‏ > data("roomwidth", package = "HSAUR")‏ > convert <- ifelse(roomwidth$unit == "feet", 1, 3.28)‏ > tapply(roomwidth$width * convert, roomwidth$unit, summary)‏ $feet Min. 1st Qu. Median Mean 3rd Qu. Max. 24.0 36.0 42.0 43.7 48.0 94.0 $metres Min. 1st Qu. Median Mean 3rd Qu. Max. 26.24 36.08 49.20 52.55 55.76 131.20 > tapply(roomwidth$width * convert, roomwidth$unit, sd)‏ feet metres 12.49742 23.43444 > layout(matrix(c(1,2,1,3), nrow=2, ncol=2, byrow=FALSE))‏ > boxplot(I(width * convert) ~ unit, data = roomwidth, ylab = "Estimated width (feet)", varwidth = TRUE, names = c(“Estimates in feet", "Estimates in meteres (converted to feet)"))‏ > feet <- roomwidth$unit == "feet" > qqnorm(roomwidth$width[feet], ylab = "Estimated width (feet)")‏ > qqline(roomwidth$width[feet])‏ > qqnorm(roomwidth$width[!feet], ylab = "Estimated width (metres)")‏ > qqline(roomwidth$width[!feet])‏

10. Output

11. Graphical Analysis - Layout Input sets up the layout of the box plot and graphs Input creates top boxplot on previous screen –boxplot(I(width * convert) ~ unit, data = roomwidth, ylab = "Estimated width (feet)", varwidth = TRUE, names = c(“Estimates in feet", "Estimates in metres (converted to feet)"))‏ Lables –ylab –varwidth Histograms –>hist()‏ > layout(matrix(c(1,2,1,3), nrow=2, ncol=2, byrow=FALSE))‏

12. Two Sample t-test using R We are performing a two sample t-test assuming equal variances

13. Wilcoxon Mann-Whitney Rank Sum Test Using R Notice additional command at end of function to display confidence interval

14. Example 2.3.2 One Sample t-test Example of paired t-test using difference in two mooring methods in wave energy experiment (p 22)‏

15. Example 2.3.3 Correlation Test Using R Choose two factors that you want to test for correlation ex. mortality + hardness in water data