observations on various characteristics were made using minichamheis of three different types: (1) cooler (PVC frames covered with shade cloth), (2) control (PVC frames only), and (3) warmer (PVC frames covered with plastic). One of the article's authors kindly supplied the accompany-ing data on the difference between air and soil temperatures (°C). a. Compare measures of center for the three different samples. b. Calculate, interpret, and compare the standard deviations for the three different samples. c. Do the fourth spreads for the three samples convey the same message as do the standard deviations about relative variability? d. Construct a comparative boxplot (which was included in the cited article) and comment on any interesting features.
Answer: Step 1 of 4 a. Compare measures of center for the three different samples. Arranging the data in increasing order Using Excel function =median( ) Cooler Control Warmer 0.83 0.53 0.12 1.26 1.12 0.84 1.34 1.52 1.58 1.43 1.78 1.91 1.57 1.84 1.93 1.59 1.9 2.13 1.72 1.92 2.3 1.76 2 2.31 1.79 2.03 2.53 1.86 2.19 2.57 1.88 2.45 2.6 1.9 2.65 1.91 2.74 2.34 2.86 2.41 Median 1.76 1.9 2.305 Stdev 0.400835 0.531321 0.777873 Since all three distributions are somewhat skewed and two contain outliers, medians are the more appropriate central measures. The medians are Cooler: 1.760°C, Control: 1.900°C, Warmer: 2.305°C The median difference between air and soil temperature increases as the conditions of the mini chambers transition from cooler to warmer (1.76 < 1.9 < 2.305). Step 2 of 4 b. Calculate, interpret, and compare the standard deviations for the three different samples. Using Excel function = stdev( ) With the aid of software, the standard deviations are Cooler: 0.401°C, Control: 0.531°C, Warmer: 0.778°C For the 15 observations under the “cooler” conditions, the typical deviation between an observed temperature difference and the mean temperature difference (1.760°C) is roughly 0.4°C. A similar interpretation applies to the other two standard deviations. We see that, according to the standard deviations, variability increases as the conditions of the mini chambers transition from cooler to warmer (0.401 < 0.531 < 0.778).