Note:

On the first question, you must use the pvalue from the ANOVA table. That is the pvalue that assesses whether all group means are equal or not. Tukey’s multiple comparisons are only used to assess difference in paired means AFTER it has been determined that there is a difference in means. The linear models coefficients table is not appropriate for answering that question either as it does not assess all pairs of means (you should get out of the habit of using
summary()
on yourlm()
results).  The second question should include a plot of means with appropriate significance letters. Note that when using Tukey’s method that there should be letters on each point. With Dunnett’s method it may be appropriate to leave one point without a letter, but this should be explained in the figure label.
 In the second to last questions, make sure to clearly indicate which group is greater (or lesser). Don’t just say that you are 95% confident that the difference is between suchandsuch.
 I round my pvalues to four decimal places. As such, if the fifth decimal place is less than 5, then the pvalue would round to “0.0000”, which does not make much sense. Thus, if the fifth decimal place is less than 5 then I will report my pvalues as “<0.00005.” You will see examples of this in the answers below.
 Note how concise the answer key is. Please work to get your answers this concise.
Temperature and Turtle Hatchlings II
 The mean days to hatch is significantly different among the four temperature groups (p<0.00005; Table 1).
 It appears that the mean days to hatch for the 30^{o}C group is significantly lower than the mean days to hatch for 15^{o}C (p<0.00005), 20^{o}C (p=0.0008), and 25^{o}C (p=0.0001) groups (Table 2). The mean days to hatch for all other pairs of temperature groups are not significantly different (Table 2). These results are shown visually in Figure 1.
 The mean days to hatch for sea turtles at 30^{o}C is between 22.7 and 53.9 days lower than that at 15^{o}C, between 8.9 and 40.1 days lower than that at 20^{o}C, and between 13.5 and 44.7 days lower than that at 25^{o}C (Table 3).
 It appears that mean days to hatch is longer at 15, 20, and 25^{o}C than at 30^{o}C. Thus, it appears that the days to hatch will not decrease substantially until temperatures rise above somewhere between 25 and 30^{o}C.
Table 1: Analysis of variance table for the days to hatch by temperature group.
Df Sum Sq Mean Sq F value Pr(>F)
Temperature 3 8025.5 2675.16 15.978 9.082e07
Residuals 36 6027.3 167.42
Table 2: Tukey’s multiple comparison results for the days to hatch by sea turles at various temperature groups.
Estimate Std. Error t value p value
20  15 = 0 13.8 5.786623 2.3848108 9.819862e02
25  15 = 0 9.2 5.786623 1.5898739 3.970328e01
30  15 = 0 38.3 5.786623 6.6187141 4.147556e07
25  20 = 0 4.6 5.786623 0.7949369 8.562519e01
30  20 = 0 24.5 5.786623 4.2339033 7.910900e04
30  25 = 0 29.1 5.786623 5.0288402 6.706843e05
Figure 1: Plot of mean (with 95% CI) days to hatch by sea turtles at various temperature groups. Different letters indicate means that are significantly different.
Table 3: Tukey’s confidence interval results for the difference in mean days to hatch by sea turtles for each pair of temperature groups.
Estimate lwr upr
20  15 13.8 29.38918 1.789182
25  15 9.2 24.78918 6.389182
30  15 38.3 53.88918 22.710818
25  20 4.6 10.98918 20.189182
30  20 24.5 40.08918 8.910818
30  25 29.1 44.68918 13.510818
R Appendix.
library(multcomp)
d < read.csv("turtles.csv")
d$Temperature < factor(d$Temperature)
lm1 < lm(Days~Temperature,data=d)
anova(lm1)
mc1 < glht(lm1,mcp(Temperature="Tukey"))
summary(mc1)
confint(mc1)
fitPlot(lm1,xlab="Temperature (C)",ylab="Days to Hatch")
addSigLetters(lm1,c("b","b","b","a"),pos=c(2,2,4,4))