Question

3. You perform an experiment to determine the effects of temperature on development in an insect species. You do so by incubating randomly selected eggs and larvae at 4 different and constant temperatures and measure the length (in mm) of the third leg after the last immature ecdysis event, with results shown below (each cell represents an individual insect). Perform a one-way ANOVA on your results (/10) Tema A Temp BTemp. Temo D 12.4 14.5 12.8 13.610.5 0.5 8.7 10.1 9.6 8.1 8 8.4 7.9 7.9 8.7 8.5 8 12.1 10.48.4

Answer 1

One-way ANOVA: C4 versus C5

Source DF SS MS F P
C5 3 77.946 25.982 79.27 0.000
Error 16 5.244 0.328
Total 19 83.190

S = 0.5725 R-Sq = 93.70% R-Sq(adj) = 92.51%

Individual 95% CIs For Mean Based on
Pooled StDev
Level N Mean StDev ---------+---------+---------+---------+
Temp A 5 13.080 0.973 (--*---)
Temp B 5 10.220 0.383 (--*---)
Temp C 5 8.320 0.277 (--*---)
Temp D 5 8.200 0.374 (---*--)

Since p-value=0.000<0.05 hence there is at least one significant difference between the limb lengths in insects reared at different temperature.

So we want to perform Tukey test.

$Critical~difference=q_{0.025,4,16}\sqrt{MSE/5}=1.0373\\ MSE=0.328,~q_{0.025,4,16}=4.05 \\\begin{matrix} Comparison & Absolute~difference& Critical~difference & Significant\\ A~and~B&13.080-10.220=2.86 & 1.0373 &Yes \\ A~and~C&13.080-8.320=4.76 &1.0373 &Yes \\ A~and~D & 13.080-8.200=4.88 &1.0373 &Yes \\ B~and~C & 10.220-8.320=1.9& 1.0373& Yes\\ B~and~D&10.220-8.200=2.02 & 1.0373 & Yes\\ C~and~D&8.320-8.200= 0.12 & 1.0373 & No \end{matrix}$