Question

The leaf-mining moth, Cameraria hamadryadella, is found at higher densities low in the crown of white oak trees (Quercus alba). To test the hypothesis that this pattern is due to differences in foliage quality between low and high foliage, potted trees which had been treated identically prior to the experiment, so should have similar foliage quality, were randomly assigned to 3 different heights (0, 1.25, and 3.25 m above the ground), and intervening foliage was placed under half the trees in each height treatment. Intervening foliage was non-oak foliage and used to simulate the interference that moths emerging from the leaf litter might encounter when seeking oak foliage. Because of the limited availability of potted trees, the sample sizes differed among treatment combinations. Use the cameraria.csv, which contains data on the density of leaf mines on each experimental tree (number/leaf) to test all relevant hypotheses concerning the effects of height and intervening foliage on leaf miner density.

	internointer	height	density
1	inter	low	3.969301638
2	inter	low	5.369349006
3	inter	low	6.120053591
4	inter	low	3.190005159
5	inter	low	6.453230805
6	inter	mid	2.813480706
7	inter	mid	3.285403337
8	inter	mid	2.783487491
9	inter	mid	1.688735491
10	inter	high	0.872423761
11	inter	high	1.841925999
12	inter	high	1.141709711
13	inter	high	0.842030114
14	inter	high	0.919231785
15	inter	high	1.451467222
16	nointer	low	4.750133954
17	nointer	low	7.501487512
18	nointer	low	6.14694701
19	nointer	low	8.315185552
20	nointer	low	7.381864028
21	nointer	low	6.90325985
22	nointer	low	6.277508028
23	nointer	mid	3.560923065
24	nointer	mid	0.862755771
25	nointer	mid	2.951119764
26	nointer	mid	2.104355678
27	nointer	mid	1.545405652
28	nointer	mid	2.50297984
29	nointer	high	1.069940668
30	nointer	high	1.794883662
31	nointer	high	1.266284994
32	nointer	high	1.850744346
33	nointer	high	1.529635938

Answer 1

The leaf-mining moth, Cameraria hamadryadella, is found at higher densities low in the crown of white oak trees (Quercus alba). To test the hypothesis that this pattern is due to differences in foliage quality between low and high foliage, potted trees which had been treated identically prior to the experiment, so should have similar foliage quality, were randomly assigned to 3 different heights (0, 1.25, and 3.25 m above the ground), and intervening foliage was placed under half the trees in each height treatment. Intervening foliage was non-oak foliage and used to simulate the interference that moths emerging from the leaf litter might encounter when seeking oak foliage. Because of the limited availability of potted trees, the sample sizes differed among treatment combinations. Use the cameraria.csv, which contains data on the density of leaf mines on each experimental tree (number/leaf) to test all relevant hypotheses concerning the effects of height and intervening foliage on leaf miner density.

MINTAB used .

General Linear Model: density versus internointer, height

Method

Factor coding

(-1, 0, +1)

Factor Information

Factor	Type	Levels	Values
internointer	Fixed	2	inter, nointer
height	Fixed	3	high, low, mid

Analysis of Variance

Source	DF	Adj SS	Adj MS	F-Value	P-Value
internointer	1	2.475	2.4745	2.88	0.101
height	2	126.929	63.4645	73.89	0.000
internointer*height	2	6.294	3.1468	3.66	0.039
Error	27	23.191	0.8589
Total	32	172.806

Model Summary

S	R-sq	R-sq(adj)	R-sq(pred)
0.926791	86.58%	84.09%	80.18%

Coefficients

Term	Coef	SE Coef	T-Value	P-Value	VIF
Constant	3.225	0.164	19.68	0.000
internointer
inter	-0.278	0.164	-1.70	0.101	1.02
height
high	-1.885	0.230	-8.18	0.000	1.30
low	2.662	0.227	11.74	0.000	1.31
internointer*height
inter high	0.116	0.230	0.50	0.618	1.28
inter low	-0.588	0.227	-2.60	0.015	1.32

Regression Equation

density

=

3.225 - 0.278 internointer_inter + 0.278 internointer_nointer - 1.885 height_high + 2.662 height_low - 0.777 height_mid + 0.116 internointer*height_inter high - 0.588 internointer*height_inter low + 0.472 internointer*height_inter mid - 0.116 internointer*height_nointer high + 0.588 internointer*height_nointer low - 0.472 internointer*height_nointer mid

Fits and Diagnostics for Unusual Observations

Obs	density	Fit	Resid	Std Resid
4	3.190	5.020	-1.830	-2.21	R
16	4.750	6.754	-2.004	-2.34	R

R Large residual

To test the effect of intervening foliage on leaf miner density,

Calculated F=2.88, P=0.101 which is > 0.05 level of significance. intervening foliage has no effect on density.

To test the effect of height on leaf miner density,

Calculated F=73.89, P=0.000 which is < 0.05 level of significance. height has significant effect on density.

To test the effect of interaction between height and intervening foliage on density,

Calculated F=3.66, P=0.039 which is < 0.05 level of significance. Interaction has significant effect on density.