Question

4. A n experiment was set up to compare the effect of different soil pH and calcium additives on the increase in trunk diameters for orange trees. Annual applications of elemental sulfur, gypsum, soda ash, and other ingredients were applied to provide pH value levels of 4, 5, 6, and 7. Three levels of a calcium supplement (100, 200, and 300 pounds per acre) were also applied. All factor-level combinations of these two variables were used in the experiment. At the end of a 2-year period, four diameters were examined at each factor-level combination. The data appear in the table below: Calcium pH Value 100 52200 5.9 6.3 6.1 7.1 7.4 7.5 7.2 7.6 7.2 7.4 7.0 7.2 7.5 7.2 7.3 300 6.3 6.7 6.1 6.4 7.3 7.5 7.2 7.0 7.2 7.3 7.0 7.2 6.8 6.6 6.4 6.5 4.0 7.4 7.0 7.6 7.2 7.4 7.3 7.1 7.0 7.6 7.5 7.8 7.9 7.4 7.0 6.9 7.1 5.0 6.0 7.0 a. Construct a profile plo....what do the data suggest? b. Write an appropriate statistical model. c. Perform an analysis of variance (create the ANOVA table) and identify the experimental design. Let alpha 0.05 and run the test

Answer 1

Data Entered
	Col 1	Col 2	Col 3	Col 4
Row 1	5.2 5.9 6.3	7.4 7.0 7.6	6.3 6.7 6.1	---
Row 2	7.1 7.4 7.5	7.4 7.3 7.1	7.3 7.5 7.2	---
Row 3	7.6 7.2 7.4	7.6 7.5 7.8	7.2 7.3 7.0	---
Row 4	7.2 7.5 7.2	7.4 7.0 6.9	6.8 6.6 6.4	---

Summary Data		Within each box:   Item 1 = N     Item 2 = X     Item 3 = Mean   Item 4 = X2     Item 5 = Variance   Item 6 = Std. Dev.     Item 7 = Std. Err.
	C1	C2	C3	C4	Tot.
R1	3 17.400000000000002 5.8 101.54 0.31 0.56 0.32	3 22 7.3333 161.52 0.09 0.31 0.18	3 19.1 6.3667 121.78999999999999 0.09 0.31 0.18	---	9 58.5 6.5 384.85 0.58 0.76 0.25
R2	3 22 7.3333 161.42000000000002 0.04 0.21 0.12	3 21.799999999999997 7.2667 158.46 0.02 0.15 0.09	3 22 7.3333 161.38 0.02 0.15 0.09	---	9 65.8 7.3111 481.26 0.02 0.15 0.05
R3	3 22.200000000000003 7.4 164.36 0.04 0.2 0.12	3 22.9 7.6333 174.85 0.02 0.15 0.09	3 21.5 7.1667 154.13 0.02 0.15 0.09	---	9 66.6 7.4 493.34 0.06 0.25 0.08
R4	3 21.9 7.3 159.93 0.03 0.17 0.1	3 21.3 7.1 151.37 0.07 0.26 0.15	3 19.799999999999997 6.6 130.76 0.04 0.2 0.12	---	9 63 7 442.06 0.13 0.36 0.12
Tot.	12 83.5 6.9583 587.25 0.57 0.75 0.22	12 88 7.3333 646.2 0.08 0.28 0.08	12 82.4 6.8667 568.06 0.2 0.45 0.13	---	36 253.9 7.0528 1801.51 0.31 0.56 0.09

ANOVA Summary
Source	SS	df	MS	F	P
Rows	4.46	3	1.49	21.89	<.0001
Columns	1.47	2	0.74	10.82	0.0004
r x c	3.25	6	0.54	7.98	0.0001
Error	1.63	24	0.07
Total	10.81	35

Critical Values for the Tukey HSD Test
	HSD[.05]	HSD[.01]	HSD=the absolute [unsigned] difference between any two means (row means, column means, or cell means) required for significance at the designated level: HSD[.05] for the .05 level; HSD[.01] for the .01 level. The HSD test between row means can be meaningfully performed only if the row effect is significant; between column means, only if the column effect is significant; and between cell means, only if the interaction effect is significant.
Rows [4]	0.34	0.43
Columns[3]	0.27	0.34
Cells[12]	0.77	0.92

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