Question

Johnson and Leone describe an experiment to investigate warping of copper plates. The two factors studied were the temperature and the copper content of the plates. The response variable was a measure of the amount of warping. The data are as follows:

Copper Content(%) Temperature 406080 100 50 75 100 125 17, 20 16,21 24,22 28, 27 12,9 18, 13 17, 12 27, 31 16, 12 18,2 25,2330, 23 21,17 23, 21 23, 22 29, 31

Answer 1

Hello,

To find the intraction of the data run Two way anova

ummary DataWithin 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	2 37 18.5 689 4.5 2.12 1.5	2 37 18.5 697 12.5 3.54 2.5	2 46 23 1060 2 1.41 1	2 55 27.5 1513 0.5 0.71 0.5	8 175 21.875 3959 18.7 4.32 1.53
R2	2 21 10.5 225 4.5 2.12 1.5	2 31 15.5 493 12.5 3.54 2.5	2 29 14.5 433 12.5 3.54 2.5	2 58 29 1690 8 2.83 2	8 139 17.375 2841 60.84 7.8 2.76
R3	2 28 14 400 8 2.83 2	2 39 19.5 765 4.5 2.12 1.5	2 48 24 1154 2 1.41 1	2 53 26.5 1429 24.5 4.95 3.5	8 168 21 3748 31.43 5.61 1.98
R4	2 38 19 730 8 2.83 2	2 44 22 970 2 1.41 1	2 45 22.5 1013 0.5 0.71 0.5	2 60 30 1802 2 1.41 1	8 187 23.375 4515 20.55 4.53 1.6
Tot.	8 124 15.5 2044 17.43 4.17 1.48	8 151 18.875 2925 10.7 3.27 1.16	8 168 21 3660 18.86 4.34 1.54	8 226 28.25 6434 7.07 2.66 0.94	32 669 20.9063 15063 34.73 5.89 1.04

ANOVA Summary
Source	SS	df	MS	F	P
Rows	156.09	3	52.03	7.67	0.0021
Columns	698.34	3	232.78	34.33	<.0001
r x c	113.79	9	12.64	1.86	0.1336
Error	108.5	16	6.78
Total	1076.72	31

Here is the p-value is larger that means there no intraction between the two variables

Critical Values for the Tukey HSD Test
	HSD[.05]		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. 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]	3.73
Columns [4]	3.73
Cells [16]	10.4

The man diffreance between the 80 and 100 is 6.44 and for same HSD value is 3.75 , we reject the null hypothesis

and conclude that there is significant diffreance between the two copper values

Thanks

that means there is significant diffrance between the two mans