Question

A trial is conducted to measure the effect of five different fertilising
methods and three different pots on the fruit yield of pepper trees. The
weight of fruit produced for each of 120 pepper trees was measured, and
the results grouped according to fertilising method and type of pot. The
data is shown in Dataset. Carry out an appropriate statistical test to see if
anyone of the five methods or the three types of pot yields more fruit than
the others.

DataSet:

	Method 1	Method 2	Method 3	Method 4	Method 5
	152.14	152.03	149.67	151.26	146.75
Pot A	151.84	152.22	149.75	151.22	146.68
	151.60	151.98	150.21	151.01	147.12
	151.21	151.81	150.31	151.56	147.41
	151.27	151.96	149.87	151.87	147.98
	151.62	151.48	149.37	151.49	147.47
	151.92	152.05	149.75	151.16	147.54
	152.12	151.54	150.20	150.89	146.98
	151.59	151.35	150.56	151.50	146.89
Pot B	151.04	150.82	150.85	151.30	147.00
	150.97	150.60	150.50	151.87	146.49
	150.50	150.95	149.95	151.41	146.47
	150.40	151.29	149.71	151.46	145.91
	150.60	152.69	149.21	151.71	146.95
	150.22	152.18	149.77	151.27	197.95
	150.55	151.98	149.64	151.01	197.69
	150.74	151.50	150.09	151.20	197.83
Pot C	151.29	152.05	150.40	151.56	197.42
	151.75	152.21	151.37	152.14	197.58
	151.79	152.78	151.11	151.61	197.13
	151.59	152.28	151.57	151.08	196.57
	151.05	152.62	151.67	150.56	196.64
	150.57	152.13	151.32	150.47	197.21
	151.02	152.55	150.76	150.38	196.71

Answer 1

From ANOVA table we see that interaction effect between Method and Pot is present (since p-value<0.05) so no need to test main effect individually. Hence since interaction present so method should depend on Pot or Pot depends on Method. Hence yield of fruits depends on interaction between Pot and Method.