Pot Trial Plant Heights and Dry Weights

Question:

Pot Trial Plant Heights
Treatment	Replication	Leaf Height mm
T1	1	290
T1	1	275
T1	1	210
T1	1	260
T1	1	270
T1	1	245
T1	1	254
T1	1	294
T1	1	274
T1	1	291
T1	1	282
T1	1	281
T1	1	301
T1	1	275
T1	1	275
T1	1	245
T1	2	259
T1	2	285
T1	2	300
T1	2	285
T1	2	265
T1	2	240
T1	2	240
T1	2	229
T1	2	250
T1	2	215
T1	2	258
T1	2	217
T1	2	190
T1	2	286
T1	2	310
T1	2	250
T1	3	290
T1	3	325
T1	3	315
T1	3	320
T1	3	273
T1	3	291
T1	3	283
T1	3	185
T1	3	240
T1	3	223
T1	3	223
T1	3	278
T1	3	285
T1	3	252
T1	3	236
T1	3	272
T2	1	190
T2	1	195
T2	1	220
T2	1	210
T2	1	265
T2	1	200
T2	1	230
T2	1	150
T2	1	205
T2	1	214
T2	1	190
T2	1	168
T2	1	162
T2	1	197
T2	1	170
T2	1	175
T2	2	210
T2	2	195
T2	2	184
T2	2	252
T2	2	170
T2	2	193
T2	2	202
T2	2	244
T2	2	112
T2	2	154
T2	2	159
T2	2	175
T2	2	170
T2	2	177
T2	2	157
T2	2	156
T2	3	192
T2	3	183
T2	3	172
T2	3	260
T2	3	164
T2	3	195
T2	3	186
T2	3	196
T2	3	192
T2	3	183
T2	3	172
T2	3	260
T2	3	164
T2	3	195
T2	3	186
T2	3	196
T3	1	250
T3	1	240
T3	1	215
T3	1	200
T3	1	245
T3	1	195
T3	1	230
T3	1	245
T3	1	220
T3	1	192
T3	1	155
T3	1	170
T3	1	191
T3	1	179
T3	1	165
T3	1	190
T3	2	230
T3	2	215
T3	2	180
T3	2	224
T3	2	222
T3	2	200
T3	2	240
T3	2	220
T3	2	224
T3	2	177
T3	2	243
T3	2	266
T3	2	252
T3	2	240
T3	2	187
T3	2	186
T3	3	171
T3	3	184
T3	3	244
T3	3	186
T3	3	212
T3	3	214
T3	3	246
T3	3	244
T3	3	198
T3	3	245
T3	3	179
T3	3	196
T3	3	218
T3	3	147
T3	3	175
T3	3	174
AGS107 Pot Trial Dry Weights
Treatment	Rep	Plant dry wt. grams
T1	1	0.42
T1	1	0.44
T1	1	0.29
T1	1	0.41
T1	1	0.29
T1	1	0.2
T1	1	0.21
T1	1	0.33
T1	1	0.2
T1	1	0.49
T1	2	0.41
T1	2	0.88
T1	2	0.93
T1	2	0.48
T1	2	0.79
T1	2	0.74
T1	2	0.88
T1	2	0.91
T1	2	0.74
T1	2	1.09
T1	3	1.05
T1	3	0.96
T1	3	1.11
T1	3	1.25
T1	3	0.99
T1	3	1.21
T1	3	1.12
T1	3	1.05
T1	3	1.36
T1	3	1.46
T2	1	0.13
T2	1	0.09
T2	1	0.09
T2	1	0.13
T2	1	0.05
T2	1	0.15
T2	1	0.05
T2	1	0.13
T2	1	0.05
T2	1	0.08
T2	2	0.39
T2	2	0.18
T2	2	0.42
T2	2	0.54
T2	2	0.62
T2	2	0.25
T2	2	0.39
T2	2	0.54
T2	2	0.35
T2	2	0.66
T2	3	0.57
T2	3	0.56
T2	3	0.67
T2	3	0.56
T2	3	0.77
T2	3	0.56
T2	3	0.45
T2	3	0.57
T2	3	0.66
T2	3	0.76
T3	1	0.18
T3	1	0.07
T3	1	0.06
T3	1	0.32
T3	1	0.19
T3	1	0.31
T3	1	0.06
T3	1	0.06
T3	1	0.06
T3	1	0.07
T3	2	0.75
T3	2	0.47
T3	2	0.54
T3	2	0.71
T3	2	0.54
T3	2	0.4
T3	2	0.52
T3	2	0.59
T3	2	0.71
T3	2	0.68
T3	3	0.74
T3	3	0.54
T3	3	0.95
T3	3	0.48
T3	3	0.52
T3	3	0.57
T3	3	0.81
T3	3	0.69
T3	3	0.71
T3	3	0.73

Answer:

Pot Trial Plant Heights
Treatment	Replication	Leaf Height mm
T1	1	290
T1	1	275
T1	1	210
T1	1	260
T1	1	270
T1	1	245
T1	1	254
T1	1	294
T1	1	274
T1	1	291
T1	1	282
T1	1	281
T1	1	301
T1	1	275
T1	1	275
T1	1	245
T1	2	259
T1	2	285
T1	2	300
T1	2	285
T1	2	265
T1	2	240
T1	2	240
T1	2	229
T1	2	250
T1	2	215
T1	2	258
T1	2	217
T1	2	190
T1	2	286
T1	2	310
T1	2	250
T1	3	290
T1	3	325
T1	3	315
T1	3	320
T1	3	273
T1	3	291
T1	3	283
T1	3	185
T1	3	240
T1	3	223
T1	3	223
T1	3	278
T1	3	285
T1	3	252
T1	3	236
T1	3	272
T2	1	190
T2	1	195
T2	1	220
T2	1	210
T2	1	265
T2	1	200
T2	1	230
T2	1	150
T2	1	205
T2	1	214
T2	1	190
T2	1	168
T2	1	162
T2	1	197
T2	1	170
T2	1	175
T2	2	210
T2	2	195
T2	2	184
T2	2	252
T2	2	170
T2	2	193
T2	2	202
T2	2	244
T2	2	112
T2	2	154
T2	2	159
T2	2	175
T2	2	170
T2	2	177
T2	2	157
T2	2	156
T2	3	192
T2	3	183
T2	3	172
T2	3	260
T2	3	164
T2	3	195
T2	3	186
T2	3	196
T2	3	192
T2	3	183
T2	3	172
T2	3	260
T2	3	164
T2	3	195
T2	3	186
T2	3	196
T3	1	250
T3	1	240
T3	1	215
T3	1	200
T3	1	245
T3	1	195
T3	1	230
T3	1	245
T3	1	220
T3	1	192
T3	1	155
T3	1	170
T3	1	191
T3	1	179
T3	1	165
T3	1	190
T3	2	230
T3	2	215
T3	2	180
T3	2	224
T3	2	222
T3	2	200
T3	2	240
T3	2	220
T3	2	224
T3	2	177
T3	2	243
T3	2	266
T3	2	252
T3	2	240
T3	2	187
T3	2	186
T3	3	171
T3	3	184
T3	3	244
T3	3	186
T3	3	212
T3	3	214
T3	3	246
T3	3	244
T3	3	198
T3	3	245
T3	3	179
T3	3	196
T3	3	218
T3	3	147
T3	3	175
T3	3	174

Treatment	Rep	Plant dry wt. grams
T3	1	0.18
T3	1	0.07
T3	1	0.06
T3	1	0.32
T3	1	0.19
T3	1	0.31
T3	1	0.06
T3	1	0.06
T3	1	0.06
T3	1	0.07
T3	2	0.75
T3	2	0.47
T3	2	0.54
T3	2	0.71
T3	2	0.54
T3	2	0.4
T3	2	0.52
T3	2	0.59
T3	2	0.71
T3	2	0.68
T3	3	0.74
T3	3	0.54
T3	3	0.95
T3	3	0.48
T3	3	0.52
T3	3	0.57
T3	3	0.81
T3	3	0.69
T3	3	0.71
T3	3	0.73

T2	T3
190	250		NULL HYPOTHESIS TO BE TESTED
195	240		H11:	Means of observations of leaf height of plants grouped by replicated groups(1, 2 and 3) ONLY are the same
220	215		H12:	Means of observations of leaf height of plants grouped by soil type of treatment (T1, T2 and T3) ONLY are the same
210	200		H13:	There is no interaction between the two factors, soil type and group with respect to plant's leaf height
265	245
200	195
230	230			Anova: Two-Factor With Replication
150	245
205	220			SUMMARY	T1	T2	T3	Total
214	192		The summary measures for Replication group 1	1
190	155			Count	16	16	16	48
168	170			Sum	4322	3141	3282	10745
162	191			Average	270.125	196.3125	205.125	223.8542
197	179			Variance	529.3167	823.6958	941.05	1838.638
170	165				T1	T2	T3	Total
175	190		The summary measures for Replication group 2	2
210	230			Count	16	16	16	48
195	215			Sum	4079	2910	3506	10495
184	180			Average	254.9375	181.875	219.125	218.6458
252	224			Variance	1092.063	1206.517	714.1167	1870.234
170	222				T1	T2	T3	Total
193	200		The summary measures for Replication group 3	3
202	240			Count	16	16	16	48
244	220			Sum	4291	3096	3233	10620
112	224			Average	268.1875	193.5	202.0625	221.25
154	177			Variance	1522.163	790.9333	964.8625	2183.638
159	243				T1	T2	T3
175	266		The overall summary measures over all replication groups	Total
170	252			Count	48	48	48
177	240			Sum	12692	9147	10021
157	187			Average	264.4167	190.5625	208.7708
156	186			Variance	1049.78	940.2513	892.5208
192	171
183	184
172	244			ANOVA
260	186			Source of Variation	SS	df	MS	F	P-value	F crit
164	212			Sample	651.0417	2	325.5208	0.341268	0.71148	3.063204	(due to groups)	insignificant
195	214			Columns	142119	2	71059.52	74.49701	1.58E-22	3.063204	(due to soil type)	significant
186	246			Interaction	6058.167	4	1514.542	1.587807	0.181104	2.438739	(interaction effect)	insignificant
196	244			Within	128770.8	135	953.8574
192	198
183	245			Total	277599	143
172	179
260	196		RESULTS
164	218		1. Could not reject H11 at 5% significance
195	147		2.Reject H12 at 5% level of significance
186	175		3. Could not reject H13 at 5% level of significance
196	174		Conclusions
			1. The hypothesis that there is no difference between the leaf height of the plants in the replicated groups could not be rejected at 0.05 level of significance since p-value of variation from source "sample" is greater than 0.05
			2.The hypothesis that there is no difference in height among soil types is rejected at 0.05 level of significance since p-value is less than 0.05 for variation due to source, "columns".
			3. There is insignificant ( at level of significant 5%) interaction between soil type and the replicated groups in terms of leaf heights of plants since p-value greater than 0.05.

T1	T2	T3		NULL HYPOTHESIS TO BE TESTED
0.42	0.13	0.18		H21:	Means of observations of dry weight of plants grouped by replicated groups(1, 2 and 3) ONLY are the same
0.44	0.09	0.07		H22:	Means of observations of dry weight of plants grouped by soil type of treatment (T1, T2 and T3) ONLY are the same
0.29	0.09	0.06		H23:	There is no interaction between the two factors, soil type and group with respect to plant's dry weight
0.41	0.13	0.32
0.29	0.05	0.19			Anova: Two-Factor With Replication
0.2	0.15	0.31
0.21	0.05	0.06			SUMMARY	T1	T2	T3	Total
0.33	0.13	0.06		The summary measures for Replication group 1	1
0.2	0.05	0.06			Count	10	10	10	30
0.49	0.08	0.07			Sum	3.28	0.95	1.38	5.61
0.41	0.39	0.75			Average	0.328	0.095	0.138	0.187
0.88	0.18	0.47			Variance	0.011507	0.00145	0.011196	0.018098
0.93	0.42	0.54				T1	T2	T3	Total
0.48	0.54	0.71		The summary measures for Replication group 2	2
0.79	0.62	0.54			Count	10	10	10	30
0.74	0.25	0.4			Sum	7.85	4.34	5.91	18.1
0.88	0.39	0.52			Average	0.785	0.434	0.591	0.603333
0.91	0.54	0.59			Variance	0.042828	0.024182	0.013654	0.046354
0.74	0.35	0.71				T1	T2	T3	Total
1.09	0.66	0.68		The summary measures for Replication group 3	3
1.05	0.57	0.74			Count	10	10	10	30
0.96	0.56	0.54			Sum	11.56	6.13	6.74	24.43
1.11	0.67	0.95			Average	1.156	0.613	0.674	0.814333
1.25	0.56	0.48			Variance	0.026404	0.010046	0.021538	0.079019
0.99	0.77	0.52				T1	T2	T3
1.21	0.56	0.57		The overall summary measures over all replication groups	Total
1.12	0.45	0.81			Count	30	30	30
1.05	0.57	0.69			Sum	22.69	11.42	14.03
1.36	0.66	0.71			Average	0.756333	0.380667	0.467667
1.46	0.76	0.73			Variance	0.143686	0.058806	0.071798


					ANOVA
					Source of Variation	SS	df	MS	F	P-value	F crit
					Sample	6.114016	2	3.057008	168.9946	1.24E-29	3.109311	(due to groups)	significant
					Columns	2.320229	2	1.160114	64.13234	2.02E-17	3.109311	(due to soil type)	significant
					Interaction	0.375164	4	0.093791	5.184871	0.000905	2.484441	(interaction effect)	significant
					Within	1.46524	81	0.018089

					Total	10.27465	89

				RESULTS
				1. Reject H21 at 5% level of significance
				2.Reject H22 at 5% level of significance
				3.Reject H23 at 5% level of significance
				Conclusions
				1. The hypothesis that there is no difference among the dry weights of plants in the relicated groups is rejected at 0.05 level of significance since p-vale of variation from sourse "sample" is less than 0.05
				2.The hypothesis that there is no difference in dry weight of plants due to soil types is rejected at 0.05 level of significance since p-value is less than 0.05 for variation due to source, "columns".
				3. There is significant (level being taken as 5%) interaction between soil type and the replicated groups in terma of dry weight of plants since p-value less than 0.05.