Question

What is the F statistic to test for a difference in mean THC yield between the control and heat-treated seeds?

PlotID	Column	Treat	THC
1	1	Control	13.5
2	2	Control	18.7
3	3	Control	16
4	4	Control	19
5	5	Heat	22
6	6	Heat	23.8
7	7	Heat	25.2
8	8	Heat	24.6
9	1	Control	14.5
10	2	Control	15.1
11	3	Control	16.4
12	4	Control	21.6
13	5	Heat	26.7
14	6	Heat	24
15	7	Heat	26.4
16	8	Heat	24.8
17	1	Control	16.3
18	2	Control	18.7
19	3	Control	20.5
20	4	Control	17.3
21	5	Heat	22.1
22	6	Heat	23.8
23	7	Heat	21.5
24	8	Heat	24.3
25	1	Control	14.8
26	2	Control	15.2
27	3	Control	22.7
28	4	Control	20.3
29	5	Heat	23.4
30	6	Heat	23.3
31	7	Heat	27
32	8	Heat	25
33	1	Control	18.1
34	2	Control	17.2
35	3	Control	17.2
36	4	Control	18.3
37	5	Heat	20
38	6	Heat	23.7
39	7	Heat	23.6
40	8	Heat	28.3
41	1	Control	19.4
42	2	Control	14.7
43	3	Control	17.7
44	4	Control	16.9
45	5	Heat	22.9
46	6	Heat	20.6
47	7	Heat	23
48	8	Heat	25.5

Answer 1

Given Data:

n=1

r=1

PlotID	Column	Treat	THC
1	1	Control	13.5
2	2	Control	18.7
3	3	Control	16
4	4	Control	19
5	5	Heat	22
6	6	Heat	23.8
7	7	Heat	25.2
8	8	Heat	24.6
9	1	Control	14.5
10	2	Control	15.1
11	3	Control	16.4
12	4	Control	21.6
13	5	Heat	26.7
14	6	Heat	24
15	7	Heat	26.4
16	8	Heat	24.8
17	1	Control	16.3
18	2	Control	18.7
19	3	Control	20.5
20	4	Control	17.3
21	5	Heat	22.1
22	6	Heat	23.8
23	7	Heat	21.5
24	8	Heat	24.3
25	1	Control	14.8
26	2	Control	15.2
27	3	Control	22.7
28	4	Control	20.3
29	5	Heat	23.4
30	6	Heat	23.3
31	7	Heat	27
32	8	Heat	25
33	1	Control	18.1
34	2	Control	17.2
35	3	Control	17.2
36	4	Control	18.3
37	5	Heat	20
38	6	Heat	23.7
39	7	Heat	23.6
40	8	Heat	28.3
41	1	Control	19.4
42	2	Control	14.7
43	3	Control	17.7
44	4	Control	16.9
45	5	Heat	22.9
46	6	Heat	20.6
47	7	Heat	23
48	8	Heat	25.5

Control treatment data:

Treat	THC
Control	13.5
Control	18.7
Control	16
Control	19
Control	14.5
Control	15.1
Control	16.4
Control	21.6
Control	16.3
Control	18.7
Control	20.5
Control	17.3
Control	14.8
Control	15.2
Control	22.7
Control	20.3
Control	18.1
Control	17.2
Control	17.2
Control	18.3
Control	19.4
Control	14.7
Control	17.7
Control	16.9

Heat treatment data:

Treat	THC
Heat	22
Heat	23.8
Heat	25.2
Heat	24.6
Heat	26.7
Heat	24
Heat	26.4
Heat	24.8
Heat	22.1
Heat	23.8
Heat	21.5
Heat	24.3
Heat	23.4
Heat	23.3
Heat	27
Heat	25
Heat	20
Heat	23.7
Heat	23.6
Heat	28.3
Heat	22.9
Heat	20.6
Heat	23
Heat	25.5

by use Excel data analysis, put above data:

Descriptions	Control	Heat
Mean	17.50	23.98
Variance	5.53	3.96
Observations	24	24
df	23	23
F	1.40
P(F<=f) one-tail	0.22
F Critical one-tail	2.01

Group mean = 20.74 THC.

Treat	THC	(Xi-mean)^2
Control	13.5	16.0
Control	18.7	1.4
Control	16	2.3
Control	19	2.2
Control	14.5	9.0
Control	15.1	5.8
Control	16.4	1.2
Control	21.6	16.8
Control	16.3	1.5
Control	18.7	1.4
Control	20.5	9.0
Control	17.3	0.0
Control	14.8	7.3
Control	15.2	5.3
Control	22.7	27.0
Control	20.3	7.8
Control	18.1	0.4
Control	17.2	0.1
Control	17.2	0.1
Control	18.3	0.6
Control	19.4	3.6
Control	14.7	7.9
Control	17.7	0.0
Control	16.9	0.4
Mean	17.5	127.1

SSBL =127.1

Treat	THC	(Xi-mean)^2
Heat	22	3.92
Heat	23.8	0.03
Heat	25.2	1.49
Heat	24.6	0.39
Heat	26.7	7.40
Heat	24	0.00
Heat	26.4	5.86
Heat	24.8	0.67
Heat	22.1	3.53
Heat	23.8	0.03
Heat	21.5	6.15
Heat	24.3	0.10
Heat	23.4	0.34
Heat	23.3	0.46
Heat	27	9.13
Heat	25	1.04
Heat	20	15.83
Heat	23.7	0.08
Heat	23.6	0.14
Heat	28.3	18.67
Heat	22.9	1.16
Heat	20.6	11.42
Heat	23	0.96
Heat	25.5	2.31
mean	23.979	91.1

SSTR = 91.1

PlotID	Column	Treat	THC	(Xi-mean)^2
1	1	Control	13.5	52.4
2	2	Control	18.7	4.2
3	3	Control	16	22.5
4	4	Control	19	3.0
5	5	Heat	22	1.6
6	6	Heat	23.8	9.4
7	7	Heat	25.2	19.9
8	8	Heat	24.6	14.9
9	1	Control	14.5	39.0
10	2	Control	15.1	31.8
11	3	Control	16.4	18.9
12	4	Control	21.6	0.7
13	5	Heat	26.7	35.5
14	6	Heat	24	10.6
15	7	Heat	26.4	32.0
16	8	Heat	24.8	16.5
17	1	Control	16.3	19.7
18	2	Control	18.7	4.2
19	3	Control	20.5	0.1
20	4	Control	17.3	11.8
21	5	Heat	22.1	1.8
22	6	Heat	23.8	9.4
23	7	Heat	21.5	0.6
24	8	Heat	24.3	12.7
25	1	Control	14.8	35.3
26	2	Control	15.2	30.7
27	3	Control	22.7	3.8
28	4	Control	20.3	0.2
29	5	Heat	23.4	7.1
30	6	Heat	23.3	6.5
31	7	Heat	27	39.2
32	8	Heat	25	18.1
33	1	Control	18.1	7.0
34	2	Control	17.2	12.5
35	3	Control	17.2	12.5
36	4	Control	18.3	6.0
37	5	Heat	20	0.6
38	6	Heat	23.7	8.8
39	7	Heat	23.6	8.2
40	8	Heat	28.3	57.1
41	1	Control	19.4	1.8
42	2	Control	14.7	36.5
43	3	Control	17.7	9.3
44	4	Control	16.9	14.8
45	5	Heat	22.9	4.7
46	6	Heat	20.6	0.0
47	7	Heat	23	5.1
48	8	Heat	25.5	22.6
		average	20.7
		SSE		721.4

Source of variance	Sum of Sqrs	Degree of freedom	mean sqr	F ratio
Control	SSBL	n-1	MSBL=SSBL/N-1	F= MSBL/MSTR
heat	SSTR	r-1	MSTR=SSTR/r-1
Error	SSE	(n-1)*(r-1)	MSE=SSE/((n-1)*(r-1))
Total

Source of variance	Sum of Sqrs	Degree of freedom	mean sqr	F ratio
Control	127.1	23	5.53	1.40
heat	91.1	23	3.96
Error	721.4	529	1.36
Total		575

F=1.4