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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_Two Factor ANOVA.wasp
Title produced by softwareTwo-Way ANOVA
Date of computationMon, 27 Dec 2010 15:02:16 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/27/t12934620851ms8p9vtlsszc6t.htm/, Retrieved Sun, 05 May 2024 13:32:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=116021, Retrieved Sun, 05 May 2024 13:32:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact117

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Two-Way ANOVA] [] [2010-11-17 17:05:22] [e45804683e9a4263debf179d74e04a01]
-   PD    [Two-Way ANOVA] [] [2010-12-27 15:02:16] [82d760768aff8bf374d9817688c406af] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
40	1	27	5	26	49	35
45	1	36	4	25	45	34
38	1	25	4	17	54	13
28	1	27	3	37	36	35
NA	2	25	3	35	36	28
38	2	44	3	15	53	32
39	1	50	4	27	46	35
37	1	41	4	36	42	36
30	1	48	5	25	41	27
30	2	43	4	30	45	29
30	2	47	2	27	47	27
26	2	41	3	33	42	28
29	1	44	2	29	45	29
31	2	47	5	30	40	28
27	2	40	3	25	45	30
25	2	46	3	23	40	25
39	1	28	3	26	42	15
35	1	56	3	24	45	33
27	2	49	4	35	47	31
40	2	25	4	39	31	37
34	2	41	4	23	46	37
32	2	26	3	32	34	34
34	1	50	5	29	43	32
38	1	47	4	26	45	21
21	1	52	2	21	42	25
33	2	37	5	35	51	32
27	2	41	3	23	44	28
35	1	45	4	21	47	22
33	2	26	4	28	47	25
36	1	NA	3	30	41	26
NA	1	52	4	21	44	34
37	1	46	2	29	51	34
37	1	58	3	28	46	36
37	1	54	5	19	47	36
32	1	29	3	26	46	26
25	2	50	3	33	38	26
31	1	43	2	34	50	34
33	2	30	3	33	48	33
18	2	47	2	40	36	31
42	1	45	3	24	51	33
26	2	48	1	35	35	22
26	2	48	3	35	49	29
32	2	26	4	32	38	24
31	1	46	5	20	47	37
29	2	NA	3	35	36	32
35	2	50	3	35	47	23
44	1	25	4	21	46	29
35	1	47	2	33	43	35
30	2	47	2	40	53	20
32	1	41	3	22	55	28
24	2	45	2	35	39	26
34	2	41	4	20	55	36
27	2	45	5	28	41	26
31	2	40	3	46	33	33
38	1	29	4	18	52	25
41	2	34	5	22	42	29
40	1	45	5	20	56	32
25	2	52	3	25	46	35
19	2	41	4	31	33	24
33	2	48	3	21	51	31
27	2	45	3	23	46	29
45	1	54	2	26	46	27
27	2	25	3	34	50	29
30	2	26	4	31	46	29
42	1	28	4	23	51	27
21	2	50	4	31	48	34
32	2	48	4	26	44	32
31	2	51	3	36	38	31
36	2	53	3	28	42	31
34	1	37	3	34	39	31
11	1	56	2	25	45	16
35	1	43	3	33	31	25
39	1	34	3	46	29	27
32	1	42	3	24	48	32
28	2	32	3	32	38	28
45	2	31	5	33	55	25
18	1	46	3	42	32	25
35	2	30	5	17	51	36
35	2	47	4	36	53	36
36	2	33	4	40	47	36
34	1	25	4	30	45	27
34	1	25	5	19	33	29
38	2	21	4	33	49	32
28	2	36	5	35	46	29
23	2	50	3	23	42	31
37	2	48	3	15	56	34
29	2	48	2	38	35	27
28	1	25	3	37	40	28
30	1	48	4	23	44	32
24	2	49	5	41	46	33
36	1	27	5	34	46	29
40	1	28	3	38	39	32
37	2	43	2	45	35	35
27	2	48	3	27	48	33
25	2	48	4	46	42	27
22	1	25	1	26	39	16
21	2	49	4	44	39	32
28	1	26	3	36	41	26
34	1	51	3	20	52	32
32	2	25	4	44	45	38
23	1	29	3	27	42	24
29	1	29	4	27	44	26
35	1	43	2	41	33	19
31	2	46	3	30	42	37
36	1	44	3	33	46	25
32	1	25	3	37	45	24
35	1	51	2	30	40	23
45	1	42	5	20	48	28
29	2	53	5	44	32	38
41	1	25	4	20	53	28
36	2	49	2	33	39	28
37	1	51	3	31	45	26
25	2	20	3	23	36	21
36	2	44	3	33	38	35
34	2	38	4	33	49	31
33	1	46	5	32	46	34
32	2	42	4	25	43	30
40	1	29	NA	22	37	30
27	2	46	4	16	48	24
24	2	49	2	36	45	27
26	2	51	3	35	32	26
NA	1	38	3	25	46	30
13	1	41	1	27	20	15
22	2	47	3	32	42	28
29	2	44	3	36	45	34
30	2	47	3	51	29	29
24	2	46	3	30	51	26
NA	1	44	4	20	55	31
26	2	28	3	29	50	28
37	2	47	4	26	44	33
36	2	28	4	20	41	32
38	1	41	5	40	40	33
34	2	45	4	29	47	31
35	2	46	4	32	42	37
32	1	46	4	33	40	27
44	2	22	3	32	51	19
40	2	33	3	34	43	27
24	1	41	4	24	45	31
36	2	47	5	25	41	38
20	1	25	3	41	41	22
28	2	42	3	39	37	35
18	2	47	3	21	46	35
23	2	50	3	38	38	30
28	1	55	5	28	39	41
30	1	21	3	37	45	25
30	1	NA	3	26	46	28
43	1	52	3	30	39	45
20	2	49	4	25	21	21
37	2	46	4	38	31	33
24	1	NA	4	31	35	25
33	2	45	3	31	49	29
43	2	52	3	27	40	31
27	1	NA	3	21	45	29
22	2	40	4	26	46	31
28	2	49	4	37	45	31
18	1	38	5	28	34	25
38	1	32	5	29	41	27
23	2	46	4	33	43	26
38	2	32	3	41	45	26
21	2	41	3	19	48	23
25	2	43	3	37	43	27
NA	1	44	4	36	45	24
30	1	47	5	27	45	35
25	2	28	3	33	34	24
17	1	52	1	29	40	32
26	1	27	2	42	40	24
39	2	45	5	27	55	24
27	1	27	4	47	44	38
33	1	25	4	17	44	36
47	1	28	4	34	48	24
37	1	25	3	32	51	18
34	1	52	4	25	49	34
24	1	44	3	27	33	23
25	2	43	3	37	43	35
20	2	47	4	34	44	22
34	2	52	4	27	44	34
22	2	40	2	37	41	28
39	1	42	3	32	45	34
33	1	45	5	26	44	32
35	1	45	2	29	44	24
26	1	50	5	28	40	34
32	1	49	3	19	48	33
22	1	52	2	46	49	33
39	2	48	3	31	46	29
35	2	51	3	42	49	38
21	2	49	4	33	55	24
27	2	31	4	39	51	25
31	2	43	3	27	46	37
20	2	31	3	35	37	33
28	2	28	4	23	43	30
26	2	43	4	32	41	22
36	2	31	3	22	45	28
16	2	51	3	17	39	24
34	2	58	4	35	38	33
30	2	25	5	34	41	37

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 4 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116021&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116021&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116021&T=0

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24






ANOVA Model
Response ~ Treatment_A * Treatment_B
means17.3338.66712.83315.318.21716.25522.667-11.056-11.973-14.383-9.088NA

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & 17.333 & 8.667 & 12.833 & 15.3 & 18.217 & 16.255 & 22.667 & -11.056 & -11.973 & -14.383 & -9.088 & NA \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116021&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]Response ~ Treatment_A * Treatment_B[/C][/ROW]
[ROW][C]means[/C][C]17.333[/C][C]8.667[/C][C]12.833[/C][C]15.3[/C][C]18.217[/C][C]16.255[/C][C]22.667[/C][C]-11.056[/C][C]-11.973[/C][C]-14.383[/C][C]-9.088[/C][C]NA[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116021&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116021&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

ANOVA Model
Response ~ Treatment_A * Treatment_B
means17.3338.66712.83315.318.21716.25522.667-11.056-11.973-14.383-9.088NA






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
1
Treatment_A1405.255405.2559.7540.002
Treatment_B1967.976193.5954.6590.001
Treatment_A:Treatment_B1244.87861.2191.4730.212
Residuals1797437.36541.55 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 1 &  &  &  &  \tabularnewline
Treatment_A & 1 & 405.255 & 405.255 & 9.754 & 0.002 \tabularnewline
Treatment_B & 1 & 967.976 & 193.595 & 4.659 & 0.001 \tabularnewline
Treatment_A:Treatment_B & 1 & 244.878 & 61.219 & 1.473 & 0.212 \tabularnewline
Residuals & 179 & 7437.365 & 41.55 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116021&T=2

[TABLE]
[ROW][C]ANOVA Statistics[/C][/ROW]
[ROW][C] [/C][C]Df[/C][C]Sum Sq[/C][C]Mean Sq[/C][C]F value[/C][C]Pr(>F)[/C][/ROW]
[ROW][C][/C][C]1[/C][C][/C][C][/C][C][/C][C][/C][/ROW]
[ROW][C]Treatment_A[/C][C]1[/C][C]405.255[/C][C]405.255[/C][C]9.754[/C][C]0.002[/C][/ROW]
[ROW][C]Treatment_B[/C][C]1[/C][C]967.976[/C][C]193.595[/C][C]4.659[/C][C]0.001[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]1[/C][C]244.878[/C][C]61.219[/C][C]1.473[/C][C]0.212[/C][/ROW]
[ROW][C]Residuals[/C][C]179[/C][C]7437.365[/C][C]41.55[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116021&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116021&T=2

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
1
Treatment_A1405.255405.2559.7540.002
Treatment_B1967.976193.5954.6590.001
Treatment_A:Treatment_B1244.87861.2191.4730.212
Residuals1797437.36541.55






Tukey Honest Significant Difference Comparisons
difflwruprp adj
2-1-2.944-4.805-1.0840.002
2-110.1690.03820.2990.049
3-112.1722.65621.6890.004
4-113.5323.92123.1420.001
5-114.3964.49224.3010.001
NA-119.764-0.99840.5250.072
3-22.004-2.5556.5630.803
4-23.363-1.3898.1150.325
5-24.227-1.0939.5480.204
NA-29.595-9.41128.6020.694
4-31.359-1.8854.6030.833
5-32.224-1.8086.2550.607
NA-37.591-11.09526.2780.85
5-40.864-3.3845.1130.992
NA-46.232-12.50324.9670.93
NA-55.368-13.51924.2550.964
2:1-1:18.667-15.98433.3170.991
1:2-1:112.833-0.94726.6130.094
2:2-1:110.444-3.78724.6760.391
1:3-1:115.32.37328.2270.007
2:3-1:111.993-0.70424.690.084
1:4-1:118.2174.99931.4340.001
2:4-1:112.5-0.32825.3280.064
1:5-1:116.2552.88629.6230.005
2:5-1:115.8332.05329.6130.01
1:NA-1:122.667-1.98447.3170.104
2:NA-1:1NANANANA
1:2-2:14.167-18.05326.3861
2:2-2:11.778-20.72524.281
1:3-2:16.633-15.06728.3340.997
2:3-2:13.327-18.23824.8911
1:4-2:19.55-12.32531.4250.953
2:4-2:13.833-17.80925.4761
1:5-2:17.588-14.37929.5550.992
2:5-2:17.167-15.05329.3860.996
1:NA-2:114-16.19144.1910.929
2:NA-2:1NANANANA
2:2-1:2-2.389-11.8027.0251
1:3-1:22.467-4.8259.7580.993
2:3-1:2-0.84-7.7166.0361
1:4-1:25.383-2.41213.1780.49
2:4-1:2-0.333-7.4496.7831
1:5-1:23.422-4.62711.4710.961
2:5-1:23-5.71511.7150.992
1:NA-1:29.833-12.38632.0530.948
2:NA-1:2NANANANA
1:3-2:24.856-3.25812.9690.705
2:3-2:21.549-6.1939.2911
1:4-2:27.772-0.79716.3410.116
2:4-2:22.056-5.910.0110.999
1:5-2:25.81-2.9914.6110.561
2:5-2:25.389-4.02514.8020.76
1:NA-2:212.222-10.2834.7250.817
2:NA-2:2NANANANA
2:3-1:3-3.307-8.2561.6420.543
1:4-1:32.917-3.2469.0790.918
2:4-1:3-2.8-8.0772.4770.838
1:5-1:30.955-5.5267.4361
2:5-1:30.533-6.7587.8251
1:NA-1:37.367-14.33429.0670.993
2:NA-1:3NANANANA
1:4-2:36.2230.55911.8880.018
2:4-2:30.507-4.1795.1931
1:5-2:34.262-1.74710.2710.446
2:5-2:33.84-3.03610.7160.788
1:NA-2:310.673-10.89132.2380.892
2:NA-2:3NANANANA
2:4-1:4-5.717-11.670.2370.073
1:5-1:4-1.962-9.0045.0810.999
2:5-1:4-2.383-10.1785.4120.997
1:NA-1:44.45-17.42526.3251
2:NA-1:4NANANANA
1:5-2:43.755-2.52710.0370.707
2:5-2:43.333-3.78310.4490.924
1:NA-2:410.167-11.47631.8090.922
2:NA-2:4NANANANA
2:5-1:5-0.422-8.4717.6271
1:NA-1:56.412-15.55528.3790.998
2:NA-1:5NANANANA
1:NA-2:56.833-15.38629.0530.997
2:NA-2:5NANANANA
2:NA-1:NANANANANA

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
2-1 & -2.944 & -4.805 & -1.084 & 0.002 \tabularnewline
2-1 & 10.169 & 0.038 & 20.299 & 0.049 \tabularnewline
3-1 & 12.172 & 2.656 & 21.689 & 0.004 \tabularnewline
4-1 & 13.532 & 3.921 & 23.142 & 0.001 \tabularnewline
5-1 & 14.396 & 4.492 & 24.301 & 0.001 \tabularnewline
NA-1 & 19.764 & -0.998 & 40.525 & 0.072 \tabularnewline
3-2 & 2.004 & -2.555 & 6.563 & 0.803 \tabularnewline
4-2 & 3.363 & -1.389 & 8.115 & 0.325 \tabularnewline
5-2 & 4.227 & -1.093 & 9.548 & 0.204 \tabularnewline
NA-2 & 9.595 & -9.411 & 28.602 & 0.694 \tabularnewline
4-3 & 1.359 & -1.885 & 4.603 & 0.833 \tabularnewline
5-3 & 2.224 & -1.808 & 6.255 & 0.607 \tabularnewline
NA-3 & 7.591 & -11.095 & 26.278 & 0.85 \tabularnewline
5-4 & 0.864 & -3.384 & 5.113 & 0.992 \tabularnewline
NA-4 & 6.232 & -12.503 & 24.967 & 0.93 \tabularnewline
NA-5 & 5.368 & -13.519 & 24.255 & 0.964 \tabularnewline
2:1-1:1 & 8.667 & -15.984 & 33.317 & 0.991 \tabularnewline
1:2-1:1 & 12.833 & -0.947 & 26.613 & 0.094 \tabularnewline
2:2-1:1 & 10.444 & -3.787 & 24.676 & 0.391 \tabularnewline
1:3-1:1 & 15.3 & 2.373 & 28.227 & 0.007 \tabularnewline
2:3-1:1 & 11.993 & -0.704 & 24.69 & 0.084 \tabularnewline
1:4-1:1 & 18.217 & 4.999 & 31.434 & 0.001 \tabularnewline
2:4-1:1 & 12.5 & -0.328 & 25.328 & 0.064 \tabularnewline
1:5-1:1 & 16.255 & 2.886 & 29.623 & 0.005 \tabularnewline
2:5-1:1 & 15.833 & 2.053 & 29.613 & 0.01 \tabularnewline
1:NA-1:1 & 22.667 & -1.984 & 47.317 & 0.104 \tabularnewline
2:NA-1:1 & NA & NA & NA & NA \tabularnewline
1:2-2:1 & 4.167 & -18.053 & 26.386 & 1 \tabularnewline
2:2-2:1 & 1.778 & -20.725 & 24.28 & 1 \tabularnewline
1:3-2:1 & 6.633 & -15.067 & 28.334 & 0.997 \tabularnewline
2:3-2:1 & 3.327 & -18.238 & 24.891 & 1 \tabularnewline
1:4-2:1 & 9.55 & -12.325 & 31.425 & 0.953 \tabularnewline
2:4-2:1 & 3.833 & -17.809 & 25.476 & 1 \tabularnewline
1:5-2:1 & 7.588 & -14.379 & 29.555 & 0.992 \tabularnewline
2:5-2:1 & 7.167 & -15.053 & 29.386 & 0.996 \tabularnewline
1:NA-2:1 & 14 & -16.191 & 44.191 & 0.929 \tabularnewline
2:NA-2:1 & NA & NA & NA & NA \tabularnewline
2:2-1:2 & -2.389 & -11.802 & 7.025 & 1 \tabularnewline
1:3-1:2 & 2.467 & -4.825 & 9.758 & 0.993 \tabularnewline
2:3-1:2 & -0.84 & -7.716 & 6.036 & 1 \tabularnewline
1:4-1:2 & 5.383 & -2.412 & 13.178 & 0.49 \tabularnewline
2:4-1:2 & -0.333 & -7.449 & 6.783 & 1 \tabularnewline
1:5-1:2 & 3.422 & -4.627 & 11.471 & 0.961 \tabularnewline
2:5-1:2 & 3 & -5.715 & 11.715 & 0.992 \tabularnewline
1:NA-1:2 & 9.833 & -12.386 & 32.053 & 0.948 \tabularnewline
2:NA-1:2 & NA & NA & NA & NA \tabularnewline
1:3-2:2 & 4.856 & -3.258 & 12.969 & 0.705 \tabularnewline
2:3-2:2 & 1.549 & -6.193 & 9.291 & 1 \tabularnewline
1:4-2:2 & 7.772 & -0.797 & 16.341 & 0.116 \tabularnewline
2:4-2:2 & 2.056 & -5.9 & 10.011 & 0.999 \tabularnewline
1:5-2:2 & 5.81 & -2.99 & 14.611 & 0.561 \tabularnewline
2:5-2:2 & 5.389 & -4.025 & 14.802 & 0.76 \tabularnewline
1:NA-2:2 & 12.222 & -10.28 & 34.725 & 0.817 \tabularnewline
2:NA-2:2 & NA & NA & NA & NA \tabularnewline
2:3-1:3 & -3.307 & -8.256 & 1.642 & 0.543 \tabularnewline
1:4-1:3 & 2.917 & -3.246 & 9.079 & 0.918 \tabularnewline
2:4-1:3 & -2.8 & -8.077 & 2.477 & 0.838 \tabularnewline
1:5-1:3 & 0.955 & -5.526 & 7.436 & 1 \tabularnewline
2:5-1:3 & 0.533 & -6.758 & 7.825 & 1 \tabularnewline
1:NA-1:3 & 7.367 & -14.334 & 29.067 & 0.993 \tabularnewline
2:NA-1:3 & NA & NA & NA & NA \tabularnewline
1:4-2:3 & 6.223 & 0.559 & 11.888 & 0.018 \tabularnewline
2:4-2:3 & 0.507 & -4.179 & 5.193 & 1 \tabularnewline
1:5-2:3 & 4.262 & -1.747 & 10.271 & 0.446 \tabularnewline
2:5-2:3 & 3.84 & -3.036 & 10.716 & 0.788 \tabularnewline
1:NA-2:3 & 10.673 & -10.891 & 32.238 & 0.892 \tabularnewline
2:NA-2:3 & NA & NA & NA & NA \tabularnewline
2:4-1:4 & -5.717 & -11.67 & 0.237 & 0.073 \tabularnewline
1:5-1:4 & -1.962 & -9.004 & 5.081 & 0.999 \tabularnewline
2:5-1:4 & -2.383 & -10.178 & 5.412 & 0.997 \tabularnewline
1:NA-1:4 & 4.45 & -17.425 & 26.325 & 1 \tabularnewline
2:NA-1:4 & NA & NA & NA & NA \tabularnewline
1:5-2:4 & 3.755 & -2.527 & 10.037 & 0.707 \tabularnewline
2:5-2:4 & 3.333 & -3.783 & 10.449 & 0.924 \tabularnewline
1:NA-2:4 & 10.167 & -11.476 & 31.809 & 0.922 \tabularnewline
2:NA-2:4 & NA & NA & NA & NA \tabularnewline
2:5-1:5 & -0.422 & -8.471 & 7.627 & 1 \tabularnewline
1:NA-1:5 & 6.412 & -15.555 & 28.379 & 0.998 \tabularnewline
2:NA-1:5 & NA & NA & NA & NA \tabularnewline
1:NA-2:5 & 6.833 & -15.386 & 29.053 & 0.997 \tabularnewline
2:NA-2:5 & NA & NA & NA & NA \tabularnewline
2:NA-1:NA & NA & NA & NA & NA \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116021&T=3

[TABLE]
[ROW][C]Tukey Honest Significant Difference Comparisons[/C][/ROW]
[ROW][C] [/C][C]diff[/C][C]lwr[/C][C]upr[/C][C]p adj[/C][/ROW]
[ROW][C]2-1[/C][C]-2.944[/C][C]-4.805[/C][C]-1.084[/C][C]0.002[/C][/ROW]
[ROW][C]2-1[/C][C]10.169[/C][C]0.038[/C][C]20.299[/C][C]0.049[/C][/ROW]
[ROW][C]3-1[/C][C]12.172[/C][C]2.656[/C][C]21.689[/C][C]0.004[/C][/ROW]
[ROW][C]4-1[/C][C]13.532[/C][C]3.921[/C][C]23.142[/C][C]0.001[/C][/ROW]
[ROW][C]5-1[/C][C]14.396[/C][C]4.492[/C][C]24.301[/C][C]0.001[/C][/ROW]
[ROW][C]NA-1[/C][C]19.764[/C][C]-0.998[/C][C]40.525[/C][C]0.072[/C][/ROW]
[ROW][C]3-2[/C][C]2.004[/C][C]-2.555[/C][C]6.563[/C][C]0.803[/C][/ROW]
[ROW][C]4-2[/C][C]3.363[/C][C]-1.389[/C][C]8.115[/C][C]0.325[/C][/ROW]
[ROW][C]5-2[/C][C]4.227[/C][C]-1.093[/C][C]9.548[/C][C]0.204[/C][/ROW]
[ROW][C]NA-2[/C][C]9.595[/C][C]-9.411[/C][C]28.602[/C][C]0.694[/C][/ROW]
[ROW][C]4-3[/C][C]1.359[/C][C]-1.885[/C][C]4.603[/C][C]0.833[/C][/ROW]
[ROW][C]5-3[/C][C]2.224[/C][C]-1.808[/C][C]6.255[/C][C]0.607[/C][/ROW]
[ROW][C]NA-3[/C][C]7.591[/C][C]-11.095[/C][C]26.278[/C][C]0.85[/C][/ROW]
[ROW][C]5-4[/C][C]0.864[/C][C]-3.384[/C][C]5.113[/C][C]0.992[/C][/ROW]
[ROW][C]NA-4[/C][C]6.232[/C][C]-12.503[/C][C]24.967[/C][C]0.93[/C][/ROW]
[ROW][C]NA-5[/C][C]5.368[/C][C]-13.519[/C][C]24.255[/C][C]0.964[/C][/ROW]
[ROW][C]2:1-1:1[/C][C]8.667[/C][C]-15.984[/C][C]33.317[/C][C]0.991[/C][/ROW]
[ROW][C]1:2-1:1[/C][C]12.833[/C][C]-0.947[/C][C]26.613[/C][C]0.094[/C][/ROW]
[ROW][C]2:2-1:1[/C][C]10.444[/C][C]-3.787[/C][C]24.676[/C][C]0.391[/C][/ROW]
[ROW][C]1:3-1:1[/C][C]15.3[/C][C]2.373[/C][C]28.227[/C][C]0.007[/C][/ROW]
[ROW][C]2:3-1:1[/C][C]11.993[/C][C]-0.704[/C][C]24.69[/C][C]0.084[/C][/ROW]
[ROW][C]1:4-1:1[/C][C]18.217[/C][C]4.999[/C][C]31.434[/C][C]0.001[/C][/ROW]
[ROW][C]2:4-1:1[/C][C]12.5[/C][C]-0.328[/C][C]25.328[/C][C]0.064[/C][/ROW]
[ROW][C]1:5-1:1[/C][C]16.255[/C][C]2.886[/C][C]29.623[/C][C]0.005[/C][/ROW]
[ROW][C]2:5-1:1[/C][C]15.833[/C][C]2.053[/C][C]29.613[/C][C]0.01[/C][/ROW]
[ROW][C]1:NA-1:1[/C][C]22.667[/C][C]-1.984[/C][C]47.317[/C][C]0.104[/C][/ROW]
[ROW][C]2:NA-1:1[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C]1:2-2:1[/C][C]4.167[/C][C]-18.053[/C][C]26.386[/C][C]1[/C][/ROW]
[ROW][C]2:2-2:1[/C][C]1.778[/C][C]-20.725[/C][C]24.28[/C][C]1[/C][/ROW]
[ROW][C]1:3-2:1[/C][C]6.633[/C][C]-15.067[/C][C]28.334[/C][C]0.997[/C][/ROW]
[ROW][C]2:3-2:1[/C][C]3.327[/C][C]-18.238[/C][C]24.891[/C][C]1[/C][/ROW]
[ROW][C]1:4-2:1[/C][C]9.55[/C][C]-12.325[/C][C]31.425[/C][C]0.953[/C][/ROW]
[ROW][C]2:4-2:1[/C][C]3.833[/C][C]-17.809[/C][C]25.476[/C][C]1[/C][/ROW]
[ROW][C]1:5-2:1[/C][C]7.588[/C][C]-14.379[/C][C]29.555[/C][C]0.992[/C][/ROW]
[ROW][C]2:5-2:1[/C][C]7.167[/C][C]-15.053[/C][C]29.386[/C][C]0.996[/C][/ROW]
[ROW][C]1:NA-2:1[/C][C]14[/C][C]-16.191[/C][C]44.191[/C][C]0.929[/C][/ROW]
[ROW][C]2:NA-2:1[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C]2:2-1:2[/C][C]-2.389[/C][C]-11.802[/C][C]7.025[/C][C]1[/C][/ROW]
[ROW][C]1:3-1:2[/C][C]2.467[/C][C]-4.825[/C][C]9.758[/C][C]0.993[/C][/ROW]
[ROW][C]2:3-1:2[/C][C]-0.84[/C][C]-7.716[/C][C]6.036[/C][C]1[/C][/ROW]
[ROW][C]1:4-1:2[/C][C]5.383[/C][C]-2.412[/C][C]13.178[/C][C]0.49[/C][/ROW]
[ROW][C]2:4-1:2[/C][C]-0.333[/C][C]-7.449[/C][C]6.783[/C][C]1[/C][/ROW]
[ROW][C]1:5-1:2[/C][C]3.422[/C][C]-4.627[/C][C]11.471[/C][C]0.961[/C][/ROW]
[ROW][C]2:5-1:2[/C][C]3[/C][C]-5.715[/C][C]11.715[/C][C]0.992[/C][/ROW]
[ROW][C]1:NA-1:2[/C][C]9.833[/C][C]-12.386[/C][C]32.053[/C][C]0.948[/C][/ROW]
[ROW][C]2:NA-1:2[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C]1:3-2:2[/C][C]4.856[/C][C]-3.258[/C][C]12.969[/C][C]0.705[/C][/ROW]
[ROW][C]2:3-2:2[/C][C]1.549[/C][C]-6.193[/C][C]9.291[/C][C]1[/C][/ROW]
[ROW][C]1:4-2:2[/C][C]7.772[/C][C]-0.797[/C][C]16.341[/C][C]0.116[/C][/ROW]
[ROW][C]2:4-2:2[/C][C]2.056[/C][C]-5.9[/C][C]10.011[/C][C]0.999[/C][/ROW]
[ROW][C]1:5-2:2[/C][C]5.81[/C][C]-2.99[/C][C]14.611[/C][C]0.561[/C][/ROW]
[ROW][C]2:5-2:2[/C][C]5.389[/C][C]-4.025[/C][C]14.802[/C][C]0.76[/C][/ROW]
[ROW][C]1:NA-2:2[/C][C]12.222[/C][C]-10.28[/C][C]34.725[/C][C]0.817[/C][/ROW]
[ROW][C]2:NA-2:2[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C]2:3-1:3[/C][C]-3.307[/C][C]-8.256[/C][C]1.642[/C][C]0.543[/C][/ROW]
[ROW][C]1:4-1:3[/C][C]2.917[/C][C]-3.246[/C][C]9.079[/C][C]0.918[/C][/ROW]
[ROW][C]2:4-1:3[/C][C]-2.8[/C][C]-8.077[/C][C]2.477[/C][C]0.838[/C][/ROW]
[ROW][C]1:5-1:3[/C][C]0.955[/C][C]-5.526[/C][C]7.436[/C][C]1[/C][/ROW]
[ROW][C]2:5-1:3[/C][C]0.533[/C][C]-6.758[/C][C]7.825[/C][C]1[/C][/ROW]
[ROW][C]1:NA-1:3[/C][C]7.367[/C][C]-14.334[/C][C]29.067[/C][C]0.993[/C][/ROW]
[ROW][C]2:NA-1:3[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C]1:4-2:3[/C][C]6.223[/C][C]0.559[/C][C]11.888[/C][C]0.018[/C][/ROW]
[ROW][C]2:4-2:3[/C][C]0.507[/C][C]-4.179[/C][C]5.193[/C][C]1[/C][/ROW]
[ROW][C]1:5-2:3[/C][C]4.262[/C][C]-1.747[/C][C]10.271[/C][C]0.446[/C][/ROW]
[ROW][C]2:5-2:3[/C][C]3.84[/C][C]-3.036[/C][C]10.716[/C][C]0.788[/C][/ROW]
[ROW][C]1:NA-2:3[/C][C]10.673[/C][C]-10.891[/C][C]32.238[/C][C]0.892[/C][/ROW]
[ROW][C]2:NA-2:3[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C]2:4-1:4[/C][C]-5.717[/C][C]-11.67[/C][C]0.237[/C][C]0.073[/C][/ROW]
[ROW][C]1:5-1:4[/C][C]-1.962[/C][C]-9.004[/C][C]5.081[/C][C]0.999[/C][/ROW]
[ROW][C]2:5-1:4[/C][C]-2.383[/C][C]-10.178[/C][C]5.412[/C][C]0.997[/C][/ROW]
[ROW][C]1:NA-1:4[/C][C]4.45[/C][C]-17.425[/C][C]26.325[/C][C]1[/C][/ROW]
[ROW][C]2:NA-1:4[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C]1:5-2:4[/C][C]3.755[/C][C]-2.527[/C][C]10.037[/C][C]0.707[/C][/ROW]
[ROW][C]2:5-2:4[/C][C]3.333[/C][C]-3.783[/C][C]10.449[/C][C]0.924[/C][/ROW]
[ROW][C]1:NA-2:4[/C][C]10.167[/C][C]-11.476[/C][C]31.809[/C][C]0.922[/C][/ROW]
[ROW][C]2:NA-2:4[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C]2:5-1:5[/C][C]-0.422[/C][C]-8.471[/C][C]7.627[/C][C]1[/C][/ROW]
[ROW][C]1:NA-1:5[/C][C]6.412[/C][C]-15.555[/C][C]28.379[/C][C]0.998[/C][/ROW]
[ROW][C]2:NA-1:5[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C]1:NA-2:5[/C][C]6.833[/C][C]-15.386[/C][C]29.053[/C][C]0.997[/C][/ROW]
[ROW][C]2:NA-2:5[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C]2:NA-1:NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116021&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116021&T=3

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Tukey Honest Significant Difference Comparisons
difflwruprp adj
2-1-2.944-4.805-1.0840.002
2-110.1690.03820.2990.049
3-112.1722.65621.6890.004
4-113.5323.92123.1420.001
5-114.3964.49224.3010.001
NA-119.764-0.99840.5250.072
3-22.004-2.5556.5630.803
4-23.363-1.3898.1150.325
5-24.227-1.0939.5480.204
NA-29.595-9.41128.6020.694
4-31.359-1.8854.6030.833
5-32.224-1.8086.2550.607
NA-37.591-11.09526.2780.85
5-40.864-3.3845.1130.992
NA-46.232-12.50324.9670.93
NA-55.368-13.51924.2550.964
2:1-1:18.667-15.98433.3170.991
1:2-1:112.833-0.94726.6130.094
2:2-1:110.444-3.78724.6760.391
1:3-1:115.32.37328.2270.007
2:3-1:111.993-0.70424.690.084
1:4-1:118.2174.99931.4340.001
2:4-1:112.5-0.32825.3280.064
1:5-1:116.2552.88629.6230.005
2:5-1:115.8332.05329.6130.01
1:NA-1:122.667-1.98447.3170.104
2:NA-1:1NANANANA
1:2-2:14.167-18.05326.3861
2:2-2:11.778-20.72524.281
1:3-2:16.633-15.06728.3340.997
2:3-2:13.327-18.23824.8911
1:4-2:19.55-12.32531.4250.953
2:4-2:13.833-17.80925.4761
1:5-2:17.588-14.37929.5550.992
2:5-2:17.167-15.05329.3860.996
1:NA-2:114-16.19144.1910.929
2:NA-2:1NANANANA
2:2-1:2-2.389-11.8027.0251
1:3-1:22.467-4.8259.7580.993
2:3-1:2-0.84-7.7166.0361
1:4-1:25.383-2.41213.1780.49
2:4-1:2-0.333-7.4496.7831
1:5-1:23.422-4.62711.4710.961
2:5-1:23-5.71511.7150.992
1:NA-1:29.833-12.38632.0530.948
2:NA-1:2NANANANA
1:3-2:24.856-3.25812.9690.705
2:3-2:21.549-6.1939.2911
1:4-2:27.772-0.79716.3410.116
2:4-2:22.056-5.910.0110.999
1:5-2:25.81-2.9914.6110.561
2:5-2:25.389-4.02514.8020.76
1:NA-2:212.222-10.2834.7250.817
2:NA-2:2NANANANA
2:3-1:3-3.307-8.2561.6420.543
1:4-1:32.917-3.2469.0790.918
2:4-1:3-2.8-8.0772.4770.838
1:5-1:30.955-5.5267.4361
2:5-1:30.533-6.7587.8251
1:NA-1:37.367-14.33429.0670.993
2:NA-1:3NANANANA
1:4-2:36.2230.55911.8880.018
2:4-2:30.507-4.1795.1931
1:5-2:34.262-1.74710.2710.446
2:5-2:33.84-3.03610.7160.788
1:NA-2:310.673-10.89132.2380.892
2:NA-2:3NANANANA
2:4-1:4-5.717-11.670.2370.073
1:5-1:4-1.962-9.0045.0810.999
2:5-1:4-2.383-10.1785.4120.997
1:NA-1:44.45-17.42526.3251
2:NA-1:4NANANANA
1:5-2:43.755-2.52710.0370.707
2:5-2:43.333-3.78310.4490.924
1:NA-2:410.167-11.47631.8090.922
2:NA-2:4NANANANA
2:5-1:5-0.422-8.4717.6271
1:NA-1:56.412-15.55528.3790.998
2:NA-1:5NANANANA
1:NA-2:56.833-15.38629.0530.997
2:NA-2:5NANANANA
2:NA-1:NANANANANA






Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group100.6580.762
179 

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 10 & 0.658 & 0.762 \tabularnewline
  & 179 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116021&T=4

[TABLE]
[ROW][C]Levenes Test for Homogeneity of Variance[/C][/ROW]
[ROW][C] [/C][C]Df[/C][C]F value[/C][C]Pr(>F)[/C][/ROW]
[ROW][C]Group[/C][C]10[/C][C]0.658[/C][C]0.762[/C][/ROW]
[ROW][C] [/C][C]179[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116021&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116021&T=4

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group100.6580.762
179


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = 2 ; par3 = 4 ; par4 = TRUE ;
Parameters (R input):
par1 = 1 ; par2 = 2 ; par3 = 4 ; par4 = TRUE ;
R code (references can be found in the software module):
cat1 <- as.numeric(par1) #
cat2<- as.numeric(par2) #
cat3 <- as.numeric(par3)
intercept<-as.logical(par4)
x <- t(x)
x1<-as.numeric(x[,cat1])
f1<-as.character(x[,cat2])
f2 <- as.character(x[,cat3])
xdf<-data.frame(x1,f1, f2)
(V1<-dimnames(y)[[1]][cat1])
(V2<-dimnames(y)[[1]][cat2])
(V3 <-dimnames(y)[[1]][cat3])
names(xdf)<-c('Response', 'Treatment_A', 'Treatment_B')
if(intercept == FALSE) (lmxdf<-lm(Response ~ Treatment_A * Treatment_B- 1, data = xdf) ) else (lmxdf<-lm(Response ~ Treatment_A * Treatment_B, data = xdf) )
(aov.xdf<-aov(lmxdf) )
(anova.xdf<-anova(lmxdf) )
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'ANOVA Model', length(lmxdf$coefficients)+1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, lmxdf$call['formula'],length(lmxdf$coefficients)+1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'means',,TRUE)
for(i in 1:length(lmxdf$coefficients)){
a<-table.element(a, round(lmxdf$coefficients[i], digits=3),,FALSE)
}
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'ANOVA Statistics', 5+1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, ' ',,TRUE)
a<-table.element(a, 'Df',,FALSE)
a<-table.element(a, 'Sum Sq',,FALSE)
a<-table.element(a, 'Mean Sq',,FALSE)
a<-table.element(a, 'F value',,FALSE)
a<-table.element(a, 'Pr(>F)',,FALSE)
a<-table.row.end(a)
for(i in 1 : length(rownames(anova.xdf))-1){
a<-table.row.start(a)
a<-table.element(a,rownames(anova.xdf)[i] ,,TRUE)
a<-table.element(a, anova.xdf$Df[1],,FALSE)
a<-table.element(a, round(anova.xdf$'Sum Sq'[i], digits=3),,FALSE)
a<-table.element(a, round(anova.xdf$'Mean Sq'[i], digits=3),,FALSE)
a<-table.element(a, round(anova.xdf$'F value'[i], digits=3),,FALSE)
a<-table.element(a, round(anova.xdf$'Pr(>F)'[i], digits=3),,FALSE)
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a, 'Residuals',,TRUE)
a<-table.element(a, anova.xdf$'Df'[i+1],,FALSE)
a<-table.element(a, round(anova.xdf$'Sum Sq'[i+1], digits=3),,FALSE)
a<-table.element(a, round(anova.xdf$'Mean Sq'[i+1], digits=3),,FALSE)
a<-table.element(a, ' ',,FALSE)
a<-table.element(a, ' ',,FALSE)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
bitmap(file='anovaplot.png')
boxplot(Response ~ Treatment_A + Treatment_B, data=xdf, xlab=V2, ylab=V1, main='Boxplots of ANOVA Groups')
dev.off()
bitmap(file='designplot.png')
xdf2 <- xdf # to preserve xdf make copy for function
names(xdf2) <- c(V1, V2, V3)
plot.design(xdf2, main='Design Plot of Group Means')
dev.off()
bitmap(file='interactionplot.png')
interaction.plot(xdf$Treatment_A, xdf$Treatment_B, xdf$Response, xlab=V2, ylab=V1, trace.label=V3, main='Possible Interactions Between Anova Groups')
dev.off()
if(intercept==TRUE){
thsd<-TukeyHSD(aov.xdf)
names(thsd) <- c(V2, V3, paste(V2, ':', V3, sep=''))
bitmap(file='TukeyHSDPlot.png')
layout(matrix(c(1,2,3,3), 2,2))
plot(thsd, las=1)
dev.off()
}
if(intercept==TRUE){
ntables<-length(names(thsd))
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Tukey Honest Significant Difference Comparisons', 5,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, ' ', 1, TRUE)
for(i in 1:4){
a<-table.element(a,colnames(thsd[[1]])[i], 1, TRUE)
}
a<-table.row.end(a)
for(nt in 1:ntables){
for(i in 1:length(rownames(thsd[[nt]]))){
a<-table.row.start(a)
a<-table.element(a,rownames(thsd[[nt]])[i], 1, TRUE)
for(j in 1:4){
a<-table.element(a,round(thsd[[nt]][i,j], digits=3), 1, FALSE)
}
a<-table.row.end(a)
}
} # end nt
a<-table.end(a)
table.save(a,file='hsdtable.tab')
}#end if hsd tables
if(intercept==FALSE){
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'TukeyHSD Message', 1,TRUE)
a<-table.row.end(a)
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Must Include Intercept to use Tukey Test ', 1, FALSE)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable2.tab')
}
library(car)
lt.lmxdf<-levene.test(lmxdf)
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Levenes Test for Homogeneity of Variance', 4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,' ', 1, TRUE)
for (i in 1:3){
a<-table.element(a,names(lt.lmxdf)[i], 1, FALSE)
}
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Group', 1, TRUE)
for (i in 1:3){
a<-table.element(a,round(lt.lmxdf[[i]][1], digits=3), 1, FALSE)
}
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,' ', 1, TRUE)
a<-table.element(a,lt.lmxdf[[1]][2], 1, FALSE)
a<-table.element(a,' ', 1, FALSE)
a<-table.element(a,' ', 1, FALSE)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')