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R Software Module

rwasp_Two Factor ANOVA.wasp

Title produced by software

Two-Way ANOVA

Date of computation

Sat, 13 Apr 2024 11:07:27 +0200

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2024/Apr/13/t17130010471xdmi4prtabh4ah.htm/, Retrieved Thu, 23 Apr 2026 07:50:16 +0200

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Thu, 23 Apr 2026 07:50:16 +0200

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Estimated Impact

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1.166	'A'	'H'
0.932	'A'	'H'
1.132	'A'	'H'
0.56	'B'	'H'
0.439	'B'	'H'
0.486	'B'	'H'
0.424	'C'	'H'
0.342	'C'	'H'
0.222	'C'	'H'
0.605	'D'	'H'
0.476	'D'	'H'
0.555	'D'	'H'
0.627	'E'	'H'
0.538	'E'	'H'
0.596	'E'	'H'
1.218	'F'	'H'
1.696	'F'	'H'
1.261	'F'	'H'
1	'A'	'I'
1.021	'A'	'I'
1.246	'A'	'I'
0.613	'B'	'I'
0.539	'B'	'I'
0.92	'B'	'I'
0.502	'C'	'I'
0.585	'C'	'I'
0.474	'C'	'I'
0.515	'D'	'I'
0.432	'D'	'I'
0.855	'D'	'I'
0.809	'E'	'I'
0.81	'E'	'I'
0.716	'E'	'I'
1.651	'F'	'I'
1.294	'F'	'I'
1.414	'F'	'I'

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	Big Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=0

[TABLE]
[ROW]

Summary of computational transaction[/C][/ROW] [ROW]

Raw Input[/C]

view raw input (R code) [/C][/ROW] [ROW]

Raw Output[/C]

view raw output of R engine [/C][/ROW] [ROW]

Computing time[/C]

2 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=&T=0

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

As an alternative you can also use a QR Code:

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

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	Big Analytics Cloud Computing Center

ANOVA Model
Response ~ Treatment_A * Treatment_B
means	1.077	-0.582	-0.747	-0.531	-0.49	0.315	0.012	0.183	0.179	0.043	0.179	0.049

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & 1.077 & -0.582 & -0.747 & -0.531 & -0.49 & 0.315 & 0.012 & 0.183 & 0.179 & 0.043 & 0.179 & 0.049 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]Response ~ Treatment_A * Treatment_B[/C][/ROW]
[ROW][C]means[/C][C]1.077[/C][C]-0.582[/C][C]-0.747[/C][C]-0.531[/C][C]-0.49[/C][C]0.315[/C][C]0.012[/C][C]0.183[/C][C]0.179[/C][C]0.043[/C][C]0.179[/C][C]0.049[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

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

As an alternative you can also use a QR Code:

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

ANOVA Model
Response ~ Treatment_A * Treatment_B
means	1.077	-0.582	-0.747	-0.531	-0.49	0.315	0.012	0.183	0.179	0.043	0.179	0.049

ANOVA Statistics
	Df	Sum Sq	Mean Sq	F value	Pr(>F)
	5
Treatment_A	5	4.297	0.859	40.424	0
Treatment_B	5	0.125	0.125	5.878	0.023
Treatment_A:Treatment_B	5	0.053	0.011	0.494	0.777
Residuals	24	0.51	0.021

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 5 &  &  &  &  \tabularnewline
Treatment_A & 5 & 4.297 & 0.859 & 40.424 & 0 \tabularnewline
Treatment_B & 5 & 0.125 & 0.125 & 5.878 & 0.023 \tabularnewline
Treatment_A:Treatment_B & 5 & 0.053 & 0.011 & 0.494 & 0.777 \tabularnewline
Residuals & 24 & 0.51 & 0.021 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]5[/C][C][/C][C][/C][C][/C][C][/C][/ROW]
[ROW][C]Treatment_A[/C][C]5[/C][C]4.297[/C][C]0.859[/C][C]40.424[/C][C]0[/C][/ROW]
[ROW][C]Treatment_B[/C][C]5[/C][C]0.125[/C][C]0.125[/C][C]5.878[/C][C]0.023[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]5[/C][C]0.053[/C][C]0.011[/C][C]0.494[/C][C]0.777[/C][/ROW]
[ROW][C]Residuals[/C][C]24[/C][C]0.51[/C][C]0.021[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

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

As an alternative you can also use a QR Code:

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

ANOVA Statistics
	Df	Sum Sq	Mean Sq	F value	Pr(>F)
	5
Treatment_A	5	4.297	0.859	40.424	0
Treatment_B	5	0.125	0.125	5.878	0.023
Treatment_A:Treatment_B	5	0.053	0.011	0.494	0.777
Residuals	24	0.51	0.021

Tukey Honest Significant Difference Comparisons
	diff	lwr	upr	p adj
B-A	-0.49	-0.75	-0.23	0
C-A	-0.658	-0.918	-0.398	0
D-A	-0.51	-0.77	-0.25	0
E-A	-0.4	-0.66	-0.14	0.001
F-A	0.339	0.079	0.6	0.006
C-B	-0.168	-0.428	0.092	0.374
D-B	-0.02	-0.28	0.24	1
E-B	0.09	-0.17	0.35	0.889
F-B	0.829	0.569	1.09	0
D-C	0.148	-0.112	0.408	0.508
E-C	0.258	-0.002	0.518	0.053
F-C	0.997	0.737	1.258	0
E-D	0.11	-0.151	0.37	0.781
F-D	0.849	0.589	1.11	0
F-E	0.74	0.479	1	0
I-H	0.118	0.018	0.218	0.023
B:H-A:H	-0.582	-1.011	-0.152	0.003
C:H-A:H	-0.747	-1.177	-0.318	0
D:H-A:H	-0.531	-0.961	-0.102	0.007
E:H-A:H	-0.49	-0.919	-0.06	0.016
F:H-A:H	0.315	-0.114	0.744	0.309
A:I-A:H	0.012	-0.417	0.442	1
B:I-A:H	-0.386	-0.815	0.043	0.106
C:I-A:H	-0.556	-0.986	-0.127	0.004
D:I-A:H	-0.476	-0.905	-0.047	0.021
E:I-A:H	-0.298	-0.728	0.131	0.382
F:I-A:H	0.376	-0.053	0.806	0.125
C:H-B:H	-0.166	-0.595	0.264	0.954
D:H-B:H	0.05	-0.379	0.48	1
E:H-B:H	0.092	-0.337	0.521	1
F:H-B:H	0.897	0.467	1.326	0
A:I-B:H	0.594	0.165	1.023	0.002
B:I-B:H	0.196	-0.234	0.625	0.876
C:I-B:H	0.025	-0.404	0.455	1
D:I-B:H	0.106	-0.324	0.535	0.999
E:I-B:H	0.283	-0.146	0.713	0.454
F:I-B:H	0.958	0.529	1.387	0
D:H-C:H	0.216	-0.213	0.645	0.796
E:H-C:H	0.258	-0.172	0.687	0.587
F:H-C:H	1.062	0.633	1.492	0
A:I-C:H	0.76	0.33	1.189	0
B:I-C:H	0.361	-0.068	0.791	0.158
C:I-C:H	0.191	-0.238	0.62	0.891
D:I-C:H	0.271	-0.158	0.701	0.515
E:I-C:H	0.449	0.02	0.878	0.035
F:I-C:H	1.124	0.694	1.553	0
E:H-D:H	0.042	-0.388	0.471	1
F:H-D:H	0.846	0.417	1.276	0
A:I-D:H	0.544	0.114	0.973	0.006
B:I-D:H	0.145	-0.284	0.575	0.982
C:I-D:H	-0.025	-0.454	0.404	1
D:I-D:H	0.055	-0.374	0.485	1
E:I-D:H	0.233	-0.196	0.662	0.715
F:I-D:H	0.908	0.478	1.337	0
F:H-E:H	0.805	0.375	1.234	0
A:I-E:H	0.502	0.073	0.931	0.013
B:I-E:H	0.104	-0.326	0.533	0.999
C:I-E:H	-0.067	-0.496	0.363	1
D:I-E:H	0.014	-0.416	0.443	1
E:I-E:H	0.191	-0.238	0.621	0.89
F:I-E:H	0.866	0.437	1.295	0
A:I-F:H	-0.303	-0.732	0.127	0.362
B:I-F:H	-0.701	-1.13	-0.272	0
C:I-F:H	-0.871	-1.301	-0.442	0
D:I-F:H	-0.791	-1.22	-0.362	0
E:I-F:H	-0.613	-1.043	-0.184	0.001
F:I-F:H	0.061	-0.368	0.491	1
B:I-A:I	-0.398	-0.828	0.031	0.086
C:I-A:I	-0.569	-0.998	-0.139	0.003
D:I-A:I	-0.488	-0.918	-0.059	0.016
E:I-A:I	-0.311	-0.74	0.119	0.327
F:I-A:I	0.364	-0.065	0.793	0.152
C:I-B:I	-0.17	-0.6	0.259	0.945
D:I-B:I	-0.09	-0.519	0.339	1
E:I-B:I	0.088	-0.342	0.517	1
F:I-B:I	0.762	0.333	1.192	0
D:I-C:I	0.08	-0.349	0.51	1
E:I-C:I	0.258	-0.171	0.687	0.585
F:I-C:I	0.933	0.503	1.362	0
E:I-D:I	0.178	-0.252	0.607	0.929
F:I-D:I	0.852	0.423	1.282	0
F:I-E:I	0.675	0.245	1.104	0

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
B-A & -0.49 & -0.75 & -0.23 & 0 \tabularnewline
C-A & -0.658 & -0.918 & -0.398 & 0 \tabularnewline
D-A & -0.51 & -0.77 & -0.25 & 0 \tabularnewline
E-A & -0.4 & -0.66 & -0.14 & 0.001 \tabularnewline
F-A & 0.339 & 0.079 & 0.6 & 0.006 \tabularnewline
C-B & -0.168 & -0.428 & 0.092 & 0.374 \tabularnewline
D-B & -0.02 & -0.28 & 0.24 & 1 \tabularnewline
E-B & 0.09 & -0.17 & 0.35 & 0.889 \tabularnewline
F-B & 0.829 & 0.569 & 1.09 & 0 \tabularnewline
D-C & 0.148 & -0.112 & 0.408 & 0.508 \tabularnewline
E-C & 0.258 & -0.002 & 0.518 & 0.053 \tabularnewline
F-C & 0.997 & 0.737 & 1.258 & 0 \tabularnewline
E-D & 0.11 & -0.151 & 0.37 & 0.781 \tabularnewline
F-D & 0.849 & 0.589 & 1.11 & 0 \tabularnewline
F-E & 0.74 & 0.479 & 1 & 0 \tabularnewline
I-H & 0.118 & 0.018 & 0.218 & 0.023 \tabularnewline
B:H-A:H & -0.582 & -1.011 & -0.152 & 0.003 \tabularnewline
C:H-A:H & -0.747 & -1.177 & -0.318 & 0 \tabularnewline
D:H-A:H & -0.531 & -0.961 & -0.102 & 0.007 \tabularnewline
E:H-A:H & -0.49 & -0.919 & -0.06 & 0.016 \tabularnewline
F:H-A:H & 0.315 & -0.114 & 0.744 & 0.309 \tabularnewline
A:I-A:H & 0.012 & -0.417 & 0.442 & 1 \tabularnewline
B:I-A:H & -0.386 & -0.815 & 0.043 & 0.106 \tabularnewline
C:I-A:H & -0.556 & -0.986 & -0.127 & 0.004 \tabularnewline
D:I-A:H & -0.476 & -0.905 & -0.047 & 0.021 \tabularnewline
E:I-A:H & -0.298 & -0.728 & 0.131 & 0.382 \tabularnewline
F:I-A:H & 0.376 & -0.053 & 0.806 & 0.125 \tabularnewline
C:H-B:H & -0.166 & -0.595 & 0.264 & 0.954 \tabularnewline
D:H-B:H & 0.05 & -0.379 & 0.48 & 1 \tabularnewline
E:H-B:H & 0.092 & -0.337 & 0.521 & 1 \tabularnewline
F:H-B:H & 0.897 & 0.467 & 1.326 & 0 \tabularnewline
A:I-B:H & 0.594 & 0.165 & 1.023 & 0.002 \tabularnewline
B:I-B:H & 0.196 & -0.234 & 0.625 & 0.876 \tabularnewline
C:I-B:H & 0.025 & -0.404 & 0.455 & 1 \tabularnewline
D:I-B:H & 0.106 & -0.324 & 0.535 & 0.999 \tabularnewline
E:I-B:H & 0.283 & -0.146 & 0.713 & 0.454 \tabularnewline
F:I-B:H & 0.958 & 0.529 & 1.387 & 0 \tabularnewline
D:H-C:H & 0.216 & -0.213 & 0.645 & 0.796 \tabularnewline
E:H-C:H & 0.258 & -0.172 & 0.687 & 0.587 \tabularnewline
F:H-C:H & 1.062 & 0.633 & 1.492 & 0 \tabularnewline
A:I-C:H & 0.76 & 0.33 & 1.189 & 0 \tabularnewline
B:I-C:H & 0.361 & -0.068 & 0.791 & 0.158 \tabularnewline
C:I-C:H & 0.191 & -0.238 & 0.62 & 0.891 \tabularnewline
D:I-C:H & 0.271 & -0.158 & 0.701 & 0.515 \tabularnewline
E:I-C:H & 0.449 & 0.02 & 0.878 & 0.035 \tabularnewline
F:I-C:H & 1.124 & 0.694 & 1.553 & 0 \tabularnewline
E:H-D:H & 0.042 & -0.388 & 0.471 & 1 \tabularnewline
F:H-D:H & 0.846 & 0.417 & 1.276 & 0 \tabularnewline
A:I-D:H & 0.544 & 0.114 & 0.973 & 0.006 \tabularnewline
B:I-D:H & 0.145 & -0.284 & 0.575 & 0.982 \tabularnewline
C:I-D:H & -0.025 & -0.454 & 0.404 & 1 \tabularnewline
D:I-D:H & 0.055 & -0.374 & 0.485 & 1 \tabularnewline
E:I-D:H & 0.233 & -0.196 & 0.662 & 0.715 \tabularnewline
F:I-D:H & 0.908 & 0.478 & 1.337 & 0 \tabularnewline
F:H-E:H & 0.805 & 0.375 & 1.234 & 0 \tabularnewline
A:I-E:H & 0.502 & 0.073 & 0.931 & 0.013 \tabularnewline
B:I-E:H & 0.104 & -0.326 & 0.533 & 0.999 \tabularnewline
C:I-E:H & -0.067 & -0.496 & 0.363 & 1 \tabularnewline
D:I-E:H & 0.014 & -0.416 & 0.443 & 1 \tabularnewline
E:I-E:H & 0.191 & -0.238 & 0.621 & 0.89 \tabularnewline
F:I-E:H & 0.866 & 0.437 & 1.295 & 0 \tabularnewline
A:I-F:H & -0.303 & -0.732 & 0.127 & 0.362 \tabularnewline
B:I-F:H & -0.701 & -1.13 & -0.272 & 0 \tabularnewline
C:I-F:H & -0.871 & -1.301 & -0.442 & 0 \tabularnewline
D:I-F:H & -0.791 & -1.22 & -0.362 & 0 \tabularnewline
E:I-F:H & -0.613 & -1.043 & -0.184 & 0.001 \tabularnewline
F:I-F:H & 0.061 & -0.368 & 0.491 & 1 \tabularnewline
B:I-A:I & -0.398 & -0.828 & 0.031 & 0.086 \tabularnewline
C:I-A:I & -0.569 & -0.998 & -0.139 & 0.003 \tabularnewline
D:I-A:I & -0.488 & -0.918 & -0.059 & 0.016 \tabularnewline
E:I-A:I & -0.311 & -0.74 & 0.119 & 0.327 \tabularnewline
F:I-A:I & 0.364 & -0.065 & 0.793 & 0.152 \tabularnewline
C:I-B:I & -0.17 & -0.6 & 0.259 & 0.945 \tabularnewline
D:I-B:I & -0.09 & -0.519 & 0.339 & 1 \tabularnewline
E:I-B:I & 0.088 & -0.342 & 0.517 & 1 \tabularnewline
F:I-B:I & 0.762 & 0.333 & 1.192 & 0 \tabularnewline
D:I-C:I & 0.08 & -0.349 & 0.51 & 1 \tabularnewline
E:I-C:I & 0.258 & -0.171 & 0.687 & 0.585 \tabularnewline
F:I-C:I & 0.933 & 0.503 & 1.362 & 0 \tabularnewline
E:I-D:I & 0.178 & -0.252 & 0.607 & 0.929 \tabularnewline
F:I-D:I & 0.852 & 0.423 & 1.282 & 0 \tabularnewline
F:I-E:I & 0.675 & 0.245 & 1.104 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]B-A[/C][C]-0.49[/C][C]-0.75[/C][C]-0.23[/C][C]0[/C][/ROW]
[ROW][C]C-A[/C][C]-0.658[/C][C]-0.918[/C][C]-0.398[/C][C]0[/C][/ROW]
[ROW][C]D-A[/C][C]-0.51[/C][C]-0.77[/C][C]-0.25[/C][C]0[/C][/ROW]
[ROW][C]E-A[/C][C]-0.4[/C][C]-0.66[/C][C]-0.14[/C][C]0.001[/C][/ROW]
[ROW][C]F-A[/C][C]0.339[/C][C]0.079[/C][C]0.6[/C][C]0.006[/C][/ROW]
[ROW][C]C-B[/C][C]-0.168[/C][C]-0.428[/C][C]0.092[/C][C]0.374[/C][/ROW]
[ROW][C]D-B[/C][C]-0.02[/C][C]-0.28[/C][C]0.24[/C][C]1[/C][/ROW]
[ROW][C]E-B[/C][C]0.09[/C][C]-0.17[/C][C]0.35[/C][C]0.889[/C][/ROW]
[ROW][C]F-B[/C][C]0.829[/C][C]0.569[/C][C]1.09[/C][C]0[/C][/ROW]
[ROW][C]D-C[/C][C]0.148[/C][C]-0.112[/C][C]0.408[/C][C]0.508[/C][/ROW]
[ROW][C]E-C[/C][C]0.258[/C][C]-0.002[/C][C]0.518[/C][C]0.053[/C][/ROW]
[ROW][C]F-C[/C][C]0.997[/C][C]0.737[/C][C]1.258[/C][C]0[/C][/ROW]
[ROW][C]E-D[/C][C]0.11[/C][C]-0.151[/C][C]0.37[/C][C]0.781[/C][/ROW]
[ROW][C]F-D[/C][C]0.849[/C][C]0.589[/C][C]1.11[/C][C]0[/C][/ROW]
[ROW][C]F-E[/C][C]0.74[/C][C]0.479[/C][C]1[/C][C]0[/C][/ROW]
[ROW][C]I-H[/C][C]0.118[/C][C]0.018[/C][C]0.218[/C][C]0.023[/C][/ROW]
[ROW][C]B:H-A:H[/C][C]-0.582[/C][C]-1.011[/C][C]-0.152[/C][C]0.003[/C][/ROW]
[ROW][C]C:H-A:H[/C][C]-0.747[/C][C]-1.177[/C][C]-0.318[/C][C]0[/C][/ROW]
[ROW][C]D:H-A:H[/C][C]-0.531[/C][C]-0.961[/C][C]-0.102[/C][C]0.007[/C][/ROW]
[ROW][C]E:H-A:H[/C][C]-0.49[/C][C]-0.919[/C][C]-0.06[/C][C]0.016[/C][/ROW]
[ROW][C]F:H-A:H[/C][C]0.315[/C][C]-0.114[/C][C]0.744[/C][C]0.309[/C][/ROW]
[ROW][C]A:I-A:H[/C][C]0.012[/C][C]-0.417[/C][C]0.442[/C][C]1[/C][/ROW]
[ROW][C]B:I-A:H[/C][C]-0.386[/C][C]-0.815[/C][C]0.043[/C][C]0.106[/C][/ROW]
[ROW][C]C:I-A:H[/C][C]-0.556[/C][C]-0.986[/C][C]-0.127[/C][C]0.004[/C][/ROW]
[ROW][C]D:I-A:H[/C][C]-0.476[/C][C]-0.905[/C][C]-0.047[/C][C]0.021[/C][/ROW]
[ROW][C]E:I-A:H[/C][C]-0.298[/C][C]-0.728[/C][C]0.131[/C][C]0.382[/C][/ROW]
[ROW][C]F:I-A:H[/C][C]0.376[/C][C]-0.053[/C][C]0.806[/C][C]0.125[/C][/ROW]
[ROW][C]C:H-B:H[/C][C]-0.166[/C][C]-0.595[/C][C]0.264[/C][C]0.954[/C][/ROW]
[ROW][C]D:H-B:H[/C][C]0.05[/C][C]-0.379[/C][C]0.48[/C][C]1[/C][/ROW]
[ROW][C]E:H-B:H[/C][C]0.092[/C][C]-0.337[/C][C]0.521[/C][C]1[/C][/ROW]
[ROW][C]F:H-B:H[/C][C]0.897[/C][C]0.467[/C][C]1.326[/C][C]0[/C][/ROW]
[ROW][C]A:I-B:H[/C][C]0.594[/C][C]0.165[/C][C]1.023[/C][C]0.002[/C][/ROW]
[ROW][C]B:I-B:H[/C][C]0.196[/C][C]-0.234[/C][C]0.625[/C][C]0.876[/C][/ROW]
[ROW][C]C:I-B:H[/C][C]0.025[/C][C]-0.404[/C][C]0.455[/C][C]1[/C][/ROW]
[ROW][C]D:I-B:H[/C][C]0.106[/C][C]-0.324[/C][C]0.535[/C][C]0.999[/C][/ROW]
[ROW][C]E:I-B:H[/C][C]0.283[/C][C]-0.146[/C][C]0.713[/C][C]0.454[/C][/ROW]
[ROW][C]F:I-B:H[/C][C]0.958[/C][C]0.529[/C][C]1.387[/C][C]0[/C][/ROW]
[ROW][C]D:H-C:H[/C][C]0.216[/C][C]-0.213[/C][C]0.645[/C][C]0.796[/C][/ROW]
[ROW][C]E:H-C:H[/C][C]0.258[/C][C]-0.172[/C][C]0.687[/C][C]0.587[/C][/ROW]
[ROW][C]F:H-C:H[/C][C]1.062[/C][C]0.633[/C][C]1.492[/C][C]0[/C][/ROW]
[ROW][C]A:I-C:H[/C][C]0.76[/C][C]0.33[/C][C]1.189[/C][C]0[/C][/ROW]
[ROW][C]B:I-C:H[/C][C]0.361[/C][C]-0.068[/C][C]0.791[/C][C]0.158[/C][/ROW]
[ROW][C]C:I-C:H[/C][C]0.191[/C][C]-0.238[/C][C]0.62[/C][C]0.891[/C][/ROW]
[ROW][C]D:I-C:H[/C][C]0.271[/C][C]-0.158[/C][C]0.701[/C][C]0.515[/C][/ROW]
[ROW][C]E:I-C:H[/C][C]0.449[/C][C]0.02[/C][C]0.878[/C][C]0.035[/C][/ROW]
[ROW][C]F:I-C:H[/C][C]1.124[/C][C]0.694[/C][C]1.553[/C][C]0[/C][/ROW]
[ROW][C]E:H-D:H[/C][C]0.042[/C][C]-0.388[/C][C]0.471[/C][C]1[/C][/ROW]
[ROW][C]F:H-D:H[/C][C]0.846[/C][C]0.417[/C][C]1.276[/C][C]0[/C][/ROW]
[ROW][C]A:I-D:H[/C][C]0.544[/C][C]0.114[/C][C]0.973[/C][C]0.006[/C][/ROW]
[ROW][C]B:I-D:H[/C][C]0.145[/C][C]-0.284[/C][C]0.575[/C][C]0.982[/C][/ROW]
[ROW][C]C:I-D:H[/C][C]-0.025[/C][C]-0.454[/C][C]0.404[/C][C]1[/C][/ROW]
[ROW][C]D:I-D:H[/C][C]0.055[/C][C]-0.374[/C][C]0.485[/C][C]1[/C][/ROW]
[ROW][C]E:I-D:H[/C][C]0.233[/C][C]-0.196[/C][C]0.662[/C][C]0.715[/C][/ROW]
[ROW][C]F:I-D:H[/C][C]0.908[/C][C]0.478[/C][C]1.337[/C][C]0[/C][/ROW]
[ROW][C]F:H-E:H[/C][C]0.805[/C][C]0.375[/C][C]1.234[/C][C]0[/C][/ROW]
[ROW][C]A:I-E:H[/C][C]0.502[/C][C]0.073[/C][C]0.931[/C][C]0.013[/C][/ROW]
[ROW][C]B:I-E:H[/C][C]0.104[/C][C]-0.326[/C][C]0.533[/C][C]0.999[/C][/ROW]
[ROW][C]C:I-E:H[/C][C]-0.067[/C][C]-0.496[/C][C]0.363[/C][C]1[/C][/ROW]
[ROW][C]D:I-E:H[/C][C]0.014[/C][C]-0.416[/C][C]0.443[/C][C]1[/C][/ROW]
[ROW][C]E:I-E:H[/C][C]0.191[/C][C]-0.238[/C][C]0.621[/C][C]0.89[/C][/ROW]
[ROW][C]F:I-E:H[/C][C]0.866[/C][C]0.437[/C][C]1.295[/C][C]0[/C][/ROW]
[ROW][C]A:I-F:H[/C][C]-0.303[/C][C]-0.732[/C][C]0.127[/C][C]0.362[/C][/ROW]
[ROW][C]B:I-F:H[/C][C]-0.701[/C][C]-1.13[/C][C]-0.272[/C][C]0[/C][/ROW]
[ROW][C]C:I-F:H[/C][C]-0.871[/C][C]-1.301[/C][C]-0.442[/C][C]0[/C][/ROW]
[ROW][C]D:I-F:H[/C][C]-0.791[/C][C]-1.22[/C][C]-0.362[/C][C]0[/C][/ROW]
[ROW][C]E:I-F:H[/C][C]-0.613[/C][C]-1.043[/C][C]-0.184[/C][C]0.001[/C][/ROW]
[ROW][C]F:I-F:H[/C][C]0.061[/C][C]-0.368[/C][C]0.491[/C][C]1[/C][/ROW]
[ROW][C]B:I-A:I[/C][C]-0.398[/C][C]-0.828[/C][C]0.031[/C][C]0.086[/C][/ROW]
[ROW][C]C:I-A:I[/C][C]-0.569[/C][C]-0.998[/C][C]-0.139[/C][C]0.003[/C][/ROW]
[ROW][C]D:I-A:I[/C][C]-0.488[/C][C]-0.918[/C][C]-0.059[/C][C]0.016[/C][/ROW]
[ROW][C]E:I-A:I[/C][C]-0.311[/C][C]-0.74[/C][C]0.119[/C][C]0.327[/C][/ROW]
[ROW][C]F:I-A:I[/C][C]0.364[/C][C]-0.065[/C][C]0.793[/C][C]0.152[/C][/ROW]
[ROW][C]C:I-B:I[/C][C]-0.17[/C][C]-0.6[/C][C]0.259[/C][C]0.945[/C][/ROW]
[ROW][C]D:I-B:I[/C][C]-0.09[/C][C]-0.519[/C][C]0.339[/C][C]1[/C][/ROW]
[ROW][C]E:I-B:I[/C][C]0.088[/C][C]-0.342[/C][C]0.517[/C][C]1[/C][/ROW]
[ROW][C]F:I-B:I[/C][C]0.762[/C][C]0.333[/C][C]1.192[/C][C]0[/C][/ROW]
[ROW][C]D:I-C:I[/C][C]0.08[/C][C]-0.349[/C][C]0.51[/C][C]1[/C][/ROW]
[ROW][C]E:I-C:I[/C][C]0.258[/C][C]-0.171[/C][C]0.687[/C][C]0.585[/C][/ROW]
[ROW][C]F:I-C:I[/C][C]0.933[/C][C]0.503[/C][C]1.362[/C][C]0[/C][/ROW]
[ROW][C]E:I-D:I[/C][C]0.178[/C][C]-0.252[/C][C]0.607[/C][C]0.929[/C][/ROW]
[ROW][C]F:I-D:I[/C][C]0.852[/C][C]0.423[/C][C]1.282[/C][C]0[/C][/ROW]
[ROW][C]F:I-E:I[/C][C]0.675[/C][C]0.245[/C][C]1.104[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

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

As an alternative you can also use a QR Code:

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

Tukey Honest Significant Difference Comparisons
	diff	lwr	upr	p adj
B-A	-0.49	-0.75	-0.23	0
C-A	-0.658	-0.918	-0.398	0
D-A	-0.51	-0.77	-0.25	0
E-A	-0.4	-0.66	-0.14	0.001
F-A	0.339	0.079	0.6	0.006
C-B	-0.168	-0.428	0.092	0.374
D-B	-0.02	-0.28	0.24	1
E-B	0.09	-0.17	0.35	0.889
F-B	0.829	0.569	1.09	0
D-C	0.148	-0.112	0.408	0.508
E-C	0.258	-0.002	0.518	0.053
F-C	0.997	0.737	1.258	0
E-D	0.11	-0.151	0.37	0.781
F-D	0.849	0.589	1.11	0
F-E	0.74	0.479	1	0
I-H	0.118	0.018	0.218	0.023
B:H-A:H	-0.582	-1.011	-0.152	0.003
C:H-A:H	-0.747	-1.177	-0.318	0
D:H-A:H	-0.531	-0.961	-0.102	0.007
E:H-A:H	-0.49	-0.919	-0.06	0.016
F:H-A:H	0.315	-0.114	0.744	0.309
A:I-A:H	0.012	-0.417	0.442	1
B:I-A:H	-0.386	-0.815	0.043	0.106
C:I-A:H	-0.556	-0.986	-0.127	0.004
D:I-A:H	-0.476	-0.905	-0.047	0.021
E:I-A:H	-0.298	-0.728	0.131	0.382
F:I-A:H	0.376	-0.053	0.806	0.125
C:H-B:H	-0.166	-0.595	0.264	0.954
D:H-B:H	0.05	-0.379	0.48	1
E:H-B:H	0.092	-0.337	0.521	1
F:H-B:H	0.897	0.467	1.326	0
A:I-B:H	0.594	0.165	1.023	0.002
B:I-B:H	0.196	-0.234	0.625	0.876
C:I-B:H	0.025	-0.404	0.455	1
D:I-B:H	0.106	-0.324	0.535	0.999
E:I-B:H	0.283	-0.146	0.713	0.454
F:I-B:H	0.958	0.529	1.387	0
D:H-C:H	0.216	-0.213	0.645	0.796
E:H-C:H	0.258	-0.172	0.687	0.587
F:H-C:H	1.062	0.633	1.492	0
A:I-C:H	0.76	0.33	1.189	0
B:I-C:H	0.361	-0.068	0.791	0.158
C:I-C:H	0.191	-0.238	0.62	0.891
D:I-C:H	0.271	-0.158	0.701	0.515
E:I-C:H	0.449	0.02	0.878	0.035
F:I-C:H	1.124	0.694	1.553	0
E:H-D:H	0.042	-0.388	0.471	1
F:H-D:H	0.846	0.417	1.276	0
A:I-D:H	0.544	0.114	0.973	0.006
B:I-D:H	0.145	-0.284	0.575	0.982
C:I-D:H	-0.025	-0.454	0.404	1
D:I-D:H	0.055	-0.374	0.485	1
E:I-D:H	0.233	-0.196	0.662	0.715
F:I-D:H	0.908	0.478	1.337	0
F:H-E:H	0.805	0.375	1.234	0
A:I-E:H	0.502	0.073	0.931	0.013
B:I-E:H	0.104	-0.326	0.533	0.999
C:I-E:H	-0.067	-0.496	0.363	1
D:I-E:H	0.014	-0.416	0.443	1
E:I-E:H	0.191	-0.238	0.621	0.89
F:I-E:H	0.866	0.437	1.295	0
A:I-F:H	-0.303	-0.732	0.127	0.362
B:I-F:H	-0.701	-1.13	-0.272	0
C:I-F:H	-0.871	-1.301	-0.442	0
D:I-F:H	-0.791	-1.22	-0.362	0
E:I-F:H	-0.613	-1.043	-0.184	0.001
F:I-F:H	0.061	-0.368	0.491	1
B:I-A:I	-0.398	-0.828	0.031	0.086
C:I-A:I	-0.569	-0.998	-0.139	0.003
D:I-A:I	-0.488	-0.918	-0.059	0.016
E:I-A:I	-0.311	-0.74	0.119	0.327
F:I-A:I	0.364	-0.065	0.793	0.152
C:I-B:I	-0.17	-0.6	0.259	0.945
D:I-B:I	-0.09	-0.519	0.339	1
E:I-B:I	0.088	-0.342	0.517	1
F:I-B:I	0.762	0.333	1.192	0
D:I-C:I	0.08	-0.349	0.51	1
E:I-C:I	0.258	-0.171	0.687	0.585
F:I-C:I	0.933	0.503	1.362	0
E:I-D:I	0.178	-0.252	0.607	0.929
F:I-D:I	0.852	0.423	1.282	0
F:I-E:I	0.675	0.245	1.104	0

Levenes Test for Homogeneity of Variance
	Df	F value	Pr(>F)
Group	11	0.461	0.91
	24

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 11 & 0.461 & 0.91 \tabularnewline
  & 24 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]11[/C][C]0.461[/C][C]0.91[/C][/ROW]
[ROW][C] [/C][C]24[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=4

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

As an alternative you can also use a QR Code:

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

Levenes Test for Homogeneity of Variance
	Df	F value	Pr(>F)
Group	11	0.461	0.91
	24

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Figure 4

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 1 ; par2 = 2 ; par3 = 3 ; par4 = TRUE ;

Parameters (R input):

par1 = 1 ; par2 = 2 ; par3 = 3 ; par4 = TRUE ;

R code (references can be found in the software module):

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

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code