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R Software Module

rwasp_Two Factor ANOVA.wasp

Title produced by software

Two-Way ANOVA

Date of computation

Tue, 18 Dec 2012 11:23:23 -0500

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/2012/Dec/18/t135584783069omg9krn2xbs2p.htm/, Retrieved Tue, 10 Feb 2026 11:50:59 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=201484, Retrieved Tue, 10 Feb 2026 11:50:59 +0000

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IsPrivate?

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Estimated Impact

353

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [Two-Way ANOVA] [2 way anova paper] [2012-12-18 16:23:23] [239167cccea8953a8e1721fd6db07280] [Current]

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4	'Yes'	'Treatment'	NA	'NoStats'	'No'	'No'	'Good'
4	'No'	'NoTreatment'	NA	'NoStats'	'No'	'No'	'Bad'
4	'No'	'NoTreatment'	NA	'NoStats'	'No'	'No'	'Bad'
4	'No'	'NoTreatment'	NA	'NoStats'	'No'	'No'	'Bad'
4	'No'	'NoTreatment'	NA	'NoStats'	'No'	'No'	'Bad'
4	'Yes'	'NoTreatment'	NA	'NoStats'	'No'	'Yes'	'Good'
4	'No'	'NoTreatment'	NA	'NoStats'	'No'	'No'	'Bad'
4	'No'	'Treatment'	NA	'NoStats'	'No'	'No'	'Bad'
4	'No'	'NoTreatment'	NA	'NoStats'	'No'	'No'	'Good'
4	'Yes'	'NoTreatment'	NA	'NoStats'	'No'	'No'	'Bad'
4	'Yes'	'Treatment'	NA	'NoStats'	'No'	'No'	'Bad'
4	'No'	'NoTreatment'	NA	'NoStats'	'No'	'No'	'Bad'
4	'No'	'NoTreatment'	NA	'UsedStats'	'No'	'Yes'	'Bad'
4	'Yes'	'Treatment'	NA	'NoStats'	'No'	'No'	'Bad'
4	'No'	'NoTreatment'	NA	'UsedStats'	'No'	'Yes'	'Good'
4	'No'	'Treatment'	NA	'UsedStats'	'No'	'Yes'	'Good'
4	'Yes'	'Treatment'	NA	'UsedStats'	'Yes'	'Yes'	'Bad'
4	'Yes'	'Treatment'	NA	'NoStats'	'No'	'No'	'Bad'
4	'No'	'NoTreatment'	NA	'NoStats'	'No'	'No'	'Good'
4	'No'	'Treatment'	NA	'UsedStats'	'Yes'	'Yes'	'Good'
4	'Yes'	'NoTreatment'	NA	'NoStats'	'No'	'Yes'	'Bad'
4	'Yes'	'NoTreatment'	NA	'UsedStats'	'No'	'Yes'	'Good'
4	'No'	'NoTreatment'	NA	'NoStats'	'No'	'Yes'	'Good'
4	'Yes'	'NoTreatment'	NA	'NoStats'	'No'	'Yes'	'Good'
4	'No'	'Treatment'	NA	'UsedStats'	'No'	'No'	'Good'
4	'No'	'NoTreatment'	NA	'UsedStats'	'No'	'Yes'	'Bad'
4	'Yes'	'NoTreatment'	NA	'NoStats'	'No'	'No'	'Good'
4	'No'	'NoTreatment'	NA	'UsedStats'	'No'	'No'	'Bad'
4	'No'	'NoTreatment'	NA	'NoStats'	'No'	'No'	'Good'
4	'No'	'NoTreatment'	NA	'NoStats'	'No'	'Yes'	'Bad'
4	'No'	'NoTreatment'	NA	'NoStats'	'No'	'No'	'Bad'
4	'Yes'	'NoTreatment'	NA	'NoStats'	'No'	'No'	'Bad'
4	'Yes'	'NoTreatment'	NA	'NoStats'	'No'	'Yes'	'Bad'
4	'No'	'Treatment'	NA	'NoStats'	'No'	'No'	'Good'
4	'No'	'NoTreatment'	NA	'NoStats'	'No'	'No'	'Bad'
4	'No'	'NoTreatment'	NA	'NoStats'	'No'	'No'	'Bad'
4	'Yes'	'Treatment'	NA	'UsedStats'	'No'	'Yes'	'Bad'
4	'No'	'NoTreatment'	NA	'UsedStats'	'No'	'No'	'Good'
4	'No'	'NoTreatment'	NA	'NoStats'	'No'	'Yes'	'Good'
4	'No'	'Treatment'	NA	'NoStats'	'No'	'Yes'	'Bad'
4	'No'	'NoTreatment'	NA	'UsedStats'	'Yes'	'Yes'	'Good'
4	'No'	'NoTreatment'	NA	'UsedStats'	'No'	'No'	'Good'
4	'Yes'	'NoTreatment'	NA	'NoStats'	'No'	'Yes'	'Good'
4	'Yes'	'Treatment'	NA	'NoStats'	'No'	'No'	'Bad'
4	'No'	'NoTreatment'	NA	'NoStats'	'No'	'Yes'	'Bad'
4	'No'	'NoTreatment'	NA	'NoStats'	'No'	'Yes'	'Good'
4	'No'	'NoTreatment'	NA	'NoStats'	'No'	'No'	'Bad'
4	'No'	'NoTreatment'	NA	'NoStats'	'No'	'No'	'Good'
4	'No'	'NoTreatment'	NA	'NoStats'	'No'	'Yes'	'Good'
4	'No'	'NoTreatment'	NA	'NoStats'	'No'	'No'	'Bad'
4	'No'	'Treatment'	NA	'UsedStats'	'No'	'No'	'Bad'
4	'Yes'	'Treatment'	NA	'UsedStats'	'Yes'	'Yes'	'Bad'
4	'No'	'NoTreatment'	NA	'NoStats'	'No'	'No'	'Good'
4	'No'	'NoTreatment'	NA	'UsedStats'	'Yes'	'No'	'Bad'
4	'No'	'NoTreatment'	NA	'NoStats'	'No'	'No'	'Bad'
4	'No'	'Treatment'	NA	'UsedStats'	'No'	'No'	'Good'
4	'No'	'NoTreatment'	NA	'UsedStats'	'No'	'Yes'	'Good'
4	'No'	'NoTreatment'	NA	'NoStats'	'No'	'No'	'Good'
4	'No'	'NoTreatment'	NA	'NoStats'	'No'	'No'	'Good'
4	'Yes'	'Treatment'	NA	'UsedStats'	'Yes'	'Yes'	'Good'
4	'Yes'	'Treatment'	NA	'NoStats'	'No'	'No'	'Good'
4	'No'	'NoTreatment'	NA	'UsedStats'	'No'	'Yes'	'Bad'
4	'No'	'NoTreatment'	NA	'NoStats'	'No'	'No'	'Bad'
4	'Yes'	'Treatment'	NA	'NoStats'	'No'	'No'	'Good'
4	'No'	'NoTreatment'	NA	'NoStats'	'No'	'No'	'Bad'
4	'No'	'NoTreatment'	NA	'NoStats'	'No'	'No'	'Bad'
4	'No'	'Treatment'	NA	'UsedStats'	'Yes'	'Yes'	'Bad'
4	'Yes'	'NoTreatment'	NA	'NoStats'	'No'	'No'	'Bad'
4	'No'	'NoTreatment'	NA	'NoStats'	'No'	'No'	'Good'
4	'No'	'NoTreatment'	NA	'UsedStats'	'No'	'No'	'Bad'
4	'No'	'NoTreatment'	NA	'NoStats'	'No'	'No'	'Bad'
4	'No'	'NoTreatment'	NA	'NoStats'	'No'	'No'	'Good'
4	'No'	'NoTreatment'	NA	'UsedStats'	'No'	'No'	'Good'
4	'Yes'	'NoTreatment'	NA	'UsedStats'	'No'	'No'	'Bad'
4	'No'	'NoTreatment'	NA	'NoStats'	'No'	'No'	'Good'
4	'No'	'Treatment'	NA	'NoStats'	'No'	'Yes'	'Good'
4	'No'	'NoTreatment'	NA	'NoStats'	'No'	'No'	'Good'
4	'No'	'NoTreatment'	NA	'UsedStats'	'No'	'Yes'	'Good'
4	'No'	'Treatment'	NA	'UsedStats'	'Yes'	'No'	'Good'
4	'No'	'Treatment'	NA	'NoStats'	'No'	'Yes'	'Bad'
4	'No'	'NoTreatment'	NA	'NoStats'	'No'	'No'	'Bad'
4	'Yes'	'NoTreatment'	NA	'UsedStats'	'No'	'No'	'Good'
4	'No'	'NoTreatment'	NA	'NoStats'	'No'	'No'	'Bad'
4	'No'	'NoTreatment'	NA	'UsedStats'	'Yes'	'No'	'Bad'
4	'No'	'NoTreatment'	NA	'NoStats'	'No'	'Yes'	'Good'
4	'Yes'	'NoTreatment'	NA	'NoStats'	'No'	'No'	'Bad'
2	'Yes'	NA	'NoTreatment'	'NoStats'	'No'	'No'	'Good'
2	'Yes'	NA	'Treatment'	'UsedStats'	'No'	'No'	'Good'
2	'No'	NA	'NoTreatment'	'NoStats'	'No'	'No'	'Bad'
2	'No'	NA	'NoTreatment'	'NoStats'	'No'	'No'	'Good'
2	'No'	NA	'NoTreatment'	'NoStats'	'No'	'Yes'	'Bad'
2	'Yes'	NA	'Treatment'	'NoStats'	'No'	'No'	'Bad'
2	'Yes'	NA	'NoTreatment'	'NoStats'	'No'	'Yes'	'Bad'
2	'No'	NA	'NoTreatment'	'NoStats'	'No'	'No'	'Bad'
2	'No'	NA	'Treatment'	'NoStats'	'No'	'No'	'Bad'
2	'No'	NA	'NoTreatment'	'NoStats'	'No'	'No'	'Good'
2	'Yes'	NA	'Treatment'	'NoStats'	'No'	'No'	'Bad'
2	'No'	NA	'NoTreatment'	'NoStats'	'No'	'No'	'Bad'
2	'Yes'	NA	'NoTreatment'	'NoStats'	'No'	'No'	'Bad'
2	'No'	NA	'NoTreatment'	'NoStats'	'No'	'No'	'Good'
2	'Yes'	NA	'NoTreatment'	'NoStats'	'No'	'No'	'Good'
2	'No'	NA	'NoTreatment'	'NoStats'	'No'	'No'	'Bad'
2	'No'	NA	'NoTreatment'	'NoStats'	'No'	'No'	'Bad'
2	'No'	NA	'NoTreatment'	'NoStats'	'No'	'No'	'Bad'
2	'No'	NA	'Treatment'	'UsedStats'	'No'	'No'	'Bad'
2	'No'	NA	'NoTreatment'	'NoStats'	'No'	'No'	'Bad'
2	'No'	NA	'NoTreatment'	'NoStats'	'No'	'No'	'Bad'
2	'Yes'	NA	'Treatment'	'UsedStats'	'No'	'No'	'Bad'
2	'No'	NA	'NoTreatment'	'NoStats'	'No'	'No'	'Bad'
2	'Yes'	NA	'NoTreatment'	'NoStats'	'No'	'No'	'Bad'
2	'Yes'	NA	'Treatment'	'UsedStats'	'No'	'Yes'	'Bad'
2	'No'	NA	'Treatment'	'NoStats'	'No'	'No'	'Bad'
2	'No'	NA	'NoTreatment'	'UsedStats'	'No'	'No'	'Bad'
2	'Yes'	NA	'Treatment'	'UsedStats'	'No'	'No'	'Bad'
2	'Yes'	NA	'NoTreatment'	'NoStats'	'No'	'No'	'Bad'
2	'No'	NA	'NoTreatment'	'NoStats'	'No'	'No'	'Bad'
2	'Yes'	NA	'NoTreatment'	'NoStats'	'No'	'No'	'Good'
2	'Yes'	NA	'NoTreatment'	'NoStats'	'No'	'No'	'Bad'
2	'No'	NA	'NoTreatment'	'NoStats'	'No'	'No'	'Bad'
2	'No'	NA	'NoTreatment'	'NoStats'	'No'	'No'	'Good'
2	'Yes'	NA	'NoTreatment'	'NoStats'	'No'	'No'	'Bad'
2	'No'	NA	'NoTreatment'	'NoStats'	'No'	'No'	'Bad'
2	'Yes'	NA	'Treatment'	'UsedStats'	'No'	'No'	'Bad'
2	'No'	NA	'NoTreatment'	'UsedStats'	'No'	'Yes'	'Good'
2	'No'	NA	'NoTreatment'	'NoStats'	'No'	'No'	'Good'
2	'No'	NA	'Treatment'	'NoStats'	'No'	'No'	'Bad'
2	'No'	NA	'NoTreatment'	'NoStats'	'No'	'Yes'	'Bad'
2	'No'	NA	'NoTreatment'	'NoStats'	'No'	'No'	'Good'
2	'No'	NA	'NoTreatment'	'NoStats'	'No'	'No'	'Bad'
2	'No'	NA	'NoTreatment'	'NoStats'	'No'	'No'	'Good'
2	'Yes'	NA	'NoTreatment'	'NoStats'	'No'	'No'	'Bad'
2	'Yes'	NA	'NoTreatment'	'NoStats'	'No'	'No'	'Good'
2	'Yes'	NA	'NoTreatment'	'UsedStats'	'No'	'No'	'Bad'
2	'No'	NA	'NoTreatment'	'NoStats'	'No'	'No'	'Bad'
2	'No'	NA	'NoTreatment'	'NoStats'	'No'	'No'	'Bad'
2	'No'	NA	'NoTreatment'	'NoStats'	'No'	'No'	'Bad'
2	'Yes'	NA	'NoTreatment'	'UsedStats'	'No'	'Yes'	'Good'
2	'Yes'	NA	'Treatment'	'UsedStats'	'No'	'Yes'	'Good'
2	'No'	NA	'Treatment'	'NoStats'	'No'	'No'	'Bad'
2	'No'	NA	'NoTreatment'	'NoStats'	'No'	'No'	'Bad'
2	'No'	NA	'NoTreatment'	'UsedStats'	'Yes'	'No'	'Good'
2	'No'	NA	'Treatment'	'UsedStats'	'No'	'No'	'Good'
2	'Yes'	NA	'NoTreatment'	'NoStats'	'No'	'No'	'Bad'
2	'No'	NA	'NoTreatment'	'NoStats'	'No'	'Yes'	'Good'
2	'No'	NA	'NoTreatment'	'NoStats'	'No'	'Yes'	'Bad'
2	'No'	NA	'Treatment'	'NoStats'	'No'	'No'	'Good'
2	'No'	NA	'Treatment'	'UsedStats'	'No'	'No'	'Bad'
2	'No'	NA	'Treatment'	'NoStats'	'No'	'No'	'Bad'
2	'Yes'	NA	'NoTreatment'	'NoStats'	'No'	'No'	'Bad'
2	'No'	NA	'NoTreatment'	'NoStats'	'No'	'Yes'	'Good'
2	'No'	NA	'NoTreatment'	'NoStats'	'No'	'No'	'Good'
2	'Yes'	NA	'NoTreatment'	'UsedStats'	'Yes'	'No'	'Bad'
2	'Yes'	NA	'NoTreatment'	'UsedStats'	'Yes'	'Yes'	'Bad'
2	'Yes'	NA	'NoTreatment'	'UsedStats'	'No'	'No'	'Bad'

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	4 seconds
R Server	'Sir Maurice George Kendall' @ kendall.wessa.net

\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 Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=201484&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 Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=201484&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=201484&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	4 seconds
R Server	'Sir Maurice George Kendall' @ kendall.wessa.net

ANOVA Model
Response ~ Treatment_A * Treatment_B
means	2	0	2	2	0	0

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & 2 & 0 & 2 & 2 & 0 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=201484&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]Response ~ Treatment_A * Treatment_B[/C][/ROW]
[ROW][C]means[/C][C]2[/C][C]0[/C][C]2[/C][C]2[/C][C]0[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=201484&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=201484&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	2	0	2	2	0	0

ANOVA Statistics
	Df	Sum Sq	Mean Sq	F value	Pr(>F)
	1
Treatment_A	1	1.822	1.822	2.55275087496254e+31	0
Treatment_B	1	150.074	75.037	1.05117166796495e+33	0
Treatment_A:Treatment_B	1	0	0	0.644	0.527
Residuals	148	0	0

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 1 &  &  &  &  \tabularnewline
Treatment_A & 1 & 1.822 & 1.822 & 2.55275087496254e+31 & 0 \tabularnewline
Treatment_B & 1 & 150.074 & 75.037 & 1.05117166796495e+33 & 0 \tabularnewline
Treatment_A:Treatment_B & 1 & 0 & 0 & 0.644 & 0.527 \tabularnewline
Residuals & 148 & 0 & 0 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=201484&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]1.822[/C][C]1.822[/C][C]2.55275087496254e+31[/C][C]0[/C][/ROW]
[ROW][C]Treatment_B[/C][C]1[/C][C]150.074[/C][C]75.037[/C][C]1.05117166796495e+33[/C][C]0[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]1[/C][C]0[/C][C]0[/C][C]0.644[/C][C]0.527[/C][/ROW]
[ROW][C]Residuals[/C][C]148[/C][C]0[/C][C]0[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=201484&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=201484&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)
	1
Treatment_A	1	1.822	1.822	2.55275087496254e+31	0
Treatment_B	1	150.074	75.037	1.05117166796495e+33	0
Treatment_A:Treatment_B	1	0	0	0.644	0.527
Residuals	148	0	0

Tukey Honest Significant Difference Comparisons
	diff	lwr	upr	p adj
Yes-No	-0.232	-0.232	-0.232	0
NoTreatment-NA	1.959	1.959	1.959	0
Treatment-NA	2.022	2.022	2.022	0
Treatment-NoTreatment	0.063	0.063	0.063	0
Yes:NA-No:NA	0	0	0	0
No:NoTreatment-No:NA	2	2	2	0
Yes:NoTreatment-No:NA	2	2	2	0
No:Treatment-No:NA	2	2	2	0
Yes:Treatment-No:NA	2	2	2	0
No:NoTreatment-Yes:NA	2	2	2	0
Yes:NoTreatment-Yes:NA	2	2	2	0
No:Treatment-Yes:NA	2	2	2	0
Yes:Treatment-Yes:NA	2	2	2	0
Yes:NoTreatment-No:NoTreatment	0	0	0	1
No:Treatment-No:NoTreatment	0	0	0	1
Yes:Treatment-No:NoTreatment	0	0	0	1
No:Treatment-Yes:NoTreatment	0	0	0	1
Yes:Treatment-Yes:NoTreatment	0	0	0	1
Yes:Treatment-No:Treatment	0	0	0	1

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
Yes-No & -0.232 & -0.232 & -0.232 & 0 \tabularnewline
NoTreatment-NA & 1.959 & 1.959 & 1.959 & 0 \tabularnewline
Treatment-NA & 2.022 & 2.022 & 2.022 & 0 \tabularnewline
Treatment-NoTreatment & 0.063 & 0.063 & 0.063 & 0 \tabularnewline
Yes:NA-No:NA & 0 & 0 & 0 & 0 \tabularnewline
No:NoTreatment-No:NA & 2 & 2 & 2 & 0 \tabularnewline
Yes:NoTreatment-No:NA & 2 & 2 & 2 & 0 \tabularnewline
No:Treatment-No:NA & 2 & 2 & 2 & 0 \tabularnewline
Yes:Treatment-No:NA & 2 & 2 & 2 & 0 \tabularnewline
No:NoTreatment-Yes:NA & 2 & 2 & 2 & 0 \tabularnewline
Yes:NoTreatment-Yes:NA & 2 & 2 & 2 & 0 \tabularnewline
No:Treatment-Yes:NA & 2 & 2 & 2 & 0 \tabularnewline
Yes:Treatment-Yes:NA & 2 & 2 & 2 & 0 \tabularnewline
Yes:NoTreatment-No:NoTreatment & 0 & 0 & 0 & 1 \tabularnewline
No:Treatment-No:NoTreatment & 0 & 0 & 0 & 1 \tabularnewline
Yes:Treatment-No:NoTreatment & 0 & 0 & 0 & 1 \tabularnewline
No:Treatment-Yes:NoTreatment & 0 & 0 & 0 & 1 \tabularnewline
Yes:Treatment-Yes:NoTreatment & 0 & 0 & 0 & 1 \tabularnewline
Yes:Treatment-No:Treatment & 0 & 0 & 0 & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=201484&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]Yes-No[/C][C]-0.232[/C][C]-0.232[/C][C]-0.232[/C][C]0[/C][/ROW]
[ROW][C]NoTreatment-NA[/C][C]1.959[/C][C]1.959[/C][C]1.959[/C][C]0[/C][/ROW]
[ROW][C]Treatment-NA[/C][C]2.022[/C][C]2.022[/C][C]2.022[/C][C]0[/C][/ROW]
[ROW][C]Treatment-NoTreatment[/C][C]0.063[/C][C]0.063[/C][C]0.063[/C][C]0[/C][/ROW]
[ROW][C]Yes:NA-No:NA[/C][C]0[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]No:NoTreatment-No:NA[/C][C]2[/C][C]2[/C][C]2[/C][C]0[/C][/ROW]
[ROW][C]Yes:NoTreatment-No:NA[/C][C]2[/C][C]2[/C][C]2[/C][C]0[/C][/ROW]
[ROW][C]No:Treatment-No:NA[/C][C]2[/C][C]2[/C][C]2[/C][C]0[/C][/ROW]
[ROW][C]Yes:Treatment-No:NA[/C][C]2[/C][C]2[/C][C]2[/C][C]0[/C][/ROW]
[ROW][C]No:NoTreatment-Yes:NA[/C][C]2[/C][C]2[/C][C]2[/C][C]0[/C][/ROW]
[ROW][C]Yes:NoTreatment-Yes:NA[/C][C]2[/C][C]2[/C][C]2[/C][C]0[/C][/ROW]
[ROW][C]No:Treatment-Yes:NA[/C][C]2[/C][C]2[/C][C]2[/C][C]0[/C][/ROW]
[ROW][C]Yes:Treatment-Yes:NA[/C][C]2[/C][C]2[/C][C]2[/C][C]0[/C][/ROW]
[ROW][C]Yes:NoTreatment-No:NoTreatment[/C][C]0[/C][C]0[/C][C]0[/C][C]1[/C][/ROW]
[ROW][C]No:Treatment-No:NoTreatment[/C][C]0[/C][C]0[/C][C]0[/C][C]1[/C][/ROW]
[ROW][C]Yes:Treatment-No:NoTreatment[/C][C]0[/C][C]0[/C][C]0[/C][C]1[/C][/ROW]
[ROW][C]No:Treatment-Yes:NoTreatment[/C][C]0[/C][C]0[/C][C]0[/C][C]1[/C][/ROW]
[ROW][C]Yes:Treatment-Yes:NoTreatment[/C][C]0[/C][C]0[/C][C]0[/C][C]1[/C][/ROW]
[ROW][C]Yes:Treatment-No:Treatment[/C][C]0[/C][C]0[/C][C]0[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=201484&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=201484&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
Yes-No	-0.232	-0.232	-0.232	0
NoTreatment-NA	1.959	1.959	1.959	0
Treatment-NA	2.022	2.022	2.022	0
Treatment-NoTreatment	0.063	0.063	0.063	0
Yes:NA-No:NA	0	0	0	0
No:NoTreatment-No:NA	2	2	2	0
Yes:NoTreatment-No:NA	2	2	2	0
No:Treatment-No:NA	2	2	2	0
Yes:Treatment-No:NA	2	2	2	0
No:NoTreatment-Yes:NA	2	2	2	0
Yes:NoTreatment-Yes:NA	2	2	2	0
No:Treatment-Yes:NA	2	2	2	0
Yes:Treatment-Yes:NA	2	2	2	0
Yes:NoTreatment-No:NoTreatment	0	0	0	1
No:Treatment-No:NoTreatment	0	0	0	1
Yes:Treatment-No:NoTreatment	0	0	0	1
No:Treatment-Yes:NoTreatment	0	0	0	1
Yes:Treatment-Yes:NoTreatment	0	0	0	1
Yes:Treatment-No:Treatment	0	0	0	1

Levenes Test for Homogeneity of Variance
	Df	F value	Pr(>F)
Group	5	NaN	NaN
	148

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 5 & NaN & NaN \tabularnewline
  & 148 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=201484&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]5[/C][C]NaN[/C][C]NaN[/C][/ROW]
[ROW][C] [/C][C]148[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=201484&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=201484&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	5	NaN	NaN
	148

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):

par2 = grey ; par3 = FALSE ; par4 = Unknown ;

Parameters (R input):

par1 = 1 ; par2 = 2 ; par3 = 3 ; 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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code