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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 computationSat, 22 Dec 2012 15:38:35 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Dec/22/t1356208758z96md9jvebnvnsh.htm/, Retrieved Tue, 10 Feb 2026 19:01:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=204612, Retrieved Tue, 10 Feb 2026 19:01:36 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact373

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [One-Way-Between-Groups ANOVA- Free Statistics Software (Calculator)] [] [2010-11-01 13:37:53] [b98453cac15ba1066b407e146608df68]
- RMPD  [Two-Way ANOVA] [Paper 2012, deel ...] [2012-12-21 17:59:36] [346d881f0ddec1e86442b342eb3e8104]
- R  D      [Two-Way ANOVA] [Twowayanova - aan...] [2012-12-22 20:38:35] [8dfbd7005bbb2cc4a26b500e2e7611ce] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
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'

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 5 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204612&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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204612&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204612&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 time5 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net






ANOVA Model
Response ~ Treatment_A * Treatment_B
means2.9530.4750.332-0.161

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & 2.953 & 0.475 & 0.332 & -0.161 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204612&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]Response ~ Treatment_A * Treatment_B[/C][/ROW]
[ROW][C]means[/C][C]2.953[/C][C]0.475[/C][C]0.332[/C][C]-0.161[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204612&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204612&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
means2.9530.4750.332-0.161






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
1
Treatment_A11.911.911.960.164
Treatment_B13.763.763.8590.051
Treatment_A:Treatment_B10.0690.0690.0710.79
Residuals150146.1570.974 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 1 &  &  &  &  \tabularnewline
Treatment_A & 1 & 1.91 & 1.91 & 1.96 & 0.164 \tabularnewline
Treatment_B & 1 & 3.76 & 3.76 & 3.859 & 0.051 \tabularnewline
Treatment_A:Treatment_B & 1 & 0.069 & 0.069 & 0.071 & 0.79 \tabularnewline
Residuals & 150 & 146.157 & 0.974 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204612&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]1.91[/C][C]1.91[/C][C]1.96[/C][C]0.164[/C][/ROW]
[ROW][C]Treatment_B[/C][C]1[/C][C]3.76[/C][C]3.76[/C][C]3.859[/C][C]0.051[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]1[/C][C]0.069[/C][C]0.069[/C][C]0.071[/C][C]0.79[/C][/ROW]
[ROW][C]Residuals[/C][C]150[/C][C]146.157[/C][C]0.974[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204612&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204612&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_A11.911.911.960.164
Treatment_B13.763.763.8590.051
Treatment_A:Treatment_B10.0690.0690.0710.79
Residuals150146.1570.974






Tukey Honest Significant Difference Comparisons
difflwruprp adj
Yes-No0.415-0.1711.0020.164
Good-Bad0.319-0.0020.6410.051
Yes:Bad-No:Bad0.475-0.5331.4830.612
No:Good-No:Bad0.332-0.1080.7730.208
Yes:Good-No:Bad0.647-0.5331.8260.487
No:Good-Yes:Bad-0.143-1.1710.8850.984
Yes:Good-Yes:Bad0.171-1.331.6730.991
Yes:Good-No:Good0.314-0.8831.5110.904

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
Yes-No & 0.415 & -0.171 & 1.002 & 0.164 \tabularnewline
Good-Bad & 0.319 & -0.002 & 0.641 & 0.051 \tabularnewline
Yes:Bad-No:Bad & 0.475 & -0.533 & 1.483 & 0.612 \tabularnewline
No:Good-No:Bad & 0.332 & -0.108 & 0.773 & 0.208 \tabularnewline
Yes:Good-No:Bad & 0.647 & -0.533 & 1.826 & 0.487 \tabularnewline
No:Good-Yes:Bad & -0.143 & -1.171 & 0.885 & 0.984 \tabularnewline
Yes:Good-Yes:Bad & 0.171 & -1.33 & 1.673 & 0.991 \tabularnewline
Yes:Good-No:Good & 0.314 & -0.883 & 1.511 & 0.904 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204612&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]0.415[/C][C]-0.171[/C][C]1.002[/C][C]0.164[/C][/ROW]
[ROW][C]Good-Bad[/C][C]0.319[/C][C]-0.002[/C][C]0.641[/C][C]0.051[/C][/ROW]
[ROW][C]Yes:Bad-No:Bad[/C][C]0.475[/C][C]-0.533[/C][C]1.483[/C][C]0.612[/C][/ROW]
[ROW][C]No:Good-No:Bad[/C][C]0.332[/C][C]-0.108[/C][C]0.773[/C][C]0.208[/C][/ROW]
[ROW][C]Yes:Good-No:Bad[/C][C]0.647[/C][C]-0.533[/C][C]1.826[/C][C]0.487[/C][/ROW]
[ROW][C]No:Good-Yes:Bad[/C][C]-0.143[/C][C]-1.171[/C][C]0.885[/C][C]0.984[/C][/ROW]
[ROW][C]Yes:Good-Yes:Bad[/C][C]0.171[/C][C]-1.33[/C][C]1.673[/C][C]0.991[/C][/ROW]
[ROW][C]Yes:Good-No:Good[/C][C]0.314[/C][C]-0.883[/C][C]1.511[/C][C]0.904[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204612&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204612&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
Yes-No0.415-0.1711.0020.164
Good-Bad0.319-0.0020.6410.051
Yes:Bad-No:Bad0.475-0.5331.4830.612
No:Good-No:Bad0.332-0.1080.7730.208
Yes:Good-No:Bad0.647-0.5331.8260.487
No:Good-Yes:Bad-0.143-1.1710.8850.984
Yes:Good-Yes:Bad0.171-1.331.6730.991
Yes:Good-No:Good0.314-0.8831.5110.904






Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group31.1810.319
150 

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 3 & 1.181 & 0.319 \tabularnewline
  & 150 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204612&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]3[/C][C]1.181[/C][C]0.319[/C][/ROW]
[ROW][C] [/C][C]150[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204612&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204612&T=4

As an alternative you can also use a QR Code:  
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The GUIDs for individual cells are displayed in the table below:

Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group31.1810.319
150


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = 6 ; par3 = 8 ; par4 = TRUE ;
Parameters (R input):
par1 = 1 ; par2 = 6 ; par3 = 8 ; par4 = TRUE ;
R code (references can be found in the software module):
par4 <- 'TRUE'
par3 <- '8'
par2 <- '6'
par1 <- '1'
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')