nice: Make nice ANOVA table for printing.
In afex: Analysis of Factorial Experiments
Description
Usage
Arguments
Details
Value
Author(s)
References
See Also
Examples
Description
This generic function produces a nice ANOVA table for printin for objects of class. nice_anova takes an object from Anova possible created by the convenience functions aov_ez or aov_car. When within-subject factors are present, either sphericity corrected or uncorrected degrees of freedom can be reported.
Usage
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nice(object, ...)
## S3 method for class 'afex_aov'
nice(object, es = afex_options("es_aov"),
observed = NULL, correction = afex_options("correction_aov"),
MSE = TRUE, intercept = FALSE, sig.symbols = c(" +", " *", " **",
" ***"), ...)
## S3 method for class 'anova'
nice(object, MSE = TRUE, intercept = FALSE,
sig.symbols = c(" +", " *", " **", " ***"), ...)
## S3 method for class 'mixed'
nice(object, sig.symbols = c(" +", " *", " **", " ***"), ...)
Arguments
object
An object of class "Anova.mlm" or "anova" as returned from Anova or the afex ANOVA functions (see aov_car).
...
currently ignored.
es
Effect Size to be reported. The default is given by afex_options("es_aov"), which is initially set to "ges" (i.e., reporting generalized eta-squared, see details). Also supported is partial eta-squared ("pes") or "none".
observed
character vector referring to the observed (i.e., non manipulated) variables/effects in the design. Important for calculation of generalized eta-squared (ignored if es is not "ges"), see details.
correction
Character. Which sphericity correction of the degrees of freedom should be reported for the within-subject factors. The default is given by afex_options("correction_aov"), which is initially set to "GG" corresponding to the Greenhouse-Geisser correction. Possible values are "GG", "HF" (i.e., Hyunh-Feldt correction), and "none" (i.e., no correction).
MSE
logical. Should the column containing the Mean Sqaured Error (MSE) be displayed? Default is TRUE.
intercept
logical. Should intercept (if present) be included in the ANOVA table? Default is FALSE which hides the intercept.
sig.symbols
Character. What should be the symbols designating significance? When entering an vector with length(sig.symbol) < 4 only those elements of the default (c(" +", " *", " **", " ***")) will be replaced. sig.symbols = "" will display the stars but not the +, sig.symbols = rep("", 4) will display no symbols.
Details
The returned data.frame is print-ready when adding to a document with proper methods. I recommend ascii and xtable. ascii provides conversion to AsciiDoc but most notably to org-mode (see ascii and print-ascii). xtable converts a data.frame into LaTeX code with many possible options (e.g., allowing for "longtable" or "sidewaystable"), see xtable and print.xtable. See Examples.
Conversion functions to other formats (such as HTML, ODF, or Word) can be found at the Reproducible Research Task View.
The default reports generalized eta squared (Olejnik & Algina, 2003), the "recommended effect size for repeated measured designs" (Bakeman, 2005). Note that it is important that all measured variables (as opposed to experimentally manipulated variables), such as e.g., age, gender, weight, ..., must be declared via observed to obtain the correct effect size estimate. Partial eta squared ("pes") does not require this.
Value
A data.frame with the ANOVA table consisting of characters. The columns that are always present are: Effect, df (degrees of freedom), F, and p.
ges contains the generalized eta-squared effect size measure (Bakeman, 2005), pes contains partial eta-squared (if requested).
Author(s)
The code for calculating generalized eta-squared was written by Mike Lawrence.
Everything else was written by Henrik Singmann.
References
Bakeman, R. (2005). Recommended effect size statistics for repeated measures designs. Behavior Research Methods, 37(3), 379-384. doi:10.3758/BF03192707
Olejnik, S., & Algina, J. (2003). Generalized Eta and Omega Squared Statistics: Measures of Effect Size for Some Common Research Designs. Psychological Methods, 8(4), 434-447. doi:10.1037/1082-989X.8.4.434
See Also
aov_ez and aov_car are the convenience functions to create the object appropriate for nice_anova.
Examples
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## example from Olejnik & Algina (2003)
# "Repeated Measures Design" (pp. 439):
data(md_12.1)
# create object of class afex_aov:
rmd <- aov_ez("id", "rt", md_12.1, within = c("angle", "noise"))
# use different es:
nice(rmd, es = "pes") # noise: .82
nice(rmd, es = "ges") # noise: .39
# exampel using obk.long (see ?obk.long), a long version of the OBrienKaiser dataset from car.
data(obk.long)
# create object of class afex_aov:
tmp.aov <- aov_car(value ~ treatment * gender + Error(id/phase*hour), data = obk.long)
nice(tmp.aov, observed = "gender")
nice(tmp.aov, observed = "gender", sig.symbol = rep("", 4))
## Not run:
# use package ascii or xtable for formatting of tables ready for printing.
full <- nice(tmp.aov, observed = "gender")
require(ascii)
print(ascii(full, include.rownames = FALSE, caption = "ANOVA 1"), type = "org")
require(xtable)
print.xtable(xtable(full, caption = "ANOVA 2"), include.rownames = FALSE)
## End(Not run)
Example output
Loading required package: lme4
Loading required package: Matrix
Loading required package: lsmeans
Loading required package: estimability
************
Welcome to afex. For support visit: http://afex.singmann.science/
- Functions for ANOVAs: aov_car(), aov_ez(), and aov_4()
- Methods for calculating p-values with mixed(): 'KR', 'S', 'LRT', and 'PB'
- 'afex_aov' and 'mixed' objects can be passed to lsmeans() for follow-up tests
- Get and set global package options with: afex_options()
- Set orthogonal sum-to-zero contrasts globally: set_sum_contrasts()
- For example analyses see: browseVignettes("afex")
************
Attaching package: 'afex'
The following object is masked from 'package:lme4':
lmer
Anova Table (Type 3 tests)
Response: rt
Effect df MSE F pes p.value
1 angle 1.92, 17.31 3702.02 40.72 *** .82 <.0001
2 noise 1, 9 8460.00 33.77 *** .79 .0003
3 angle:noise 1.81, 16.27 1283.22 45.31 *** .83 <.0001
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1
Sphericity correction method: GG
Anova Table (Type 3 tests)
Response: rt
Effect df MSE F ges p.value
1 angle 1.92, 17.31 3702.02 40.72 *** .39 <.0001
2 noise 1, 9 8460.00 33.77 *** .39 .0003
3 angle:noise 1.81, 16.27 1283.22 45.31 *** .19 <.0001
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1
Sphericity correction method: GG
Contrasts set to contr.sum for the following variables: treatment, gender
Anova Table (Type 3 tests)
Response: value
Effect df MSE F ges p.value
1 treatment 2, 10 22.81 3.94 + .20 .05
2 gender 1, 10 22.81 3.66 + .11 .08
3 treatment:gender 2, 10 22.81 2.86 .18 .10
4 phase 1.60, 15.99 5.02 16.13 *** .15 .0003
5 treatment:phase 3.20, 15.99 5.02 4.85 * .10 .01
6 gender:phase 1.60, 15.99 5.02 0.28 .003 .71
7 treatment:gender:phase 3.20, 15.99 5.02 0.64 .01 .61
8 hour 1.84, 18.41 3.39 16.69 *** .13 <.0001
9 treatment:hour 3.68, 18.41 3.39 0.09 .002 .98
10 gender:hour 1.84, 18.41 3.39 0.45 .004 .63
11 treatment:gender:hour 3.68, 18.41 3.39 0.62 .01 .64
12 phase:hour 3.60, 35.96 2.67 1.18 .02 .33
13 treatment:phase:hour 7.19, 35.96 2.67 0.35 .009 .93
14 gender:phase:hour 3.60, 35.96 2.67 0.93 .01 .45
15 treatment:gender:phase:hour 7.19, 35.96 2.67 0.74 .02 .65
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1
Sphericity correction method: GG
Anova Table (Type 3 tests)
Response: value
Effect df MSE F ges p.value
1 treatment 2, 10 22.81 3.94 + .20 .05
2 gender 1, 10 22.81 3.66 + .11 .08
3 treatment:gender 2, 10 22.81 2.86 .18 .10
4 phase 1.60, 15.99 5.02 16.13 *** .15 .0003
5 treatment:phase 3.20, 15.99 5.02 4.85 * .10 .01
6 gender:phase 1.60, 15.99 5.02 0.28 .003 .71
7 treatment:gender:phase 3.20, 15.99 5.02 0.64 .01 .61
8 hour 1.84, 18.41 3.39 16.69 *** .13 <.0001
9 treatment:hour 3.68, 18.41 3.39 0.09 .002 .98
10 gender:hour 1.84, 18.41 3.39 0.45 .004 .63
11 treatment:gender:hour 3.68, 18.41 3.39 0.62 .01 .64
12 phase:hour 3.60, 35.96 2.67 1.18 .02 .33
13 treatment:phase:hour 7.19, 35.96 2.67 0.35 .009 .93
14 gender:phase:hour 3.60, 35.96 2.67 0.93 .01 .45
15 treatment:gender:phase:hour 7.19, 35.96 2.67 0.74 .02 .65
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1
Sphericity correction method: GG
Loading required package: ascii
Attaching package: 'ascii'
The following object is masked from 'package:Matrix':
expand
#+CAPTION: ANOVA 1
| Effect | df | MSE | F | ges | p.value |
|-----------------------------+-------------+-------+-----------+------+---------|
| treatment | 2, 10 | 22.81 | 3.94 + | .20 | .05 |
| gender | 1, 10 | 22.81 | 3.66 + | .11 | .08 |
| treatment:gender | 2, 10 | 22.81 | 2.86 | .18 | .10 |
| phase | 1.60, 15.99 | 5.02 | 16.13 *** | .15 | .0003 |
| treatment:phase | 3.20, 15.99 | 5.02 | 4.85 * | .10 | .01 |
| gender:phase | 1.60, 15.99 | 5.02 | 0.28 | .003 | .71 |
| treatment:gender:phase | 3.20, 15.99 | 5.02 | 0.64 | .01 | .61 |
| hour | 1.84, 18.41 | 3.39 | 16.69 *** | .13 | <.0001 |
| treatment:hour | 3.68, 18.41 | 3.39 | 0.09 | .002 | .98 |
| gender:hour | 1.84, 18.41 | 3.39 | 0.45 | .004 | .63 |
| treatment:gender:hour | 3.68, 18.41 | 3.39 | 0.62 | .01 | .64 |
| phase:hour | 3.60, 35.96 | 2.67 | 1.18 | .02 | .33 |
| treatment:phase:hour | 7.19, 35.96 | 2.67 | 0.35 | .009 | .93 |
| gender:phase:hour | 3.60, 35.96 | 2.67 | 0.93 | .01 | .45 |
| treatment:gender:phase:hour | 7.19, 35.96 | 2.67 | 0.74 | .02 | .65 |
Warning messages:
1: In rep(rownames, length = nrow(x)) :
'x' is NULL so the result will be NULL
2: In rep(colnames, length = ncol(x)) :
'x' is NULL so the result will be NULL
Loading required package: xtable
% latex table generated in R 3.4.1 by xtable 1.8-2 package
% Tue Apr 3 15:31:50 2018
\begin{table}[ht]
\centering
\begin{tabular}{llllll}
\hline
Effect & df & MSE & F & ges & p.value \\
\hline
treatment & 2, 10 & 22.81 & 3.94 + & .20 & .05 \\
gender & 1, 10 & 22.81 & 3.66 + & .11 & .08 \\
treatment:gender & 2, 10 & 22.81 & 2.86 & .18 & .10 \\
phase & 1.60, 15.99 & 5.02 & 16.13 *** & .15 & .0003 \\
treatment:phase & 3.20, 15.99 & 5.02 & 4.85 * & .10 & .01 \\
gender:phase & 1.60, 15.99 & 5.02 & 0.28 & .003 & .71 \\
treatment:gender:phase & 3.20, 15.99 & 5.02 & 0.64 & .01 & .61 \\
hour & 1.84, 18.41 & 3.39 & 16.69 *** & .13 & $<$.0001 \\
treatment:hour & 3.68, 18.41 & 3.39 & 0.09 & .002 & .98 \\
gender:hour & 1.84, 18.41 & 3.39 & 0.45 & .004 & .63 \\
treatment:gender:hour & 3.68, 18.41 & 3.39 & 0.62 & .01 & .64 \\
phase:hour & 3.60, 35.96 & 2.67 & 1.18 & .02 & .33 \\
treatment:phase:hour & 7.19, 35.96 & 2.67 & 0.35 & .009 & .93 \\
gender:phase:hour & 3.60, 35.96 & 2.67 & 0.93 & .01 & .45 \\
treatment:gender:phase:hour & 7.19, 35.96 & 2.67 & 0.74 & .02 & .65 \\
\hline
\end{tabular}
\caption{ANOVA 2}
\end{table}
afex documentation built on May 2, 2019, 6:08 p.m.
R Package Documentation
Browse R Packages
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Note that we can't provide technical support on individual packages. You should contact the package authors for that.
Description Usage Arguments Details Value Author(s) References See Also Examples
Description
This generic function produces a nice ANOVA table for printin for objects of class. nice_anova takes an object from Anova possible created by the convenience functions aov_ez or aov_car. When within-subject factors are present, either sphericity corrected or uncorrected degrees of freedom can be reported.
Usage
1 2 3 4 5 6 7 8 9 10 11 12 13 14 | nice(object, ...)
## S3 method for class 'afex_aov'
nice(object, es = afex_options("es_aov"),
observed = NULL, correction = afex_options("correction_aov"),
MSE = TRUE, intercept = FALSE, sig.symbols = c(" +", " *", " **",
" ***"), ...)
## S3 method for class 'anova'
nice(object, MSE = TRUE, intercept = FALSE,
sig.symbols = c(" +", " *", " **", " ***"), ...)
## S3 method for class 'mixed'
nice(object, sig.symbols = c(" +", " *", " **", " ***"), ...)
|
Arguments
object |
An object of class |
... |
currently ignored. |
es |
Effect Size to be reported. The default is given by |
observed |
character vector referring to the observed (i.e., non manipulated) variables/effects in the design. Important for calculation of generalized eta-squared (ignored if |
correction |
Character. Which sphericity correction of the degrees of freedom should be reported for the within-subject factors. The default is given by |
MSE |
logical. Should the column containing the Mean Sqaured Error (MSE) be displayed? Default is |
intercept |
logical. Should intercept (if present) be included in the ANOVA table? Default is |
sig.symbols |
Character. What should be the symbols designating significance? When entering an vector with |
Details
The returned data.frame is print-ready when adding to a document with proper methods. I recommend ascii and xtable. ascii provides conversion to AsciiDoc but most notably to org-mode (see ascii and print-ascii). xtable converts a data.frame into LaTeX code with many possible options (e.g., allowing for "longtable" or "sidewaystable"), see xtable and print.xtable. See Examples.
Conversion functions to other formats (such as HTML, ODF, or Word) can be found at the Reproducible Research Task View.
The default reports generalized eta squared (Olejnik & Algina, 2003), the "recommended effect size for repeated measured designs" (Bakeman, 2005). Note that it is important that all measured variables (as opposed to experimentally manipulated variables), such as e.g., age, gender, weight, ..., must be declared via observed to obtain the correct effect size estimate. Partial eta squared ("pes") does not require this.
Value
A data.frame with the ANOVA table consisting of characters. The columns that are always present are: Effect, df (degrees of freedom), F, and p.
ges contains the generalized eta-squared effect size measure (Bakeman, 2005), pes contains partial eta-squared (if requested).
Author(s)
The code for calculating generalized eta-squared was written by Mike Lawrence.
Everything else was written by Henrik Singmann.
References
Bakeman, R. (2005). Recommended effect size statistics for repeated measures designs. Behavior Research Methods, 37(3), 379-384. doi:10.3758/BF03192707
Olejnik, S., & Algina, J. (2003). Generalized Eta and Omega Squared Statistics: Measures of Effect Size for Some Common Research Designs. Psychological Methods, 8(4), 434-447. doi:10.1037/1082-989X.8.4.434
See Also
aov_ez and aov_car are the convenience functions to create the object appropriate for nice_anova.
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 | ## example from Olejnik & Algina (2003)
# "Repeated Measures Design" (pp. 439):
data(md_12.1)
# create object of class afex_aov:
rmd <- aov_ez("id", "rt", md_12.1, within = c("angle", "noise"))
# use different es:
nice(rmd, es = "pes") # noise: .82
nice(rmd, es = "ges") # noise: .39
# exampel using obk.long (see ?obk.long), a long version of the OBrienKaiser dataset from car.
data(obk.long)
# create object of class afex_aov:
tmp.aov <- aov_car(value ~ treatment * gender + Error(id/phase*hour), data = obk.long)
nice(tmp.aov, observed = "gender")
nice(tmp.aov, observed = "gender", sig.symbol = rep("", 4))
## Not run:
# use package ascii or xtable for formatting of tables ready for printing.
full <- nice(tmp.aov, observed = "gender")
require(ascii)
print(ascii(full, include.rownames = FALSE, caption = "ANOVA 1"), type = "org")
require(xtable)
print.xtable(xtable(full, caption = "ANOVA 2"), include.rownames = FALSE)
## End(Not run)
|
Example output
Loading required package: lme4
Loading required package: Matrix
Loading required package: lsmeans
Loading required package: estimability
************
Welcome to afex. For support visit: http://afex.singmann.science/
- Functions for ANOVAs: aov_car(), aov_ez(), and aov_4()
- Methods for calculating p-values with mixed(): 'KR', 'S', 'LRT', and 'PB'
- 'afex_aov' and 'mixed' objects can be passed to lsmeans() for follow-up tests
- Get and set global package options with: afex_options()
- Set orthogonal sum-to-zero contrasts globally: set_sum_contrasts()
- For example analyses see: browseVignettes("afex")
************
Attaching package: 'afex'
The following object is masked from 'package:lme4':
lmer
Anova Table (Type 3 tests)
Response: rt
Effect df MSE F pes p.value
1 angle 1.92, 17.31 3702.02 40.72 *** .82 <.0001
2 noise 1, 9 8460.00 33.77 *** .79 .0003
3 angle:noise 1.81, 16.27 1283.22 45.31 *** .83 <.0001
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1
Sphericity correction method: GG
Anova Table (Type 3 tests)
Response: rt
Effect df MSE F ges p.value
1 angle 1.92, 17.31 3702.02 40.72 *** .39 <.0001
2 noise 1, 9 8460.00 33.77 *** .39 .0003
3 angle:noise 1.81, 16.27 1283.22 45.31 *** .19 <.0001
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1
Sphericity correction method: GG
Contrasts set to contr.sum for the following variables: treatment, gender
Anova Table (Type 3 tests)
Response: value
Effect df MSE F ges p.value
1 treatment 2, 10 22.81 3.94 + .20 .05
2 gender 1, 10 22.81 3.66 + .11 .08
3 treatment:gender 2, 10 22.81 2.86 .18 .10
4 phase 1.60, 15.99 5.02 16.13 *** .15 .0003
5 treatment:phase 3.20, 15.99 5.02 4.85 * .10 .01
6 gender:phase 1.60, 15.99 5.02 0.28 .003 .71
7 treatment:gender:phase 3.20, 15.99 5.02 0.64 .01 .61
8 hour 1.84, 18.41 3.39 16.69 *** .13 <.0001
9 treatment:hour 3.68, 18.41 3.39 0.09 .002 .98
10 gender:hour 1.84, 18.41 3.39 0.45 .004 .63
11 treatment:gender:hour 3.68, 18.41 3.39 0.62 .01 .64
12 phase:hour 3.60, 35.96 2.67 1.18 .02 .33
13 treatment:phase:hour 7.19, 35.96 2.67 0.35 .009 .93
14 gender:phase:hour 3.60, 35.96 2.67 0.93 .01 .45
15 treatment:gender:phase:hour 7.19, 35.96 2.67 0.74 .02 .65
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1
Sphericity correction method: GG
Anova Table (Type 3 tests)
Response: value
Effect df MSE F ges p.value
1 treatment 2, 10 22.81 3.94 + .20 .05
2 gender 1, 10 22.81 3.66 + .11 .08
3 treatment:gender 2, 10 22.81 2.86 .18 .10
4 phase 1.60, 15.99 5.02 16.13 *** .15 .0003
5 treatment:phase 3.20, 15.99 5.02 4.85 * .10 .01
6 gender:phase 1.60, 15.99 5.02 0.28 .003 .71
7 treatment:gender:phase 3.20, 15.99 5.02 0.64 .01 .61
8 hour 1.84, 18.41 3.39 16.69 *** .13 <.0001
9 treatment:hour 3.68, 18.41 3.39 0.09 .002 .98
10 gender:hour 1.84, 18.41 3.39 0.45 .004 .63
11 treatment:gender:hour 3.68, 18.41 3.39 0.62 .01 .64
12 phase:hour 3.60, 35.96 2.67 1.18 .02 .33
13 treatment:phase:hour 7.19, 35.96 2.67 0.35 .009 .93
14 gender:phase:hour 3.60, 35.96 2.67 0.93 .01 .45
15 treatment:gender:phase:hour 7.19, 35.96 2.67 0.74 .02 .65
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1
Sphericity correction method: GG
Loading required package: ascii
Attaching package: 'ascii'
The following object is masked from 'package:Matrix':
expand
#+CAPTION: ANOVA 1
| Effect | df | MSE | F | ges | p.value |
|-----------------------------+-------------+-------+-----------+------+---------|
| treatment | 2, 10 | 22.81 | 3.94 + | .20 | .05 |
| gender | 1, 10 | 22.81 | 3.66 + | .11 | .08 |
| treatment:gender | 2, 10 | 22.81 | 2.86 | .18 | .10 |
| phase | 1.60, 15.99 | 5.02 | 16.13 *** | .15 | .0003 |
| treatment:phase | 3.20, 15.99 | 5.02 | 4.85 * | .10 | .01 |
| gender:phase | 1.60, 15.99 | 5.02 | 0.28 | .003 | .71 |
| treatment:gender:phase | 3.20, 15.99 | 5.02 | 0.64 | .01 | .61 |
| hour | 1.84, 18.41 | 3.39 | 16.69 *** | .13 | <.0001 |
| treatment:hour | 3.68, 18.41 | 3.39 | 0.09 | .002 | .98 |
| gender:hour | 1.84, 18.41 | 3.39 | 0.45 | .004 | .63 |
| treatment:gender:hour | 3.68, 18.41 | 3.39 | 0.62 | .01 | .64 |
| phase:hour | 3.60, 35.96 | 2.67 | 1.18 | .02 | .33 |
| treatment:phase:hour | 7.19, 35.96 | 2.67 | 0.35 | .009 | .93 |
| gender:phase:hour | 3.60, 35.96 | 2.67 | 0.93 | .01 | .45 |
| treatment:gender:phase:hour | 7.19, 35.96 | 2.67 | 0.74 | .02 | .65 |
Warning messages:
1: In rep(rownames, length = nrow(x)) :
'x' is NULL so the result will be NULL
2: In rep(colnames, length = ncol(x)) :
'x' is NULL so the result will be NULL
Loading required package: xtable
% latex table generated in R 3.4.1 by xtable 1.8-2 package
% Tue Apr 3 15:31:50 2018
\begin{table}[ht]
\centering
\begin{tabular}{llllll}
\hline
Effect & df & MSE & F & ges & p.value \\
\hline
treatment & 2, 10 & 22.81 & 3.94 + & .20 & .05 \\
gender & 1, 10 & 22.81 & 3.66 + & .11 & .08 \\
treatment:gender & 2, 10 & 22.81 & 2.86 & .18 & .10 \\
phase & 1.60, 15.99 & 5.02 & 16.13 *** & .15 & .0003 \\
treatment:phase & 3.20, 15.99 & 5.02 & 4.85 * & .10 & .01 \\
gender:phase & 1.60, 15.99 & 5.02 & 0.28 & .003 & .71 \\
treatment:gender:phase & 3.20, 15.99 & 5.02 & 0.64 & .01 & .61 \\
hour & 1.84, 18.41 & 3.39 & 16.69 *** & .13 & $<$.0001 \\
treatment:hour & 3.68, 18.41 & 3.39 & 0.09 & .002 & .98 \\
gender:hour & 1.84, 18.41 & 3.39 & 0.45 & .004 & .63 \\
treatment:gender:hour & 3.68, 18.41 & 3.39 & 0.62 & .01 & .64 \\
phase:hour & 3.60, 35.96 & 2.67 & 1.18 & .02 & .33 \\
treatment:phase:hour & 7.19, 35.96 & 2.67 & 0.35 & .009 & .93 \\
gender:phase:hour & 3.60, 35.96 & 2.67 & 0.93 & .01 & .45 \\
treatment:gender:phase:hour & 7.19, 35.96 & 2.67 & 0.74 & .02 & .65 \\
\hline
\end{tabular}
\caption{ANOVA 2}
\end{table}
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