Rapport package team
 ANOVA Template
 2011-04-26 20:25 CET

Contents
•	Description
–	Introduction
–	Model Overview
–	Descriptives
–	Diagnostics
–	ANOVA Summary
•	Description
–	Introduction
–	Model Overview
–	Descriptives
–	Diagnostics
–	ANOVA Summary
Description
An ANOVA report with table of descriptives, diagnostic tests and ANOVA-specific statistics.
Introduction
Analysis of Variance or ANOVA is a statistical procedure that tests equality of means for several samples. It was first introduced in 1921 by famous English statistician Sir Ronald Aylmer Fisher.
Model Overview
One-Way ANOVA was carried out, with Gender as independent variable, and Internet usage in leisure time (hours per day) as a response variable. Factor interaction was taken into account.
Descriptives
In order to get more insight on the model data, a table of frequencies for ANOVA factors is displayed, as well as a table of descriptives.
Frequency Table
Below lies a frequency table for factors in ANOVA model. Note that the missing values are removed from the summary.
gender
	N
	%
	Cumul. N
	Cumul. %
	
male
	410
	60.92
	410
	60.92
	
female
	263
	39.08
	673
	100
	
Total
	673
	100
	673
	100

Descriptive Statistics
The following table displays the descriptive statistics of ANOVA model. Factor levels lie on the left-hand side, while the corresponding statistics for response variable are given on the right-hand side.
Gender
	Min
	Max
	Mean
	Std.Dev.
	Median
	IQR
	
male
	0
	12
	3.27
	1.953
	3
	3
	
female
	0
	12
	3.064
	2.355
	2
	3
	
Table continues below
Skewness
	Kurtosis
	
0.9443
	0.9858
	
1.398
	1.87

Diagnostics
Before we carry out ANOVA, we'd like to check some basic assumptions. For those purposes, normality and homoscedascity tests are carried out alongside several graphs that may help you with your decision on model's main assumptions.
Diagnostics
Univariate Normality
Method
	Statistic
	p-value
	
Lilliefors (Kolmogorov-Smirnov) normality test
	0.168
	3e-52
	
Anderson-Darling normality test
	18.75
	7.261e-44
	
Shapiro-Wilk normality test
	0.9001
	1.618e-20

So, the conclusions we can draw with the help of test statistics:
•	based on Lilliefors test, distribution of Internet usage in leisure time (hours per day) is not normal
•	Anderson-Darling test confirms violation of normality assumption
•	according to Shapiro-Wilk test, the distribution of Internet usage in leisure time (hours per day) is not normal
As you can see, the applied tests confirm departures from normality of the Internet usage in leisure time (hours per day).
Homoscedascity
In order to test homoscedascity, Bartlett and Fligner-Kileen tests are applied.
Method
	Statistic
	p-value
	
Fligner-Killeen test of homogeneity of variances
	0.4629
	0.4963
	
Bartlett test of homogeneity of variances
	10.77
	0.001032

When it comes to equality of variances, applied tests yield inconsistent results. While Fligner-Kileen test confirmed the hypotheses of homoscedascity, Bartlett's test rejected it.
Diagnostic Plots
Here you can see several diagnostic plots for ANOVA model:
•	residuals against fitted values
•	scale-location plot of square root of residuals against fitted values
•	normal Q-Q plot
•	residuals against leverages

ANOVA Summary
ANOVA Table
 
	Df
	Sum.Sq
	Mean.Sq
	F.value
	Pr..F.
	
gender
	1
	6.422
	6.422
	1.43
	0.2322
	
Residuals
	636
	2856
	4.49

	

F-test for Gender is not statistically significant, which implies that there is no Gender effect on response variable.
Post Hoc test
Results
After getting the results of the ANOVA, usually it is advisable to run a post hoc test to explore patterns that were not specified a priori. Now we are presenting Tukey's HSD test.
gender
 
	Difference
	Lower Bound
	Upper Bound
	
female-male
	-0.206
	-0.543
	0.132
	
Table continues below
 
	P value
	
female-male
	0.232

There are no categories which differ significantly here.
Plot
Below you can see the result of the post hoc test on a plot.

Description
An ANOVA report with table of descriptives, diagnostic tests and ANOVA-specific statistics.
Introduction
Analysis of Variance or ANOVA is a statistical procedure that tests equality of means for several samples. It was first introduced in 1921 by famous English statistician Sir Ronald Aylmer Fisher.
Model Overview
Two-Way ANOVA was carried out, with Gender and Relationship status as independent variables, and Internet usage in leisure time (hours per day) as a response variable. Factor interaction was taken into account.
Descriptives
In order to get more insight on the model data, a table of frequencies for ANOVA factors is displayed, as well as a table of descriptives.
Frequency Table
Below lies a frequency table for factors in ANOVA model. Note that the missing values are removed from the summary.
gender
	partner
	N
	%
	Cumul. N
	Cumul. %
	
male
	in a relationship
	150
	23.7
	150
	23.7
	
female
	in a relationship
	120
	18.96
	270
	42.65
	
male
	married
	33
	5.213
	303
	47.87
	
female
	married
	29
	4.581
	332
	52.45
	
male
	single
	204
	32.23
	536
	84.68
	
female
	single
	97
	15.32
	633
	100
	
Total
	Total
	633
	100
	633
	100

Descriptive Statistics
The following table displays the descriptive statistics of ANOVA model. Factor levels and their combinations lie on the left-hand side, while the corresponding statistics for response variable are given on the right-hand side.
Gender
	Relationship status
	Min
	Max
	Mean
	Std.Dev.
	
male
	in a relationship
	0.5
	12
	3.058
	1.969
	
male
	married
	0
	8
	2.985
	2.029
	
male
	single
	0
	10
	3.503
	1.936
	
female
	in a relationship
	0.5
	10
	3.044
	2.216
	
female
	married
	0
	10
	2.481
	1.967
	
female
	single
	0
	12
	3.323
	2.679
	
Table continues below
Median
	IQR
	Skewness
	Kurtosis
	
2.5
	2
	1.324
	2.649
	
3
	2
	0.862
	0.1509
	
3
	3
	0.7574
	0.08749
	
3
	3
	1.383
	1.831
	
2
	1.75
	2.063
	5.586
	
3
	3.5
	1.185
	0.9281

Diagnostics
Before we carry out ANOVA, we'd like to check some basic assumptions. For those purposes, normality and homoscedascity tests are carried out alongside several graphs that may help you with your decision on model's main assumptions.
Diagnostics
Univariate Normality
Method
	Statistic
	p-value
	
Lilliefors (Kolmogorov-Smirnov) normality test
	0.168
	3e-52
	
Anderson-Darling normality test
	18.75
	7.261e-44
	
Shapiro-Wilk normality test
	0.9001
	1.618e-20

So, the conclusions we can draw with the help of test statistics:
•	based on Lilliefors test, distribution of Internet usage in leisure time (hours per day) is not normal
•	Anderson-Darling test confirms violation of normality assumption
•	according to Shapiro-Wilk test, the distribution of Internet usage in leisure time (hours per day) is not normal
As you can see, the applied tests confirm departures from normality of the Internet usage in leisure time (hours per day).
Homoscedascity
In order to test homoscedascity, Bartlett and Fligner-Kileen tests are applied.
Method
	Statistic
	p-value
	
Fligner-Killeen test of homogeneity of variances
	1.123
	0.2892
	
Bartlett test of homogeneity of variances
	11.13
	0.0008509

When it comes to equality of variances, applied tests yield inconsistent results. While Fligner-Kileen test confirmed the hypotheses of homoscedascity, Bartlett's test rejected it.
Diagnostic Plots
Here you can see several diagnostic plots for ANOVA model:
•	residuals against fitted values
•	scale-location plot of square root of residuals against fitted values
•	normal Q-Q plot
•	residuals against leverages

ANOVA Summary
ANOVA Table
 
	Df
	Sum.Sq
	Mean.Sq
	F.value
	
gender
	1
	4.947
	4.947
	1.085
	
partner
	2
	31.21
	15.61
	3.424
	
gender:partner
	2
	3.038
	1.519
	0.3332
	
Residuals
	593
	2703
	4.558

Table continues below
 
	Pr..F.
	
gender
	0.2979
	
partner
	0.03324
	
gender:partner
	0.7168
	
Residuals

F-test for Gender is not statistically significant, which implies that there is no Gender effect on response variable. Effect of Relationship status on response variable is significant. Interaction between levels of Gender and Relationship status wasn't found significant (p = 0.717).
Post Hoc test
Results
After getting the results of the ANOVA, usually it is advisable to run a post hoc test to explore patterns that were not specified a priori. Now we are presenting Tukey's HSD test.
gender
 
	Difference
	Lower Bound
	Upper Bound
	
female-male
	-0.186
	-0.538
	0.165
	
Table continues below
 
	P value
	
female-male
	0.298

There are no categories which differ significantly here.
partner
 
	Difference
	Lower Bound
	
married-in a relationship
	-0.289
	-1.012
	
single-in a relationship
	0.371
	-0.061
	
single-married
	0.66
	-0.059
	
Table continues below
 
	Upper Bound
	P value
	
married-in a relationship
	0.435
	0.616
	
single-in a relationship
	0.803
	0.109
	
single-married
	1.379
	0.079

There are no categories which differ significantly here.
gender:partner
 
	Difference
	Lower Bound
	
female:in a relationship-male:in a relationship
	-0.014
	-0.777
	
male:married-male:in a relationship
	-0.073
	-1.25
	
female:married-male:in a relationship
	-0.577
	-1.877
	
male:single-male:in a relationship
	0.444
	-0.23
	
female:single-male:in a relationship
	0.264
	-0.545
	
male:married-female:in a relationship
	-0.059
	-1.266
	
female:married-female:in a relationship
	-0.563
	-1.89
	
male:single-female:in a relationship
	0.459
	-0.267
	
female:single-female:in a relationship
	0.279
	-0.574
	
female:married-male:married
	-0.504
	-2.105
	
male:single-male:married
	0.518
	-0.635
	
female:single-male:married
	0.338
	-0.899
	
male:single-female:married
	1.022
	-0.256
	
female:single-female:married
	0.842
	-0.512
	
female:single-male:single
	-0.18
	-0.955
	
Table continues below
 
	Upper Bound
	P value
	
female:in a relationship-male:in a relationship
	0.749
	1
	
male:married-male:in a relationship
	1.103
	1
	
female:married-male:in a relationship
	0.722
	0.801
	
male:single-male:in a relationship
	1.119
	0.412
	
female:single-male:in a relationship
	1.074
	0.938
	
male:married-female:in a relationship
	1.148
	1
	
female:married-female:in a relationship
	0.764
	0.83
	
male:single-female:in a relationship
	1.184
	0.461
	
female:single-female:in a relationship
	1.132
	0.938
	
female:married-male:married
	1.097
	0.946
	
male:single-male:married
	1.67
	0.794
	
female:single-male:married
	1.575
	0.971
	
male:single-female:married
	2.3
	0.201
	
female:single-female:married
	2.196
	0.481
	
female:single-male:single
	0.594
	0.986

There are no categories which differ significantly here.
Plot
Below you can see the result of the post hoc test on a plot.

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This report was generated with R (3.0.1) and rapport (0.51) in 3.431 sec on x86_64-unknown-linux-gnu platform.