h2(#description). Description An ANOVA report with table of descriptives, diagnostic tests and ANOVA-specific statistics. h3(#introduction). 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. h3(#model-overview). 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. h3(#descriptives). 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. h4(#frequency-table). 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
h4(#descriptive-statistics). 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.
Table continues below
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
Skewness Kurtosis
0.9443 0.9858
1.398 1.87
h3(#diagnostics). 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. h4(#diagnostics-1). Diagnostics h5(#univariate-normality). 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). h5(#homoscedascity). 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. h4(#diagnostic-plots). 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 "!plots/ANOVA-5.png!":plots/ANOVA-5-hires.png h3(#anova-summary). ANOVA Summary h4(#anova-table). 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. h4(#post-hoc-test). Post Hoc test h5(#results). Results After getting the results of the ANOVA, usually it is advisable to run a "post hoc test":http://en.wikipedia.org/wiki/Post-hoc_analysis to explore patterns that were not specified a priori. Now we are presenting "Tukey's HSD test":http://en.wikipedia.org/wiki/Tukey%27s_range_test. h6(#gender). gender
Table continues below
  Difference Lower Bound Upper Bound
*female-male* -0.206 -0.543 0.132
  P value
*female-male* _0.232_
There are no categories which differ significantly here. h5(#plot). Plot Below you can see the result of the post hoc test on a plot. "!plots/ANOVA-6.png!":plots/ANOVA-6-hires.png h2(#description-1). Description An ANOVA report with table of descriptives, diagnostic tests and ANOVA-specific statistics. h3(#introduction-1). 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. h3(#model-overview-1). 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. h3(#descriptives-1). 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. h4(#frequency-table-1). 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
h4(#descriptive-statistics-1). 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.
Table continues below
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
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
h3(#diagnostics-2). 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. h4(#diagnostics-3). Diagnostics h5(#univariate-normality-1). 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). h5(#homoscedascity-1). 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. h4(#diagnostic-plots-1). 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 "!plots/ANOVA-7.png!":plots/ANOVA-7-hires.png h3(#anova-summary-1). ANOVA Summary h4(#anova-table-1). ANOVA Table
Table continues below
  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
  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). h4(#post-hoc-test-1). Post Hoc test h5(#results-1). Results After getting the results of the ANOVA, usually it is advisable to run a "post hoc test":http://en.wikipedia.org/wiki/Post-hoc_analysis to explore patterns that were not specified a priori. Now we are presenting "Tukey's HSD test":http://en.wikipedia.org/wiki/Tukey%27s_range_test. h6(#gender-1). gender
Table continues below
  Difference Lower Bound Upper Bound
*female-male* -0.186 -0.538 0.165
  P value
*female-male* _0.298_
There are no categories which differ significantly here. h6(#partner). partner
Table continues below
  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
  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. h6(#genderpartner). gender:partner
Table continues below
  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
  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. h5(#plot-1). Plot Below you can see the result of the post hoc test on a plot. "!plots/ANOVA-8.png!":plots/ANOVA-8-hires.png
This report was generated with "R":http://www.r-project.org/ (3.0.1) and "rapport":https://rapporter.github.io/rapport/ (0.51) in _3.431_ sec on x86_64-unknown-linux-gnu platform. !images/logo.png!