CGPfunctions

Vignette Info

The ANOVA family of statistical techniques that allow us to compare mean differences of one outcome (dependent) variable across two or more groups (levels) of one or independent variables (factor). It is also true that ANOVA is a special case of the GLM or regression models so as the number of levels increase it might make more sense to try one of those approaches. The 2 Way ANOVA allows for comparisons of mean differences across 2 independent variables factors and varying numbers of levels.

The Plot2WayANOVA function conducts a classic analysis using existing R functions and packages in a sane and defensible manner not necessarily in the one and only manner.

Scenario and data

Imagine that you are interested in understanding whether a car’s fuel efficiency (mpg) varies based upon the type of transmission (automatic or manual) and the number of cylinders the engine has. Let’s imagine that the mtcars data set is actually a random sample of 32 cars from different manufacturers and use the mean mpg by am and cyl to help inform our thinking. While we expect variation across our sample we’re interested in whether the differences between the means by grouping of transmission type and cylinders is significantly different than what we would expect in random variation across the data.

In simplistic terms we want to know whether am matters, cyl matters or if it depends on the interaction of the two. It’s this interaction term that typically confuses novices or is difficult to “see”. That’s where a good interaction graph can hopefully play a key role, and that’s what the Plot2WayANOVA focuses on.

There’s no lack or tools or capabilities in base R or in the many packages to do this task. What this function tries to do is pull together the disparate pieces with a set of sane defaults and a simple interface to work with it. At its simplest you would require the library and then enter this command:

Plot2WayANOVA(mpg~am*cyl, mtcars) which lays our question out in R’s vernacular with a formula and a dataframe. Optionally we can specify a different confidence level and choose a line or a bar graph.

“Under the hood”, however there’s a lot of nice features at work.

1. Some basic error checking to ensure a valid formula and dataframe. The function accepts only a fully crossed formula to check for interaction term
2. It ensures the dependent (outcome) variable is numeric and that the two independent (predictor) variables already are or can be coerced to factors – the user is warned on the console if there are problems
3. A check is conducted to see if any of the variables of interest have missing cases – the user is warned on the console if there are problems
4. A summarized table of means, standard deviations, standard errors of the means, confidence intervals, and group sizes for each of the crossed combinations in our example that’s 6 groupings 3 levels of cylinder and 2 levels of automatic or manual
5. In addition to the classic ANOVA table eta squared \(\eta^2\) is calculated and appended as an additional column. If you’re unfamiliar with them and want to know more especially where the numbers come from I recommend a good introductory stats text. As noted earlier I recommend Learning Statistics with R LSR see Table 14-1 on page 432.
6. The Homogeneity of Variance assumption is tested with Brown-Forsythe
7. The normality assumption is tested with Shapiro-Wilk

Example of using the function

Plot2WayANOVA(mpg~am*cyl, mtcars)

#> # A tibble: 4 x 8
#>   Source       Df `Sum Sq` `Mean Sq` `F value`       p sigstars `eta sq`
#>   <fct>     <int>    <dbl>     <dbl>     <dbl>   <dbl> <chr>       <dbl>
#> 1 am            1     36.8     36.8       4.00  0.0560 .          0.0330
#> 2 cyl           2    456.     228.       24.8   0.     ***        0.405 
#> 3 am:cyl        2     25.4     12.7       1.40  0.269  ""         0.0230
#> 4 Residuals    26    239.       9.19     NA    NA      <NA>       0.212 
#> # A tibble: 6 x 9
#> # Groups:   am [2]
#>   am    cyl   TheMean TheSD TheSEM CIMuliplier LowerBound UpperBound     N
#>   <fct> <fct>   <dbl> <dbl>  <dbl>       <dbl>      <dbl>      <dbl> <int>
#> 1 0     4        22.9 1.45   0.839        4.30       19.3       26.5     3
#> 2 0     6        19.1 1.63   0.816        3.18       16.5       21.7     4
#> 3 0     8        15.0 2.77   0.801        2.20       13.3       16.8    12
#> 4 1     4        28.1 4.48   1.59         2.36       24.3       31.8     8
#> 5 1     6        20.6 0.751  0.433        4.30       18.7       22.4     3
#> 6 1     8        15.4 0.566  0.400       12.7        10.3       20.5     2
#> Levene's Test for Homogeneity of Variance (center = median)
#>       Df F value  Pr(>F)  
#> group  5   2.736 0.04086 *
#>       26                  
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#>  Shapiro-Wilk normality test
#> 
#> data:  MyAOV_residuals
#> W = 0.96277, p-value = 0.3263

Credits

Many thanks to Dani Navarro and the book > (Learning Statistics with R) whose etaSquared function was the genesis of neweta.

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