[R] help interpreting aov results

[David Winsemius]

On Mar 31, 2012, at 4:52 AM, Kamakshaiah wrote:

> Dear Friends,
>
> I had performed anova test on certain data frame (Health Care
> Management) and got results [summary(aov)]. I am new to R and also
> some extent to Statistics. Can somebody help me how should I interpret
> these figures. I feel difficulty in interpreting values and respective
> rows and columns.
>
> The following is the result to which I request interpretation:
>
>> anova.stress$effects

Rather than trying to pull apart a summary.aov object when you admit  
that you don't really know what you are doing, you should instead  
first look at the output of functions (including the implicit `print`  
function that will run when you simply type the object's name at the  
console.)


>      (Intercept)          heavy.drinking       perceived.health
> life.satisfaction
>  -127.7707327310     66.6366413568     58.0918782595
> -6.9519755523     -0.7947641734
>
>     6.6881854290     13.3244486754     12.0570313711
> 14.1251305762      6.9407880977
>
>     7.7357329414     12.0627416985    -11.0900101005
> 1.2013513103      0.5663285592
>
> For example if I am to talk about the very first value
> -127.7707327310; what is this value is all about? and how it is
> significant with respect to column headings. What is the last column?
>
>> anova.stress$qr
> $qr
>     (Intercept)           heavy.drinking      perceived.health
> life.satisfaction
> 1  -3.8729833462 -122.69732336064 -208.29402114263  -523.79543588447
> 2   0.2581988897  103.70798417437   82.62779609135   202.14890930300
> 3   0.2581988897    0.20254726362   71.69122174008   185.07374705668
> 4   0.2581988897   -0.65720148871    0.21700481702     7.77881765537
> 5   0.2581988897   -0.35155751874    0.49658862352     0.16955330300
> 6   0.2581988897   -0.01705521136    0.07303486380     0.13797897217
> 7   0.2581988897   -0.11154070424   -0.09755282025     0.28674472780
> 8   0.2581988897   -0.01186602555    0.26925236164    -0.12042327743
> 9   0.2581988897    0.18891427276   -0.01418690772     0.42333040781
> 10  0.2581988897   -0.34383207690   -0.59291615659    -0.25206212540
> 11  0.2581988897   -0.18887930130    0.11689140713    -0.58071444279
> 12  0.2581988897    0.13363607942   -0.35718909148     0.34481294660
> 13  0.2581988897    0.19904444749   -0.30629424692    -0.18166608573
> 14  0.2581988897    0.21462454012    0.09912429448     0.02910278133
> 15  0.2581988897    0.27300895524   -0.05280046529    -0.19460726218
>
> I some how got idea (after studying) about QR, but here how should I
> interpret these values?

Trying to teach yourself statistics this way is a bit like smashing a  
watch with a hammer and then trying to understand how it works by  
looking at each fragment.


>
> $qraux
> [1] 1.258198890 1.151445509 1.139760525 1.291373419
>
> What are these values and how should I interpret them?

I confess that I have never asked myself that question. Attempting to  
answer the question proved surprisingly difficult. The most complete  
(?) description of that vector I could find is that it is "further  
information required to recover the orthogonal part of the  
decomposition". There is an answer in SO that uses the information,  
but as to an "interpretation" I am unable to construct one:

http://stackoverflow.com/questions/3031215/mystified-by-qr-q-what-is-an-orthonormal-matrix-in-compact-form


>
>> anova.stress$rank
> [1] 4
>
> what does it mean rank 4?

Matrices have ranks. It has a variety of meanings. It specifies the  
number of independent "dimensions" that the matrix will map onto. It  
is the number of eigenvectors.

>
> How can I know R and R square?

  summary.lm(anova.stress) will have both an 'r.squared' element and  
an adj.r.squared element. Generally the authors of R and the packages  
will provided extraction functions for the summary measures they  
consider useful.

>
> Apart from the above 1) how can I interpret fitted and residuals? Can
> I put the plot and show these values referring respective points in
> the graph?

Get yourself a good introductory book or use one of the many  
contributed documents on CRAN.

>
> I request somebody to help interpret the above things?
>
>
> Regards
>
> M. Kamakshaiah
> Assistant Professor, SCDL, Pune, India
--

David Winsemius, MD
West Hartford, CT