[R] is this an ANOVA ?

From: Ubuntu Diego <ubuntu.diego_at_gmail.com>
Date: Tue, 12 Apr 2011 20:10:26 -0400

Hi all,

	I have a very easy questions (I hope). I had measure a property of plants, growing in three different substrates (A, B and C). The rest of the conditions remained constant. There was very high variation on the results. 
	I want to do address, whether there is any difference in the response (my measurement) from substrate to substrate?

x<-c('A','A','A','A','A','B','B','B','B','B','C','C','C','C','C') # Substrate type
y <- c(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15) # Results of the measurement MD<-data.frame(x,y)

        I wrote a linear model for this:


        This is the output:         

lm(formula = y ~ x, data = MD)


       Min 1Q Median 3Q Max
-2.000e+00 -1.000e+00 5.551e-17 1.000e+00 2.000e+00


            Estimate Std. Error t value Pr(>|t|)    
(Intercept)   3.0000     0.7071   4.243 0.001142 ** 
xB            5.0000     1.0000   5.000 0.000309 ***
xC           10.0000     1.0000  10.000 3.58e-07 ***


Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1

Residual standard error: 1.581 on 12 degrees of freedom Multiple R-squared: 0.8929, Adjusted R-squared: 0.875 F-statistic: 50 on 2 and 12 DF, p-value: 1.513e-06

	I conclude that there is an effect of substrate type (x). 
	NOW the questions :
		1) Do the fact that the all p-values are significant means that all the groups are different from each other ?
		2) Is there a (easy) way to plot,  mean plus/minus 2*sd for each substrate type ? (with asterisks denoting significant differences ?)


platform       x86_64-apple-darwin9.8.0     
arch           x86_64                       
os             darwin9.8.0                  
system         x86_64, darwin9.8.0          
major          2                            
minor          11.1                         
year           2010                         
month          05                           
day            31                           
svn rev        52157                        
language       R                            
version.string R version 2.11.1 (2010-05-31)

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