R: how can I create a table with mean and sd according to experimental group alongside p-values?

Question

I know how I can do all that for individual variables but I need to report this information for a large number of variables and would like to know if there is an efficient w

Answer 1

First let's make some example data. For each sample, we have a unique ID, its experimental group, and some variables for which we want to calculate the mean and SD.

## Make a data frame called "Data" with five columns
Data <- as.data.frame(cbind(1:100, sample(1:2), rnorm(100), rnorm(100), rnorm(100), rnorm(100)))
names(Data) <- c("ID", "Group", "V1", "V2", "V3", "V4")

## Now we will take a peak at the top of our data frame
> head(Data)

  ID Group         V1         V2         V3         V4
1  1     2  0.3681539 -0.5008400  1.2060665 -0.7352376
2  2     1 -0.1043180  2.2038190 -1.4367898  2.1961246
3  3     2 -0.2720279 -0.5923554 -1.4628190 -1.8776453
4  4     1 -2.3299662 -0.1216227  0.4200776  1.5504020
5  5     2 -0.3670578 -1.5903221 -0.6287083 -1.0543262
6  6     1  0.4840047 -0.3181554 -1.4596980 -0.4261827

Now we can run a for loop through the variables, pull their means and SDs and p values, and dump them all in an object called "Results".

## Define object which will receive our results
Results <- NULL
Results <- as.data.frame(Results)

## Open for loop
for (i in 3:6) {

## Run the t.test() and save it in a temporary object
temp <- t.test(Data[which(Data$Group == 1), i], Data[which(Data$Group == 2), i])

## Put the name of our variable in our results object
Results[i-2,1] <- names(Data)[i]

## Group 1 mean and SD
Results[i-2,2] <- temp$estimate[1]
Results[i-2,3] <- sd(Data[which(Data$Group == 1), i])

## Group 2 mean and SD
Results[i-2,4] <- temp$estimate[2]
Results[i-2,5] <- sd(Data[which(Data$Group == 2), i])

## P value for difference
Results[i-2,6] <- temp$p.value

rm(temp)
}

Now we can make our results pretty and print them.

## Add column names
names(Results) <- c("Variable", "Group.1.Mean", "Group.1.SD", "Group.2.Mean", "Group.2.SD", "P.Value")

## View our results
> Results

  Variable Group.1.Mean Group.1.SD Group.2.Mean Group.2.SD   P.Value
1       V1   0.21544390  0.9404104  -0.01426226  1.0570324 0.2537820
2       V2   0.26287585  1.0048291   0.22992285  0.9709686 0.8679038
3       V3  -0.06112963  0.9855287   0.17423440  1.0198694 0.2434507
4       V4   0.33848678  0.9360016   0.07905932  0.9106595 0.1632705

Answer 2

In a data object like that offered by Alexander:

 aggregate( . ~ Group, FUN=function(x) c(mn=mean(x), sd=sd(x)), data=Data[-1])
# Output
  Group       V1.mn       V1.sd       V2.mn       V2.sd
1     1  0.05336901  0.85468837  0.06833691  0.94459083
2     2 -0.01658412  0.97583110 -0.02940477  1.11880398
       V3.mn      V3.sd       V4.mn       V4.sd
1 -0.2096497  1.1732246  0.08850199  0.98906102
2  0.0674267  0.8848818 -0.11485148  0.90554914

The data argument omits the ID column because you only want the results on the data columns. The request for a collection of p-values can be accomplished with:

 sapply(names(Data)[-(1:2)], function(x) c( 
                   Mean.Grp1 = mean(Data[Data$Group==1,x]), 
                   Mean.Grp2 = mean(Data[Data$Group==2,x]), 
                   `p-value`= t.test(Data[Data$Group==1, x], 
                                     Data[Data$Group==2,x])$p.value )
          )
#---------------------------
                   V1          V2         V3          V4
Mean.Grp1  0.05336901  0.06833691 -0.2096497  0.08850199
Mean.Grp2 -0.01658412 -0.02940477  0.0674267 -0.11485148
p-value    0.70380932  0.63799544  0.1857743  0.28624585

If you wanted to add the SD's to that output the strategy seems obvious. You should note the back-quoting of the "p-value" name. Minus signs are syntactically "active" and would get interpreted as functions if not enclosed in quotes.

Answer 3

Well the code proposed does not work unless you transpose table with p-values.

Answer 4

The tables package makes everything in this except the p-values easy, and the p-values are doable. Here is a quick example:

> library(tables)
> iris2 <- iris[ iris$Species != 'versicolor', ]
> iris2$Species <- factor(iris2$Species)
> tmp <- tabular( Petal.Width+Petal.Length + Sepal.Width+Sepal.Length ~ Species* (mean+sd), data=iris2 )
> 
> tmp.p <- sapply( names(iris2)[1:4], function(x) t.test( iris2[[x]] ~ iris2$Species )$p.value )
> 
> tmp

              setosa        virginica       
              mean   sd     mean      sd    
 Petal.Width  0.246  0.1054 2.026     0.2747
 Petal.Length 1.462  0.1737 5.552     0.5519
 Sepal.Width  3.428  0.3791 2.974     0.3225
 Sepal.Length 5.006  0.3525 6.588     0.6359

> tmp2 <- cbind(tmp, tmp.p)
> colnames(tmp2) <- c('Setosa Mean','Setosa SD', 'Virginica Mean','Virginica SD',
+ 'P-value')
> tmp2
             Setosa Mean Setosa SD Virginica Mean Virginica SD P-value     
Sepal.Length 0.246       0.1053856 2.026          0.2746501    3.966867e-25
Sepal.Width  1.462       0.173664  5.552          0.5518947    4.570771e-09
Petal.Length 3.428       0.3790644 2.974          0.3224966    9.269628e-50
Petal.Width  5.006       0.3524897 6.588          0.6358796    2.437136e-48

#### Edit ####

It looks like newer versions of tabular do more checks which makes the cbind approach not work any more (and this could be a good thing, since I am not sure that it was properly matching the values if the ordering was different). I did not find a simple way to still do this using cbind (though you could convert to a matrix, pad the rows for the headers, then cbind).

Here is another approach that works, it is still a bit of a kludge since it hardcodes the species variable in the function (and the function would therefore have to be updated specifically for each table it is used in):

library(tables)
iris2 <- iris[ iris$Species != 'versicolor', ]
iris2$Species <- factor(iris2$Species)
P.value <- function(x) t.test(x ~ iris2$Species)$p.value
tmp <- tabular( Petal.Width+Petal.Length + Sepal.Width+Sepal.Length ~ Species* (mean+sd) + P.value, data=iris2 )
tmp