R Analysis
In this section we shall demonstrate how to do some basic data analysis on data in a dataframe.
Contents
Basic Data Analysis
The easiest way to find basic summary statistics on your variables contained in a dataframe is the following command:
summary(mydata)
You will find that this will provide a range of summary statistics for each variable (Minimum and Maximum, Quartiles, Mean and Median). If the dataframe contains a lot of variables, as the dataframe based on mroz.xls, this output can be somewhat lengthy. Say you are only interested in the summary statistics for two of the variables hours and husage, then you would want to select these two variables only. The way to do that is the following:
summary(mydata[c("hours","husage")])
This will produce the following output:
hours husage
Min. : 0.0 Min. :30.00
1st Qu.: 0.0 1st Qu.:38.00
Median : 288.0 Median :46.00
Mean : 740.6 Mean :45.12
3rd Qu.:1516.0 3rd Qu.:52.00
Max. :4950.0 Max. :60.00
Another extremely useful statistic is the correlation between different variables. This is achieved with the cor( ) function. Let's say we want the correlation between educ, motheduc, fatheduc, then we use in the same manner:
cor(mydata[c("educ","motheduc","fatheduc")])
resulting in the following correlation matrix
educ motheduc fatheduc educ 1.0000000 0.4353365 0.4424582 motheduc 0.4353365 1.0000000 0.5730717 fatheduc 0.4424582 0.5730717 1.0000000
Selecting variables
In what we did above we selected a small number of variables from a larger dataset (saved in a dataframe), the way we did that was to call the dataframe and then in square brackets indicate which variables we wanted to select. To understand what this does, go to your console and call
test1 = mydata[c("hours")]
which will create a new dataframe which includes only the one variable hours. This is very useful, as some functions need to be applied to a dataframe (see for example the "empirical" function in R_Packages).
There is another way to select the hours variable from the dataframe. Try:
test2 = mydata$hours
This will also select the hours variable. But if you check your environment tab you will see that the data have now been saved in a different type of R object, a list or vector. Some functions will require such an object as input (see for example the "sd" function below).
Dealing with missing observations
So far all is honky dory. Let's show some difficulties/issues. Consider we want to calculate the correlation between educ, wage
cor(mydata[c("educ","wage")])
The output we get is:
educ wage educ 1 NA wage NA 1
The reason for R's inability to calculate a correlation between these two variables can be seen here:
> summary(mydata[c("hours","wage")])
hours wage
Min. : 0.0 Min. : 0.1282
1st Qu.: 0.0 1st Qu.: 2.2626
Median : 288.0 Median : 3.4819
Mean : 740.6 Mean : 4.1777
3rd Qu.:1516.0 3rd Qu.: 4.9707
Max. :4950.0 Max. :25.0000
NA's :325
The important information is that the variable wage has 325 missing observations (NA). It is not immediately obvious how to tackle this issue. We need to consult either Dr. Google or the R help function. The latter is done by typing ?con. The help will pop up in the "Help" tab on the right hand side. You will need to read through it to find a solution to the issue. Frankly, the clever people who write the R software are not always the most skilful in writing clearly and it is often most useful to go to the bottom of the help where you can usually find some examples. If you do that you will find that the solution to our problem is the following:
> cor(mydata[c("educ","wage")],use = "complete")
educ wage
educ 1.0000000 0.3419544
wage 0.3419544 1.0000000
It is perhaps worth adding a word of explanation here. cor( ) is what is called a function. It needs some inputs to work. The first input is the data for which to calculate correlations, mydata[c("educ","wage")]. Most functions also have what are called parameters. These are like little dials and levers to the function which change how the function works. And one of these levers can be used to tell the function to only use observations that are complete, i.e. don't have missing observations, use = "complete". Read the help function to see what over levers are at your disposal.
Using Subsets of Data
Often you will want to perform some analysis on a subset of data. The way to do this in R is to use the subset function, together with a logical (boolean) statement. I will first write down the statement and then explain what it does:
mydata.sub1 <- subset(mydata, hours > 0)
On the left hand side of <- we have a new object named mydata.sub1. On the right hand side of <- we can see how that new object is defined. We are using the function subset() which has been designed to select observations and/or columns from a dataframe such as mydata. This function needs at least two inputs. The first input is the dataframe from which we are selecting observations and variables. Here we are selecting from mydata. The second element indicates which observations/rows we want to select. hours > 0 tells R to select all those observations for which the variable hours is larger than 0.
Often (if not always) you will not remember how exactly a function works. The internet is then usually a good source, but in your console you could also type ?subset which would open a help function. There you could see that you could add a third input to the subset function which would indicate which variables you want to include (e.g. select = c(hours, wage) which would only select these two variables). By not using this third input we indicate to R that it should select all variables in mydata.
Logical/Boolean Statements
The way in which we selected the observations, i.e. by using the logical statement hours > 0 is worth dwelling on for a moment. These type of logical statements create variables in R that are given the logical data type. Sometimes these are also called boolean variables.
To see what is special about these go to your console and just type something like 5>9 and then press ENTER. You will realise that R is a clever little thing and will tell you that in fact 5 is not larger than 9 by returning the answer FALSE. When provided R with hours > 0, the software, for all our 753 observations, checks whether the value of the hour variable is larger than 0 or not. It will create a variable (vector) with 753 entries and in each entry there will be either a hours >TRUE or hours >FALSE, depending on whether the respective value is larger than 0 or not.
You can create logical variables on the basis of more complicated logical statements as well. You can combine statements by noting that & represents AND, | represents OR and == checks whether two things are equal. To figure out how these work, try the following statements in your console and see whether you can guess the right answers:
(3 > 2) & (3 > 1)
(3 > 2) & (3 > 6)
(3 > 5) & (3 > 6)
(3 > 2) | (3 > 1)
(3 > 2) | (3 > 6)
(3 > 5) | (3 > 6)
((3 == 5) & (3 > 2)) | (3 > 1)
Being comfortable with these logical statements will make the life of every programmer much easier.
Some basic summary statistics
There are a number of basic summary statistics that are part of every basic data toolbox. Being able to calculate means, medians and standard deviations for a set of data. Let's take a particular variable, the wage variable. Try any of the following three commands:
mean(mydata$wage) # Sample mean
median(mydata$wage) # Median
sd(mydata$wage) # Sample standard deviation
var(mydata$wage) # Sample variance
min(mydata$wage) # minimum
max(mydata$wage) # maximum
If you try any of these you will find an unpleasant NA as a result. Why is this? If you look again at the wage data you will see that there are missing data in here. Now check the details of any of your function by, say, typing ?sd into the console. reading through the help function you will find that you will need to add the parameter na.rm=TRUE to your function call. So:
sd(mydata$wage,na.rm=TRUE)
will deliver the sample standard deviation of 3.310282.
