Using R in Nonparametric Statistics: Basic Table Analysis, Part One


Using R in Nonparametric Statistics: Basic Table Analysis, Part One

A Tutorial by D.M. Wiig
One of the most common methods displaying and analyzing data is through the use of tables. In this tutorial I will discuss setting up a basic table using R and performing an initial Chi-Square test on the table. R has an extensive set of tools for manipulating data in the form of a matrix, table, or data frame. The package ‘vcd’ is specifically designed to provide tools for table analysis. Before beginning this tutorial open an R session in your terminal window. You can install the vcd package using the following command:

>install.packages()

Depending on your R installation you may be asked to designate a CRAN reflector to download from or you may see a list of available packages in your default CRAN mirror. Select the package ‘vcd’ and download it. I might add at this point that if you are running the newest release of R, R-3.0.x you will have to reload a number of dependencies that will not work under the latest version of R. Any time you are installing a package and see the ‘non-zero exit status’ error message look the dialog over to see which packages have to be reinstalled to work with the newest version of R. If you are using R-2.xx.x the vcd package will install without any other re-installations.

In social science research we often use data that is nominal or ordinal in nature. Data is displayed in categories with associated frequency counts. In this tutorial I will use a set of hypothetical data that examines the relationship between income and political party identification among a group of registered voters. The variable “income” will be considered ordinal in nature and consists of categories of income in thousands as follows:

“< 25”; “25-50”; “51-100” and “>100”

Political party identification is nominal in nature with the following categories:

“Dem”, “Rep”, “Indep”

Frequency counts of individuals that fall into each category are numeric. In the first example we will create a table by entering the data as a data frame and displaying the results. When using this method it is a good idea to set up the table on paper before entering the data into R. This will help to make sure that all cases and factors are entered correctly. The table I want to generate will look like this:

party
income                 Dem Rep Indep
<25                             15    5      10
26-50                        20   15    15
51-100                     10   20    10
>100                            5    30    10

To enter the above into a data frame use the following on the command line:

> partydata <- data.frame(expand.grid(income=c(“<25″,”25-50″,”51-100″,”>100″), party=c(“Dem”,”Rep”, “Indep”)),count=c(15,20,10,5,5,15,20,30,10,15,10,10))
>

Make sure the syntax is exactly as shown and make sure the entire script is on the same line or has done an automatic return to the next line in your R console. When the command runs without error you can view the data by entering:

> partydata

The following output is produced:

> partydata
income                    party         count
1 <25                         Dem            15
2 25-50                    Dem            20
3 51-100                 Dem           10
4 >100                      Dem             5
5 <25                         Rep               5
6 25-50                    Rep              15
7 51-100                 Rep              20
8 >100                      Rep              30
9 <25                         Indep          10
10 25-50                 Indep          15
11 51-100              Indep          10
12 >100                   Indep          10
>

At this point the data is in frequency rather that table or matrix form. To view a summary of information about the data use the command:

>str(partydata)

You will see:

> str(partydata)
‘data.frame’: 12 obs. of 3 variables:
$ income: Factor w/ 4 levels “<25″,”26-50”,..: 1 2 3 4 1 2 3 4 1 2 …
$ party : Factor w/ 3 levels “Dem”,”Rep”,”Indep”: 1 1 1 1 2 2 2 2 3 3 …
$ count : num 15 20 10 5 5 15 20 30 10 15 …

To convert the data into tabular format use the command xtabs to perform a cross tabulation. I have named the resulting table “tabs”:

>tabs <- xtabs(count ~income + party, data=partydata)

To view the resulting table use:

> tabs
                                                        party
income                              Dem Rep Indep
<25                                        15      5        10
26-50                                   20      15      15
51-100                                10      20      10
>100                                       5       30      10
>

This produces a table in the desired format. To do a quick analysis of the table that produces a Chi-square statistic use the command:

> summary(tabs)

The output is

> summary(tabs)
Call: xtabs(formula = count ~ income + party, data = partydata)
Number of cases in table: 165
Number of factors: 2
Test for independence of all factors:
Chisq = 25.556, df = 6, p-value = 0.0002693
>

In future tutorials I will discuss many of the other resources that are available with the vcd package for manipulating and analyzing data in a tabular format.

 

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Using R in Nonparametric Statistics: Basic Table Analysis, Part Three, Using assocstats and collapse.table


A tutorial by D.M. Wiig

As discussed in a previous tutorial one of the most common methods displaying and analyzing data is through the use of tables. In this tutorial I will discuss setting up a basic table using R and exploring the use of the assocstats function to generate several commonly used nonparametric measures of association. The assocstats function will generate the association measures of the Phi-coefficient, the Contingency Coefficient and Cramer’s V, in addition to the Likelihood Ratio and Pearson’s Chi-Squared for independence. Cramer’s V and the Contigency Coefficient are commonly applied to r x c tables while the Phi-coefficient is used in the case of dichotomous variables in a 2 x 2 table.

To illustrate the use of assocstats I will use hypthetical data exploring the relationship between level of education and average annual income. Education will be measured using the nominal categories “High School”, “College”, and “Graduate”. Average annual income will be measured using ordinal categories and expressed in thousands:

“< 25”; “25-50”; “51-100” and “>100”

Frequency counts of individuals that fall into each category are numeric.

In the first example a 4 x 3 table created with hypothetical frequencies as shown below:

Income                                Education
(thousands)          High School   College   Graduate

<25                                    15                       8                  5

26-50                              12                       12                8

51-100                           10                       22                25

>100                                  5                       10                 32
The first table, table1, is entered into R as a data frame using the following commands:

#create 4 x 3 data frame
#enter table1 in frequency form
table1 <- data.frame(expand.grid(income=c(“<25″,”25-50″,”51-100″,”>100″), education=c(“HS”,”College”, “Graduate”)),count=c(15,12,10,5,8,12,22,10,5,8,25,32))

Check to make sure the data are in the right row and column categories. Notice that the data are entered in the ‘count’ list by columns.

> table1
income  education     count
1 <25             HS                  15
2 25-50        HS                  12
3 51-100     HS                 10
4 >100          HS                   5
5 <25             College         8
6 25-50        College        12
7 51-100     College        22
8 >100          College        10
9 <25             Graduate      5
10 25-50     Graduate      8
11 51-100   Graduate    25
12 >100       Graduate    32
>

If the stable structure looks correct generate the table, tab1, using the xtabs function:

> #create table tab1 from data.frame
> tab1 <- xtabs(count ~income + education, data=table1)
Show the table using the command:

>tab1
                               education
income         HS College Graduate
<25                   15     8             5
25-50             12     12           8
51-100          10     22          25
>100                 5     10          32
>
Use the assocstats function to generate measures of association for the table. Make sure that you have loaded the vcd package and the vcdExtras packages. Run assocstats with the following commands:

> assocstats(tab1)
X^2 df P(> X^2)
Likelihood Ratio 31.949 6 1.6689e-05
Pearson 32.279 6 1.4426e-05

Phi-Coefficient : 0.444
Contingency Coeff.: 0.406
Cramer’s V : 0.314
>

The measures show an association between the two variables. My intent is not to provide an analysis of how to evaluate each of the measures. There are excellent sources of documention on each measure of association in the R CRAN Literature. Since the Phi-coefficient is designed primarily to measure association between dichotomous variables in a 2 x 2 table,collapse the 4 x 3 table using the collapse.table function to get a more accurate Phi-coefficient. Since we want to go from a 4 x 3 to a 2 x 2 table we essentially collapse the table in two stages. The first stage collapses the table to a 2 x 3 table by combining the “<25” with the “25-50” and the “51-100” with the “>100” categories of income.

The resulting 2 x 3 table is seen below:

Education
Income                High School      College        Graduate

<50                                 27                        20                    13

>50                                15                        32                     57

To collapse the table use the R function collapse.table to combine the “<25” and “26-50” categories and the “50-100” and “>100” categories as discussed above:

> #collapse table tab1 to a 2 x 3 table, table2
> table2 <-collapse.table(tab1, income=c(“<50″,”<50″,”>50″,”>50″))

View the resulting table, table2, with:

> table2
                                education
income          HS        College       Graduate
<50                  27             20                   13
>50                  15             32                   57
>

Now collapse the table to a 2 x 2 table by combining the “College” and “Graduate” columns:
> #collapse 2 x 3 table2 to a 2 x2 table, table3
> table3 <-collapse.table(table2, education=c(“HS”,”College”,”College”))

View the resulting table, table3, with:

> table3
                               education
income             HS             College
<25                     27                  33
>100                  15                  89
>

Use the assocstats function to evaluated the 2 x 2 table:

> #use assocstats on the 2 x 2 table, table3
> assocstats(table3)
X^2 df P(> X^2)
Likelihood Ratio 18.220 1 1.9684e-05
Pearson 18.673 1 1.5519e-05

Phi-Coefficient : 0.337
Contingency Coeff.: 0.32
Cramer’s V : 0.337
>

There are many other table manipulation function available in the R vcd and vcdExtras packages and well as other packages to provide analysis of nonparametric data. This series of tutorials hopefully serves to illustrate some of the more basic and common table functions using these packages. The next tutorial looks at the use of the ca function to perform and graph the results of a basic Correspondence Analysis.