# Using R: Random Sample Selection and One-Way ANOVA

A tutorial by Douglas M. Wiig

In the previous tutorial we looked at the hypothesis that one’s outlook on life is influenced by the amount of education attained. Using the GSS 2014 data file we looked at the education variable ‘educ’, and the outlook on life variable ‘life’, a measure of outlook on life as ‘DULL’, ‘ROUTINE’, or ‘EXCITING.’ We selected a subset for each response category and found that there appeared to be
differences among the mean level of education measured in years for each of the categories of outlook on life. To further examine this we will first randomly select a sample from the data file, look at the
mean education for each category of outlook on life, and evaluate the means using simple one-way ANOVA.

To randomly select a sample from a population of values we can use the sample() function. There are a number of options and variations of the function that are beyond the scope of this tutorial. Since the
variable ‘educ’ is measured in years we can use the sample.int() function which is designed for use with integer values. The general format of the function is:

sample.int(n, size = n, replace = FALSE)

where: n = the size of population the sample is from
size = the size of the sample
replace = FALSE if sampling without replacement; TRUE if sampling with replacement

For this example I will select a sample of n=500 without replacement from the data file containing a total of 2538 cases. The sample data is loaded into a data matrix as it is selected. This will be
accomplished in two steps. In the first step we will load the sample.int() function with the values to use for selecting the sample and put the vector in ‘randsamp2. The code is:

randsamp2 <- sample.int(2538, size=500, replace=FALSE)

To select the sample make sure that make sure that the GSS2014 data file is loaded into the R environment. I previously loaded the data file into a data frame ‘gss14.’  To select the sample and load
it into a data frame ‘randgss2’ the code is:

randgss2 <- gss14[randsamp2,]

Once the sample has been generated we can look at the mean years of education for each of the three responses for outlook on life. We do this by selecting a subset for each response. Use the following
code:

###################################################
#look at educ means by life by selecting 3 subsets from randgss2
###################################################
life12 <- subset(randgss2, life == “DULL”, select=educ)
life22 <- subset(randgss2, life == “ROUTINE”, select=educ)
life32 <- subset(randgss2, life == “EXCITING”, select=educ)

Now run summary statistics for each subset to look at the means:

summary(life12)
summary(life22)
summary(life32)

We can now see that the means are as follows:

life12 = 13.0
life22 = 13.29
life 32 = 14.51

and we can generate a summary visual of the differences among the three subsets by doing a simple boxplot using:

###################################################
# do boxplots of the subsets to visualize differences
#boxplot using educ and life variables from the ‘randgss2’ data #frame
###################################################
boxplot(randgss2\$educ ~ randgss2\$life, main=”Education and View on Life n = 500″, xlab=”View of Life”,ylab=”Years of Education”)

The following graph will result:

As can be seen above there does appear to be a difference among these means, particularly for those who see life as ‘DULL.’ To see if these differences are significant an ANOVA will be run using the
simple one way ANOVA function aov(). The basic function is:
aov(formula, data = NULL)For our example we use:

model2 <- aov(educ ~ life, data=randgss2)

which analyzes the mean education by category of outlook on life using the randgss2 sample of n=500. The results are stored in ‘model2.’ The output from this operation is shown using the summary() function. This produces the following output:

summary(model2)

Df Sum Sq Mean Sq F value Pr(>F) life
2  171.5    85.77     10.42 4.08e-05 ***
Residuals  332     2732.2  8.23

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
165 observations deleted due to missingness

This output shows that at least one of the means differs significantly from the others. To test this difference further we can use a pair-wise comparison of means to see which means differ significantly
from each other. There are several options available. We will use a basic Tukey HSD comparison. This is accomplished using:

##################################################
#run HSD on sample
TukeyHSD(model2)
##################################################

producing the following output:

Tukey multiple comparisons of means
95% family-wise confidence level

Fit: aov(formula = educ ~ life, data = randgss2, projections = TRUE)

\$life                               diff                     lwr                upr                    p adj
ROUTINE-EXCITING -1.074404 -1.833686 -0.31512199  .0027590
DULL-EXCITING          -2.729412 -4.447386 -1.01143754  .0006325
DULL-ROUTINE           -1.655008 -3.384551 0.07453525 00640910

By looking at the p value for each comparison it can be seen that both the ROUTINE-EXCITING and DULL-EXCITING means differ significantly at p ≤ .05

I might point out that if a researcher was using the GSS 2014 data file as we used here there would need to be more data preparation prior to running any analysis. For example, there is a fair amount of
missing data as indicated by NA in the raw data file. The missing data would need to be handled in some way. R has numerous functions and packages that can assist in resolving missing data issues of
various types, but a discussion of these is a subject for a future tutorial.
8/7/15                   Douglas M. Wiig                    http://dmwiig.net

# R Tutorial: Using R to Analyze the NORC GSS2014 Database, Selecting Subsets and Comparing Means Using Student’s t Test

R Tutorial Part Three: Selecting Subsets and Comparing Means Using an Independent Sample t Test

A tutorial by Douglas M. Wiig

As discussed in previous segments of this tutorial, for anyone interested in researching social science questions there is a wealth of survey data available through the National Opinion Research Center (NORC) and its associated research universities. The Center has been conducting a national survey each year since 1972 and has compiled a massive database of data from these surveys. Most if not all of these data files can be accessed and downloaded without charge. I have been working with the 2014 edition of the data and for all part of this tutorial will use the GSS2014 data file that is available for download on the Center’s web site. (See the NORC main website at http://www.norc.org/Research/Projects/Pages/general-social-survey.aspx and at http://www3.norc.org/GSS+Website ).

`Accessing and loading the NORC GSS2014 data set was discussed in part one of this tutorial. Refer to it if you need specific information on downloading the data set in STATA or SPSS format.  In this segment we will use the subset function to select a desired set of cases from all of the cases in the data file that meet certain criteria.  As indicated in my previous tutorial the GSS2014 data set contains a total of 2588 cases and 866 variables.`
```Before starting this segment of the tutorial be sure that the foreign package is installed and loaded into your R session.  Import the GSS 2014 data file and load it into the data frame ‘Dataset’ using:

########################################################
#import GSS2014 file in SPSS .sav format
#uses foreign package
########################################################
require(foreign)
use.value.labels=TRUE, max.value.labels=Inf, to.data.frame=TRUE)```

###########################################################

In the previous segment of this tutorial we started to investigate whether or not an individual’s education had an effect on their response to a NORC survey item dealing with abortion. The item asked respondents to either ‘AGREE’ or ‘DISAGREE’ with the statement ‘A women should be allowed to obtain an abortion under any circumstances.’ We selected a subset of all of the respondents who answered ‘AGREE’ and a second subset of all the respondents who answered ‘DISAGREE’ using the following code:

##############################################

#select subset from Dataset and write to data frame SS1

```###################################################
SS1 <- subset(Dataset, abany == "YES", select=educ)```

View(SS1)

#######################################################

```######################################################
#select subset from Dataset and write to data frame SS2
######################################################
SS2 <- subset(Dataset, abany == "NO", select=educ)
View(SS2)```

A mean number of years of education can be calculated for each of the subsets using the following:

#calculate descriptive statistics for SS1 and SS2

####################################################

summary(SS1)

summary(SS2)

####################################################

Output from the above for SS1 is:

> summary(SS1)

educ

Min. : 0.0

1st Qu.:12.0

Median :15.0

Mean :14.6

3rd Qu.:16.0

Max. :20.0

Output for SS2 is:

> summary(SS2)

educ

Min. : 0.00

1st Qu.:12.00

Median :12.00

Mean :12.93

3rd Qu.:15.00

Max. :20.00

NA’s :1

As seen above there is a difference in mean years of education for the two subsets. We can use a two independent sample t test to determine whether or not the difference is large enough to not be due to chance.

In this tutorial I will use the Student’s t test function t.test that is found in the stats package. The function is used in the following form:

t.test =(x,y, alternative = c(“two.sided”, “less”, “greater”), mu=0, paired = FALSE, var.equal = FALSE, conf.level = .95)

where x and y = numeric vectors of data values

alternative = specification of a one-tailed or two-tailed test

mu = 0 specification that true difference between means is zero

paired = FALSE specification of a two independent sample test; if TRUE a paired samples test will be used

var.equal = specification of equal variances of the two samples; if TRUE the pooled variance is used otherwise a Welsh approximation of degrees of freedom is used

conf.level = confidence level of the interval

For further information see the documentation in CRAN help files for the function t.test().

Using the vectors selected from the dataset SS1, and SS2 the t test is performed using:

###########################################################

#perform a t test to compare sample means

#########################################################

t.test(SS1,SS2, alternative = c(“two.sided”), mu=0, paired=FALSE, var.equal = TRUE, conf.level = .95)

###########################################################

Resulting in output of:

```        Two Sample t-test

data:  SS1 and SS2
t = 11.1356, df = 1650, p-value < 2.2e-16
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
1.369673 1.955333
sample estimates:
mean of x mean of y
14.59517  12.93267 ```

We can see that the difference between the mean years of education for the ‘YES’ and the ‘NO’ samples is significant at an alpha level of p=.05. Subsets can also be used to compare means involving more than two samples and using simple one-way Analysis of Variance. This will be covered in the next part of the tutorial.

# R Tutorial: Using the NORC GSS2014 Data File, Creating and Using Subsets

```R Tutorial:  Using the NORC GSS2014 data file, creating and using subsets

By Douglas M. Wiig
```

As discussed in the first part of this tutorial, for anyone interested in researching social science questions there is a wealth of survey data available through the National Opinion Research Center (NORC) and its associated research universities. The Center has been conducting a national survey each year since 1972 and has compiled a massive database of data from these surveys. Most if not all of these data files can be accessed and downloaded without charge. I have been working with the 2014 edition of the data and for all part of this tutorial will use the GSS2014 data file that is available for download on the Center’s web site. (See the NORC main website at http://www.norc.org/Research/Projects/Pages/general-social-survey.aspx and at http://www3.norc.org/GSS+Website ).

```Accessing and loading the NORC GSS2014 data set was discussed in part one of this tutorial. Refer to it if you need specific information on downloading the data set in STATA or SPSS format.  In this segment we will  use the subset function to select a desired set of cases from all of the cases in the data file that meet certain criteria.  As indicated in my previous tutorial the GSS2014 data set contains a total of 2588 cases and 866 variables.

One of the areas surveyed by NORC each year deals with attitudes toward abortion. One of the questions simply asks respondents if they '...approve of abortion under any circumstances.'  The response is either YES or NO to this question.  Let's assume a researcher is interested in investigating whether or not education has an effect on how the respondent answers the question.

To look at this hypothesis we can use the abortion attitude variable mentioned above, 'abany', and an education variable 'educ' which measures education as the actual number of years of education.  Twelve years of education would be a high school graduate for example, and 16 years would be a college graduate.  We can select a subset of all respondents who indicated 'YES' on the survey question and then generate a mean years of education for this subset.  We can then select a subset of all respondents who indicated 'NO' on the question and calculate a mean years of education for the second subset.

Before starting this code segment be sure that the foreign package is installed and loaded into your R session.  Import the GSS 2014 data file and load it into the data frame ‘Dataset’ using:

########################################################
#import GSS2014 file in SPSS .sav format
#uses foreign package
########################################################
require(foreign)
use.value.labels=TRUE, max.value.labels=Inf, to.data.frame=TRUE)
########################################################

Once the GSS2014 file is loaded use the subset function to select your first subset of respondents who answered the 'abany' question with and 'YES response.  Use the following code to select the subset and store it in a data frame 'SS1':

####################################################
#select subset from Dataset and write to data frame SS1
####################################################
SS1 <- subset(Dataset, abany == "YES", select=educ)
View(SS1)
####################################################

Now select a second subset of respondents who answered the 'abany' question with a 'NO' response. Use the following code to select the subset and store in a data frame 'SS2':

######################################################
#select subset from Dataset and write to data frame SS2
######################################################
SS2 <- subset(Dataset, abany == "NO", select=educ)
View(SS2)
######################################################

In using the subset function as seen above the name of the data set is specified, the criteria for selecting rows is given, and the variables to select from each row specified.  If no 'select' option is given all variables will be shown for the selected row.
```

Using the View command to examine each subset shows the years of education for each of the 746 respondents who answered ‘YES’ and each of the 907 respondents who answered ‘NO.’ Since the variable ‘educ’ is measured as ratio level numeric data we can calculate a mean and standard deviation for each subset and perform both graphical and statistical analysis of any observed difference between the two means. This will be the subject of the next installment of the tutorial.