Tag Archives: anova

R for Beginners: Using R Commander for Basic t Tests and One Way ANOVA


R for Beginners:  Using R Commander for Basic t Tests and One Way ANOVA

A tutorial by D. M. Wiig

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I hope that you found this tutorial informative.  Stop back by to check for new installments.  I have many currently in the writing stage.

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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:

Rplotrandgss2

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

Tutorial: Using R to Analyze NORC GSS Social Science Data, Part Six, R and ANOVA


Tutorial: Using R to Analyze NORC GSS Social Science Data, Part Six, R and ANOVA

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. As I have indicated in previous tutorials, use of an IDE such as R Studio greatly facilitates entering and debugging R code when doing research such as is discussed in my tutorials.  

Import the GSS 2014 data file in SPSS format and load it into the data frame ‘gss14’ using:
#########################################################import  GSS2014 file in SPSS .sav format
#uses foreign package
########################################################require(foreign)
gss14<- read.spss("/path to your location/GSS2014.sav",                      use.value.labels=TRUE,max.value.labels=Inf, to.data.frame=TRUE)
#################################################

In this tutorial the analysis of this sample will focus on examining the hypothesis “An individual’s outlook on life is influenced by the amount of education the person has attained.” The GSS variables ‘educ’, education in number of years and ‘life’, whether the respondent rated life DULL, ROUTINE, or EXCITING. A simple approach to testing this hypothesis is to compare mean levels of education for each of the three categories of response. I will do this analysis in two stages. In the first stage I will use techniques discussed in a previous tutorial to select a subset of each response category and display the mean education level for each of the three categories.

The three subsets life1, life2, and life3 are generated using the following code:

###################################################
# create 3 subsets from gss14 view on life by years of education
##################################################

life1 <- subset(gss14, life == “DULL”, select=educ)

life2 <- subset(gss14, life ==”ROUTINE”, select=educ)

life3 <- subset(gss14, life == “EXCITING”, select=educ)

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

#The three means of the subsets are displayed using the code:

# run summary statistics for each subgroup

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

summary(life1)

summary(life2)

summary(life3)

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

resulting the following output:
educ
Min. : 0.00
1st Qu.:10.00
Median :12.00
Mean :11.78
3rd Qu.:13.00
Max. :20.00

summary(life2)
educ
Min. : 0.00
1st Qu.:12.00
Median :13.00
Mean :13.22
3rd Qu.:16.00
Max. :20.00
NA’s :1

summary(life3)
educ
Min. : 2.00
1st Qu.:12.00
Median :14.00
Mean :14.31
3rd Qu.:16.00
Max. :20.00

As is seen above there does appear to be a difference among mean years of education and the corresponding outlook on life. In order to examine whether or not these observed differences are not due to chance a simple one-way Analysis of Variance can be generated.

In the next tutorial I will discuss performing the ANOVA and using pair-wise comparisons to determine which if any means are different.

Using R for Nonparametric Statistics: The Kruskal-Wallis Test, Part Two


Using R for Nonparametric Statistics:  The Kruskal-Wallis Test, Part Two

A Tutorial by Douglas M. Wiig

Before we can run the Kruskal-Wallis test we need to define which column contains the factors (independent variables) and which contains the authoritarianism scores (dependent variable). Once we define the factor column R will match the correct score to each of the 14 observations.
As set up in the study, ‘Group’ is the factor(independent variable), and ‘authscore’ is the dependent variable. Use the command:

> Group <-factor(1,2,3)

This designates which observation belongs to each group. To make sure the data structure has been set up correctly use the command:

> str(kruskal)
‘data.frame’: 14 obs. of 2 variables:
$ Group : num 1 1 1 1 1 2 2 2 2 2 …
$ authscore: num 96 128 83 61 101 82 124 132 135 109 …
>

The output of this command shows a summary of the structure of the data frame created. We can now run the Kruskal Wallis test with the command:

> kruskal.test(authscore ~ Group, data=kruskal)

The output will be:

Kruskal-Wallis rank sum test

data: authscore by Group
Kruskal-Wallis chi-squared = 6.4057, df = 2, p-value = 0.04065

>

As seen in the above output the analysis of authoritarianism score by group indicates that the probability of differences in scores among the three groups being due to chance alone is less that the .05 alpha level that was set for the study. (pobt < .05). Further post hoc analysis would be necessary to determine the exact nature of the differences among the scores of the three groups. This will be the topic of a future tutorial.

More to come:  Part Three will explore the use of multiple comparison techniques to analyze ranked means