1.1. Important information: Statistics tutorial components

You are currently looking at a Guided learnr tutorial, which is a file that consists of both text (what you are currently reading) and several exercises that can be performed in R. Similarly, you will also be working with another file type, the R markdown that operates in the same way to a learnr tutorial, but affords more freedom to be altered by the user. You will be utilizing both kinds of files throughout this course.

You will be completing a total of 7 statistics tutorials in this course, and each tutorial will consist of two parts:

1. A guided tutorial

• This is a learnr tutorial that will introduce you to a new topic area

2. A free-form R markdown exercise to be downloaded from Amathuba (Activities | Assignments)

• This is an application exercise that will be completed using the R markdown feature, which applies what you have learnt in the learnr tutorial

You will upload one file to amathuba for each tutorial, namely your free-form R markdown exercise.

1.2. Guided tutorial features

Guided tutorials in learnr have two important features that allow us to handle data; the R code chunk and the R code. You will see an example of a code chunk directly in exercise 1.2.1, which is the entire block/chunk in which code can be executed. R code refers to the set of words and symbols used within the R code chunk that is applied to the data, to transform it.

Let’s take a look at an example!

Trait anxiety. We have a dataset called affect, which captures scores on personality, mood and trait anxiety measures.

affect

hist(affect$traitanx)

1.3. Layout of RStudio environment

Like learnr, Rstudio also allows us to run code in order to transform data, by using R markdown documents. In addition, R studio has several other helpful features including the R environment, R console and R files/help.

1.4. R programming language

R is a programming language, which means that R utilizes its own set of words and symbols to instruct R to complete certain tasks, this is also referred to R code

All R code R consists of 3 major components:

1. R objects

• R objects store information, such as data, and are named in order to allow for easy access to stored contents. For example, in Exercise 1.2.1, Personality, mood and trait anxiety data is stored in an R object called affect.

affect

survey

emotion = affect

emotion

head(emotion)

head()

?head()

1.5. R as an interactive calculator

R also acts as an interactive calculator for arithmetic operations (as well as more advanced operations)

5 + 2

## [1] 5

134*223

1.6. R scripts/markdowns

Whilst R gives you the power to execute the multiplication operation of 134*223, you may want to save the answer to use later. R scripts and markdowns are text files that give you the freedom to save your R code in order to run later. It also allows you to add descriptions about what your code is doing (commonly referred to as comments), using the #. Let’s look at a video that shows us how R scripts and markdowns work

Exercise 2.0.1

Complete and run the code chunk below to present the first 6 rows of the “media” dataframe using the head() command

head(...)

head(media)

Another way of inspecting the underlying structure of a dataframe (i.e. to see the variables present in the dataframe) without looking at the raw data is to use the str()command

Exercise 2.0.2

Complete the code chunk below to inspect the underlying structure of the “media” dataframe

str(media)

One can also look at a brief summary of the central tendency (e.g. mean and median) and spread/variability (min and max) of variables in a dataframe using the summary() command

Exercise 2.0.3

Complete the code chunk below that provides a summary all the variables in the “media” dataframe

summary(media)

Exercise 2.0.4

Plot a histogram of the presumed media influence (variable name is pmi).

hist(...$...)

hist(media$pmi)

What does this histogram tell us? Considering that higher pmi scores represent greater presumed media influence, the distribution of the data depicted in the histogram would suggest that the presumed influence of the media is considerably high amongst participants, given the higher frequency of high pmi scores relative to low pmi scores

2.1. Reading in dataframes

In order to inspect data, we first need to import or “read in” the data into R, in the form of dataframes.

Sometimes the data already exists within R, as part of an R package. If this is the case, we use the data() function to read the data into R.

head(affect)

head(x=...,n=...)

head(x= affect, n=10)

wiscsem <-read.csv("wiscsem.csv")

wiscsem = read.csv("wiscsem.csv")

Exercise 2.1.5

Check the structure of the dataframe wiscsem, using the str function

str(...)

str(wiscsem)

Exercise 3.0.1

Run the code chunk below and look at the pattern of vocabulary scores of all children participating in this study

hist(wiscsem$vocab, xlab = "Vocabulary scores", main =" Distribution of vocabulary scores on the WISCSEM measure for children")

From the histogram, we can see that there was a low frequency of children who scored very high or low on the vocabulary measure, but the majority of children appear to score approximately half-way in between.

In this example, because the majority of children’s vocabulary scores lie in the center, measures of central tendency (CT) can be used to quantify the extent to which children’s score lie in the center. There are several measures of CT,the most popular being the mean(), median() and mode()

3.1. Mean

The mean or average measures CT by dividing the sum of total data points/scores by the total number of data points/scores. See page 48-52 of Numbers, Hypotheses & Conclusions (3rd Ed)

Let’s look at some examples.

Suppose we measure children on a spatial awareness task, where scores range from 0-10 and higher scores represent better spatial awareness capabilities.

We have 3 children’s spatial awareness scores:

5, 8, 2

(5+8+2)/3

mean(...$...)

mean(wiscsem$vocab)

3.2. Median

The median is another measure of CT, which identifies the middle value within a data sample, thus splitting the sample into a lower and upper half. See page 52-55 of Numbers, Hypotheses & Conclusions (3rd Ed)

median(...$...)

median(wiscsem$vocab)

3.3. Mode

The mode is a measure of CT that identifies the value that appears most often in a data sample.

mode(...$...)

mode(wiscsem$vocab)

3.4. Central tendency (CT) measures and variable types

Use of certain measures of CT may be more appropriate depending on the type of variable in question.

Variable types include:

Nominal

Variable that is represented by categories that have no inherent numeric value, and is best measured using the mode For example: gender, eye colour, media genre preference, country of origin. All these variables have no numerical answer, but knowing which is the most common (i.e. mode) can tell you something about your data.

Ordinal

Variable that is represented by categories that can be ordered in some logical way, and is best measured using the median For example: levels of satisfaction, levels of income, severity levels of illness. Again, these variables have no “correct” numerical answer, but they are scaled and therefore knowing the middle (i.e. median) will give you more information about your data.

Scale/continuous

Variable that is quantified by numeric values, and is best measured using the mean For example weight, test scores, temperature. These variables do have a numerical answer that could tell you things like high/low observations in your data, and what the average (i.e. mean) across your data is.

Exercise 4.0.1

Run the code chunk below and look at the differences in the distribution of scores for positive and negative affect.

par(mfrow= c(1,2)) 
hist(affect$posaffect, xlab = "Positive affect", main ="Distribution of positive affect scores")
hist(affect$negaffect, xlab = "Negative affect", main ="Distribution of negative affect scores")

You should be able to notice that the empirical (data) distributions for positive and negative affect look somewhat different from each other. Notably for negative affect, there appears to be a somewhat smaller variation in scores from zero (which appears to be the mean), than for positive affect, where scores deviate more considerably from zero.

4.1. Variance & standard deviation

One way of measuring variability in data is through variance. Variance is measured as the average of squared differences between data points and the mean. Standard Deviation is another measure of variability that is calculated as the square root of variance. See page 55-61 of Numbers, Hypotheses & Conclusions (3rd Ed)

Remember that we have 3 children’s spatial awareness scores (presented below):

5, 8, 2

And we previously obtained a mean of 5

(((5-5)^2)/3)+(((8-5)^2)/3)+(((2-5)^2)/3)

var.spatial=(((5-5)^2)/3)+(((8-5)^2)/3)+(((2-5)^2)/3)
sqrt(var.spatial)

spatial.aware= c(5,8,2)
var(...)

spatial.aware= c(5,8,2)
var(spatial.aware)

... = c(...,...,...)
sd(...)

spatial.aware= c(5,8,2)
sd(spatial.aware)

4.2. Range & Interquartile range (IQR)

Other measures of variability include the range and interquartile range. The range is measured as the variation between the maximum and minimum data points and is just calculated as the difference between the two. The interquartile range is measured as the variation between the 1st and 3rd quartiles (i.e. variation associated with the middle 50% of data).See page 55-61 of Numbers, Hypotheses & Conclusions (3rd Ed)

range(...$...)

range(wiscsem$vocab)

IQR(...$...)

IQR(wiscem$vocab)

5.1. Variable types in R

When reading data into R (either as single variables or entire data frames with multiple variables), we will need to specify variable types.

A survey was conducted with statistics students from the University of Adelaide, where several variables were measured, including: gender, age and smoking frequency

str(...)

str(survey)

survey$Gender <- ifelse(survey$Gender == "1", "Male", "Female")
survey$Gender<-as.factor(survey$Gender)

...(...$...)

survey$Gender<-as.factor(survey$Gender)
str(survey$Gender)

survey$Gender <- ifelse(survey$Gender == "1", "Male", "Female")
survey$Gender<-as.factor(survey$Gender)

...(...$...)

str(survey$Gender)

...(...$...)

...$... = as...(...$...)

str(wiscsem$vocab)

wiscsem$vocab = as.integer(wiscsem$vocab)

Move on to and complete Statistics Tutorial Assignment 1 on Amathuba (Activities | Assignments)