7 Walkthrough 1: The Education Data Science Pipeline With Online Science Class Data

7.1 Topics Emphasized

For this and the remaining walkthroughs, we refer to the topics emphasized in terms of distinct but related steps involved in the process of data science. In this book, we use the six steps - described in detail in Chapter 3 - from Wickham & Grolemund (2018)’s depiction of the process.

As mentioned in Chapter 5, then, the topics emphasized are those that are the particular focus of each chapter; most of the walkthroughs contain some element of all of the five aspects, but all have specific emphases.

For this chapter on the education data science pipeline, those emphases are:

  • Tidying data
  • Transforming data

7.2 Functions Introduced

  • data.frame()
  • dplyr::summarize()
  • tidyr::pivot_longer() and tidyr::pivot_wider()
  • tidyr::left_join(), tidyr::right_join(), tidyr::semi_join(), and tidyr::anti_join()
  • lm()
  • ggplot2::ggplot()
  • apaTables::apa.cor.table()
  • sjPlot::tab_model()

7.3 Vocabulary

In this section (here and in the other walkthrough sections), we include key terms that are introduced and used in the chapter.

  • data frame
  • item
  • joins
  • keys
  • log-trace data
  • passed arguments
  • reverse scale
  • regression
  • survey
  • tibble
  • vectorize

7.4 Introduction to the Walkthroughs

This chapter is the first of eight walkthroughs included in the book. In it, we present one approach to analyzing a specific dataset. In this chapter, the approach is what we refer to as the education data science pipeline, orsome the steps taken in many data science projects, including cleaning and tidying data as well as exploring and visualizing or modeling it.

Here, we will be using data from a number of online science classes and will show the process of working with an education dataset from start to finish. While the walkthroughs are very different, the structure and section headings will be consistent throughout the walkthroughs. For example, every walkthrough will begin with a vocabulary section, followed by an introduction to the dataset and an introduction to the question or problem explored in the walkthrough.

We note that this chapter assumes familiarity with the four core concepts that comprise the foundational skills framework: projects, functions, packages, and data. If you would like a refresher about (or an introduction to) any of those, the foundational skills chapter, then reading and writing and running some of the code in the previous chapter Chapter 6 may be helpful to you.

7.5 Chapter Overview

In this walkthrough, we explore some of the key steps that are a part of many data science in education projects. In particular, we explore how to process and prepare data. These steps are sometimes referred to as “data wrangling”. To do so, we rely heavily on a set of tools that we use throughout all of the walkthroughs, those associated with the {tidyverse}.

The {tidyverse} is a set of packages for data manipulation, exploration, and visualization. that uses the design philosophy of ‘tidy’ data (Wickham, 2014). Tidy data has a specific structure: each variable is a column, each observation is a row, and each type of observational unit is a table. We’ll discuss both the {tidyverse} and tidy data much more throughout the book. For more information, see the Foundational Skills chapters or https://www.tidyverse.org/.

7.5.1 Background

The online science classes we explore in this chapter were designed and taught by instructors through a statewide online course provider designed to supplement - but not replace - students’ enrollment in their local school. For example, students may have chosen to enroll in an online physics class because one was not offered at their school. The data were originally collected for a research study, which utilized a number of different data sources to understand students’ course-related motivation. These datasets included:

  1. A self-report survey assessing three aspects of students’ motivation
  2. Log-trace data, such as data output from the learning management system
  3. Discussion board data
  4. Academic achievement data

Our high-level purpose for this walkthrough is to conduct an analysis that helps explain students’ performance in these online courses. The problem we are facing is a very common one when it comes to data science in education: the data are complex and in need of further processing before we can get to the step of running analyses. We will use this same dataset in the final walkthrough Walkthrough 8/Chapter 14, and we will provide more details there about the dataset and the context.

To understand students’ performance, we will focus on a learning management system (LMS) variable that indicates the amount of time students spent within the course LMS. We will also explore the effects of the type of science course and the section in which students are enrolled on student performance.

First, these different data sources will be described in terms of how they were provided by the school.

7.5.2 Data Sources

7.5.2.1 Data Source #1: Self-Report Survey about Students’ Motivation

The first data source is a self-report survey. This was data collected before the start of the course. The survey included ten items, each corresponding to one of three motivation measures: interest, utility value, and perceived competence. A measure is a concept that we try to make concrete and assess using survey questions. The three motivation measures we explore here come from Expectancy-Value Theory, which states that students are motivated to learn when they both believe that they can achieve something (expectancy, also known as perceived competence) and believe that the concept they are trying to learn is important (value) (Wigfield & Eccles, 2000). There are multiple types of value, but we explore two of them here: interest and utility value. Utility value is the degree to which a person is able to connect the concept being learned with something they will utilize in their future life. This survey included the following ten items:

  1. I think this course is an interesting subject. (Interest)
  2. What I am learning in this class is relevant to my life. (Utility value)
  3. I consider this topic to be one of my best subjects. (Perceived competence)
  4. I am not interested in this course. (Interest - reverse coded)
  5. I think I will like learning about this topic. (Interest)
  6. I think what we are studying in this course is useful for me to know. (Utility value)
  7. I don’t feel comfortable when it comes to answering questions in this area. (Perceived competence - reverse coded)
  8. I think this subject is interesting. (Interest)
  9. I find the content of this course to be personally meaningful. (Utility value)
  10. I’ve always wanted to learn more about this subject. (Interest)

7.5.3 Data Source #2: Log-Trace Data

Log-trace data is data generated from our interactions with digital technologies, such as archived data from social media postings (see Chapter 11 and Chapter 12). In education, an increasingly common source of log-trace data is that generated from interactions with learning management systems and other digital tools (Siemens & d Baker, 2012). The data for this walk-through is a summary type of log-trace data: the number of minutes students spent on the course. While this data type is fairly straightforward, there are even more complex sources of log-trace data out there (e.g. time stamps associated with when students started and stopped accessing the course!).

7.5.4 Data Source #3: Academic Achievement and Gradebook Data

This is a common source of data in the education realm: the graded assignments students completed. In this walkthrough, we examine only students’ final grade for the course.

7.5.5 Data Source #4: Discussion Board Data

Discussion board data is both rich and unstructured because it is made up of large chunks of text that the students wrote. While discussion board data was collected for this research project, but we do not examine it in this walkthrough. More information about analyzing text data can be found in Chapter 11.

7.5.6 Methods

In this walkthrough, we will concentrate on merging different datasets together by using the different “joins” available in the {dplyr} package. We will also start exploring how to run linear models in R.

7.6 Load Packages

This analysis uses R packages, which are collections of R code that help users code more efficiently, as you will recall from Chapter 1. We load these packages with the function library(). The specific packages we’ll use here will help us organize the structure of the data using the {tidyverse} (Wickham, 2019b),create formatted tables using {apaTables} (Stanley, 2018) and {sjPlot} (Lüdecke, 2020), and export datasets using {readxl} (Wickham & Bryan, 2019).

Install packages (if necessary)

If you have not installed any of these packages before, you will need to do so before loading them (if you run the code below prior to installing the packages, you should see a message indicating that the package is not available). If you have installed these before, then you can skip this step.

You can install a single package, such as the {tidyverse} package, as follows:

If you must install two or more packages, you can do so in a single call to the install.packages() function; the names of the packages must be provided to the function as follows:

When you’re installing a package for the first time (which may be needed for the other walkthrough chapters, as well), you will need to take these same steps, first. The good news is that you only need to install a package once, after which you can simply load it using library() (as below).

More on the installation of packages is included in the Packages section of Chapter 6.

7.7 Import Data

This code chunk loads the log-trace data and self-report survey data from the {dataedu} package. Note that we assign a dataset to an object three different times, once for each of the three different datasets. We assign each of the datasets a name using <-.

7.8 View Data

Now that we’ve successfully loaded all three log-trace datasets, we can visually inspect the data by typing the names that we assigned to each dataset. Running each line, one at a time, will show the first several rows of each dataset.

## # A tibble: 1,102 x 12
##    opdata_username opdata_CourseID Q1Maincellgroup… Q1Maincellgroup…
##    <chr>           <chr>                      <dbl>            <dbl>
##  1 _80624_1        FrScA-S116-01                  4                4
##  2 _80623_1        BioA-S116-01                   4                4
##  3 _82588_1        OcnA-S116-03                  NA               NA
##  4 _80623_1        AnPhA-S116-01                  4                3
##  5 _80624_1        AnPhA-S116-01                 NA               NA
##  6 _80624_1        AnPhA-S116-02                  4                2
##  7 _80624_1        AnPhA-T116-01                 NA               NA
##  8 _80624_1        BioA-S116-01                   5                3
##  9 _80624_1        BioA-T116-01                  NA               NA
## 10 _80624_1        PhysA-S116-01                  4                4
## # … with 1,092 more rows, and 8 more variables: Q1MaincellgroupRow3 <dbl>,
## #   Q1MaincellgroupRow4 <dbl>, Q1MaincellgroupRow5 <dbl>,
## #   Q1MaincellgroupRow6 <dbl>, Q1MaincellgroupRow7 <dbl>,
## #   Q1MaincellgroupRow8 <dbl>, Q1MaincellgroupRow9 <dbl>,
## #   Q1MaincellgroupRow10 <dbl>
## # A tibble: 29,711 x 8
##    CourseSectionOr… Bb_UserPK Gradebook_Item Grade_Category FinalGradeCEMS
##    <chr>                <dbl> <chr>          <chr>                   <dbl>
##  1 AnPhA-S116-01        60186 POINTS EARNED… <NA>                     86.3
##  2 AnPhA-S116-01        60186 WORK ATTEMPTED <NA>                     86.3
##  3 AnPhA-S116-01        60186 0.1: Message … <NA>                     86.3
##  4 AnPhA-S116-01        60186 0.2: Intro As… Hw                       86.3
##  5 AnPhA-S116-01        60186 0.3: Intro As… Hw                       86.3
##  6 AnPhA-S116-01        60186 1.1: Quiz      Qz                       86.3
##  7 AnPhA-S116-01        60186 1.2: Quiz      Qz                       86.3
##  8 AnPhA-S116-01        60186 1.3: Create a… Hw                       86.3
##  9 AnPhA-S116-01        60186 1.3: Create a… Hw                       86.3
## 10 AnPhA-S116-01        60186 1.4: Negative… Hw                       86.3
## # … with 29,701 more rows, and 3 more variables: Points_Possible <dbl>,
## #   Points_Earned <dbl>, Gender <chr>
## # A tibble: 598 x 3
##    Bb_UserPK CourseSectionOrigID TimeSpent
##        <dbl> <chr>                   <dbl>
##  1     44638 OcnA-S116-01            1383.
##  2     54346 OcnA-S116-01            1191.
##  3     57981 OcnA-S116-01            3343.
##  4     66740 OcnA-S116-01             965.
##  5     67920 OcnA-S116-01            4095.
##  6     85355 OcnA-S116-01             595.
##  7     85644 OcnA-S116-01            1632.
##  8     86349 OcnA-S116-01            1601.
##  9     86460 OcnA-S116-01            1891.
## 10     87970 OcnA-S116-01            3123.
## # … with 588 more rows

7.9 Process Data

Often, survey data needs to be processed in order to be most useful. We are going to start with one of the three datasets we just saved as objects into our environment: the dataset with the pre-survey items. Here, we process the self-report items into three scales for 1) interest, 2) perceived competence, and 3) utility value. We do this by:

  • Renaming the question variables to something more manageable
  • Reversing the response scales on questions 4 and 7
  • Categorizing each question into a measure
  • Computing the mean of each measure

Let’s take these steps in order:

  1. Take the pre-survey data and save it as a new object with the same name “pre_survey.” Rename the question columns to something much simpler. To do this, we will use the rename() function and will input first the new variable name, then the “=” sign, and then the old variable name. You’ll notice another function at the bottom called mutate_at(). We’ll explain that below this code chunk.

Let’s take a moment to discuss the {dplyr} function mutate_at(). mutate_at() is a version of mutate(), which changes the values in an existing column or creates new columns. It’s useful in education datasets because you’ll often need to transform your data before analyzing it. In the code chunk we just ran, we used mutate_at() to convert the data in all ten variables into a numeric format.

To learn a little more about mutate(), try the example below, where we create a new data frame called “df”. A data frame is a two-dimensional structure that stores tables. The table has a header and data rows and each cell stores values.

We fill this data frame with two columns: “male” and “female.” Each column has only one value, and that value is 5. In the second part of the code, we add a total_students column by adding the number of male students and female students.

Note that we create the dataset with tibble(), which is from the {tibble} package included in the tidyverse. A tibble is a special type of data frame that makes working with the tidy data a little easier. More information is available in R for Data Science (Wickham & Grolemund, 2018).

## # A tibble: 1 x 3
##    male female total_students
##   <dbl>  <dbl>          <dbl>
## 1     5      5             10

To return to our original data, we used mutate_at(), a special version of mutate() which conveniently changes the values of multiple columns. In our dataset pre_survey, we let mutate_at() know we want to change the variables q1 through q10. We do this with the argument vars(q1:q10).

  1. Next we’ll reverse the scale of the survey responses on questions 4 and 7 so the responses for all questions can be interpreted in the same way. As you can see from the survey questions we listed earlier in the chapter, the phrasing of questions 4 and 7 is opposite the phrasing of the other questions. Rather than write a lot of code once to reverse the scales for question 4 then writing it again to reverse the scales on question 7, we’ll build a function that does that job for us. Then we’ll use the same function that we wrote to recode both question 4 and question 7. This will result in much less code, and it will make it easier for us to change in the future.

We’ll use the function case_when() within our function to reverse the scale of the item responses. case_when() is useful when you need to replace the values in a column with other values based on some criteria. Education datasets use a lot of codes to describe demographics, like numerical codes for disability categories, race groups, or proficiency in a test. When you work with codes like this, you’ll often want to change the codes to values that are easier to understand. For a example, a consultant analyzing how students did on state testing might use case_when() to replace proficiency codes like 1, 2, or 3 to more descriptive words like “below proficiency”, “proficient”, or “advanced.”

case_when() lets you vectorize the rules you want to use to change values in a column. When a sequence of criteria is vectorized, R will evaluate a value in a column against each criteria in your case_when() sequence. case_when() is helpful because it does this without requiring you to write complicated code loops. Instead, you can systematically evaluate your criteria using code that is compact and readable (once you understand how all the arguments work).

The left hand side of each case_when() argument will be a formula that returns either a TRUE or a FALSE. In the function below, we’ll use logical operators in the left hand side of the formula like this: question == 1 ~ 5. Here are some logical operators you can use in the future:

  • ==: equal to
  • >: greater than
  • <: lesser than
  • >=: greater than or equal to
  • <=: lesser than or equal to
  • !=: not equal to
  • !: not
  • &: and
  • |: or

Let’s make this all concrete and use it here in our function that reverses the scale of the survey responses. In the first part of the code chunk below, we will write our function. Note that by running the first bit of code here, we won’t be changing anything in our data. Instead, we are creating a reusable, general-purpose code chunk that we will then apply to the specific survey questions we want to recode.

You’ll notice that we call the reverse_scale() function we wrote, but we call it within the mutate() function. By doing things this way, we are overwriting the previous data in the columns for questions 4 and 7 with our newly recoded values for questions 4 and 7.

  1. Next, we’ll use a function called pivot_longer() in order to transform our pre_survey dataset from wide format to long format. That means instead of having 1,102 observations of 12 variables, we will now have 11,020 observations of 4 variables. By using pivot_longer(), we make it so that each question & response pair has its own line in the data. Therefore, since we have 10 question variables (columns) in the pre_survey dataset, after we use pivot_longer(), we will end up with 10 times as many observations (rows) as before. Additionally, we no longer need a separate column for each individual question, since each question-response pair is now on its own line. What was previously one row of data now takes up ten rows of data. so pivot_longer() automatically deletes those empty columns after condensing all the data. We’ll save this new dataset as an object called measure_mean in order to represent new variables we will create in future data processing steps.
  1. Next, we’ll take our new measure_mean dataset and create a column called measure. We’ll fill that column with one of three question categories:
  • int: interest
  • uv: utility value
  • pc: perceived competence .

We will use the case_when() function we learned earlier in order to do this. When we pivoted from wide format to long format in the prior step, we ended up with one variable containing all possible question numbers (q1, q2, etc.). Now, we want to tell R which question numbers correspond to which categories. To do this, we will supply case_when() with a list of all the question numbers that correspond to each category: interest, utility value, and perceived competence. We’ll introduce a new operator in order to do this: %in!%. Practically, this operator means that R should look within a list for something. In the code below, we tell R to use questions 1, 4, 5, 8, and 10 to create the category int. We then tell R to use questions 2, 6, and 9 to calculate uv and to use questions 3 and 7 to calculate pc. We indicate the start of each list with the letter “c” and an open parenthesis, and we indicate the end of each list with a close parenthesis.

  1. Last, we’ll take that same measure_mean dataset and create a new variable called mean_response. Since we are calculating the mean by category, we will need to first group the responses together using a function called group_by(). This function helps us get set up to calculate new columns with grouped data. Next, we’ll use the function summarize() to create two new variables: mean_response and percent_NA. We’ll find the mean response of each category using the mean() function.
## # A tibble: 3 x 3
##   measure mean_response percent_NA
##   <chr>           <dbl>      <dbl>
## 1 int              4.25      0.178
## 2 pc               3.65      0.178
## 3 uv               3.74      0.178

With that last step, we have finished processing the pre_survey dataset. We have renamed the relevant variables and computed some means that we can use later.

7.9.1 Processing the Course Data

When we loaded the data earlier in the chapter, we loaded three datasets: pre_survey, course_data, and course_minutes. Next, we can process the course data that we already loaded into the environment in order to create new variables which we can use in analyses.

Information about the course subject, semester, and section are stored in a single column, CourseSectionOrigID. This format of data storage is not ideal. If we instead give each piece of information its own column, we’ll have more opportunities for later analysis. We’ll use a function called separate() to do this. Below, we will load course_data and run the separate() function to split up the subject, semester, and section so we can use them later on.

After running the code chunk above, take a look at the dataset course_data to make sure it looks the way you’d expect it to look. In this case, we are expecting that we will add 3 new variables, taking the total number of variables in this dataset from 8 to 11. We will still see the original variable CourseSectionOrigID in the data as well.

7.9.2 Joining the Data

In this chapter, we are looking at two datasets that are derived from the same courses. In order for these datasets to be most useful to us, we’d like all that data to be in one place.

To join the course data and pre-survey data, we need to create similar keys. Our goal here is to have one variable that matches across both datasets. Once we have that common variable in both datasets, we can merge the datasets on the basis of that variable.

When we look at the course_data and pre_survey datasets in our environment, we see that both have variables for the course and the student. However, this information is captured in different variable names in each dataset. Our first goal will be to rename two variables in each of our datasets so that they will match. One variable will correspond to the course, and the other will correspond to the student. We are not changing anything in the data itself at this step - instead, we are just cleaning the column headers up so that we can look at the data all in one place.

Let’s start with the pre-survey data. We will rename RespondentID and opdata_CourseID to be student_id and course_id, respectively. Here, we are going to use the same rename() function we learned earlier in this chapter.

## # A tibble: 1,102 x 12
##    student_id course_id    q1    q2    q3    q4    q5    q6    q7    q8    q9
##    <chr>      <chr>     <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
##  1 _80624_1   FrScA-S1…     4     4     4     5     5     4     5     5     5
##  2 _80623_1   BioA-S11…     4     4     3     4     4     4     4     3     4
##  3 _82588_1   OcnA-S11…    NA    NA    NA    NA    NA    NA    NA    NA    NA
##  4 _80623_1   AnPhA-S1…     4     3     3     4     3     3     3     4     2
##  5 _80624_1   AnPhA-S1…    NA    NA    NA    NA    NA    NA    NA    NA    NA
##  6 _80624_1   AnPhA-S1…     4     2     2     4     4     4     5     4     4
##  7 _80624_1   AnPhA-T1…    NA    NA    NA    NA    NA    NA    NA    NA    NA
##  8 _80624_1   BioA-S11…     5     3     3     5     5     4     5     5     3
##  9 _80624_1   BioA-T11…    NA    NA    NA    NA    NA    NA    NA    NA    NA
## 10 _80624_1   PhysA-S1…     4     4     3     4     4     4     4     4     3
## # … with 1,092 more rows, and 1 more variable: q10 <dbl>

Those variable names look better now!

When we look at the data more closely, though, we will notice that the student_id variable has another issue - the variable has some additional characters before and after the actual ID that we will need to be able to join this data with the other data sources we have. Why does this variable have these additional characters? Why is there a “1” at the end of every 5-digit ID number? We are not sure! Sometimes, educational data from different systems (used for different purposes) may have additional “meta”-data added on. In any event, here is what the variables look like before processing:

## [1] "_80624_1" "_80623_1" "_82588_1" "_80623_1" "_80624_1" "_80624_1"

What we need is the five characters in between the underscore symbols - these: _.

One way to do this is to use the str_sub() function from the {stringr} package. This function lets us subset string variables: variables that store text data. You can specify the indices of the variables you want the string to start and end with.

Here, for example, is how we can select only the content starting with the second character, skipping the first underscore in the process. This next chunk of code will not change our data, but will show you how the str_sub() function works by supplying a number-and-underscore combination to the function that is in the same format as our data.

## [1] "99888_1"

We can apply the same thinking to delete characters from the end of a string. We will use a - to indicate that we want to start from the right side of the string of characters. Interestingly, when we specify the argument end below, we will tell it the placement of the first character we want to INCLUDE. When we type end = -3, we end up deleting only the last 2 characters. Our new rightmost character will be the final 8.

## [1] "_99888"

Putting the pieces together, the following should return what we want. Try running the code below to see if it yields the 5-digit ID number we are shooting to extract.

## [1] "99888"

Note: you may receive a warning telling you that NA values were introduced by coercion. This happens when we change data types, and we will overlook this warning message for the purposes of this walkthrough.

We can apply this process to our data using mutate(). We convert the string into a number using as.numeric() in the next portion of the code. This step is important so the data can be joined to the other, numeric student_id variables (in the other datasets):

## Warning: NAs introduced by coercion

Now that the student_id and course_id variables are ready to go in the pre_survey dataset, let’s proceed to the course data. Our goal is to rename two variables that correspond to the course and the student so that we can match with the other variables we just created for the pre-survey data. In the code chunk below, we will rename both those variables.

Now that we have two variables that are consistent across both datasets - we have called them course_id and student_id - we can join the two datasets using the {dplyr} function, left_join().

left_join() is named based on the ‘direction’ that the data is being joined. Note the order of the data frames passed to our “left” join. Left joins retain all of the rows in the data frame on the “left”, and joins every matching row in the right data frame to it. We will use two variables as keys for joining the datasets, and we will specify those after the word by.

Let’s save our joined data as a new object called dat.

## # A tibble: 40,348 x 21
##    course_id subject semester section student_id Gradebook_Item Grade_Category
##    <chr>     <chr>   <chr>    <chr>        <dbl> <chr>          <chr>         
##  1 AnPhA-S1… AnPhA   S116     01           60186 POINTS EARNED… <NA>          
##  2 AnPhA-S1… AnPhA   S116     01           60186 WORK ATTEMPTED <NA>          
##  3 AnPhA-S1… AnPhA   S116     01           60186 0.1: Message … <NA>          
##  4 AnPhA-S1… AnPhA   S116     01           60186 0.2: Intro As… Hw            
##  5 AnPhA-S1… AnPhA   S116     01           60186 0.3: Intro As… Hw            
##  6 AnPhA-S1… AnPhA   S116     01           60186 1.1: Quiz      Qz            
##  7 AnPhA-S1… AnPhA   S116     01           60186 1.2: Quiz      Qz            
##  8 AnPhA-S1… AnPhA   S116     01           60186 1.3: Create a… Hw            
##  9 AnPhA-S1… AnPhA   S116     01           60186 1.3: Create a… Hw            
## 10 AnPhA-S1… AnPhA   S116     01           60186 1.4: Negative… Hw            
## # … with 40,338 more rows, and 14 more variables: FinalGradeCEMS <dbl>,
## #   Points_Possible <dbl>, Points_Earned <dbl>, Gender <chr>, q1 <dbl>,
## #   q2 <dbl>, q3 <dbl>, q4 <dbl>, q5 <dbl>, q6 <dbl>, q7 <dbl>, q8 <dbl>,
## #   q9 <dbl>, q10 <dbl>

Let’s hone in on how this code is structured. After left_join(), we see course_data and then pre_survey. In this case, course_data is the “left” data frame (passed as the first argument), while pre_survey is the “right” data frame (passed as the second argument). So, in the above code, what happens? You can run the code yourself to check.

Our aim with that code is that all of the rows in course_data are retained in our new data frame, dat, with matching rows of pre_survey joined to it. An important note is that there are not multiple matching rows of pre_survey; otherwise, you would end up with more rows in dat than expected. There is a lot packed into this one function. Joins are extremely powerful - and common - in many data analysis processing pipelines, both in education and in any field. Think of all of the times you have data in more than one data frame, but you want everything to be in a single data frame! As a result, we think that joins are well worth investing the time to be able to use.

With most types of data, left_join() is helpful for carrying out most tasks related to joining datasets. However, there are functions for other types of joins that we want to make sure you know how to use. They may be less frequently used than left_join(), but they are still worth mentioning. Note that for all of these, the “left” data frame is always the first argument, and the “right” data frame is always the second. When running the code chunks below, it can be helpful to pay attention to the number of observations and variables in the datasets before and after the joining. Eventually, the obscure names of these types of joins will start to become more intuitive as you use them more often.

7.9.2.1 semi_join()

semi_join(): joins and retains all of the matching rows in the “left” and “right” data frame. This is useful when you are only interested in keeping the rows (or cases/observations) that are able to be joined. semi_join() will not create duplicate rows of the left data frame, even when it finds multiple matches on the right data frame. It will also keep only the columns from the left data frame.

For example, the following returns only the rows that are present in both course_data and pre_survey:

## # A tibble: 28,655 x 11
##    course_id subject semester section student_id Gradebook_Item Grade_Category
##    <chr>     <chr>   <chr>    <chr>        <dbl> <chr>          <chr>         
##  1 AnPhA-S1… AnPhA   S116     01           60186 POINTS EARNED… <NA>          
##  2 AnPhA-S1… AnPhA   S116     01           60186 WORK ATTEMPTED <NA>          
##  3 AnPhA-S1… AnPhA   S116     01           60186 0.1: Message … <NA>          
##  4 AnPhA-S1… AnPhA   S116     01           60186 0.2: Intro As… Hw            
##  5 AnPhA-S1… AnPhA   S116     01           60186 0.3: Intro As… Hw            
##  6 AnPhA-S1… AnPhA   S116     01           60186 1.1: Quiz      Qz            
##  7 AnPhA-S1… AnPhA   S116     01           60186 1.2: Quiz      Qz            
##  8 AnPhA-S1… AnPhA   S116     01           60186 1.3: Create a… Hw            
##  9 AnPhA-S1… AnPhA   S116     01           60186 1.3: Create a… Hw            
## 10 AnPhA-S1… AnPhA   S116     01           60186 1.4: Negative… Hw            
## # … with 28,645 more rows, and 4 more variables: FinalGradeCEMS <dbl>,
## #   Points_Possible <dbl>, Points_Earned <dbl>, Gender <chr>

7.9.2.2 anti_join()

anti_join(): removes all of the rows in the “left” data frame that can be joined with those in the “right” data frame.

## # A tibble: 1,056 x 11
##    course_id subject semester section student_id Gradebook_Item Grade_Category
##    <chr>     <chr>   <chr>    <chr>        <dbl> <chr>          <chr>         
##  1 AnPhA-S1… AnPhA   S116     01           85865 POINTS EARNED… <NA>          
##  2 AnPhA-S1… AnPhA   S116     01           85865 WORK ATTEMPTED <NA>          
##  3 AnPhA-S1… AnPhA   S116     01           85865 0.1: Message … <NA>          
##  4 AnPhA-S1… AnPhA   S116     01           85865 0.2: Intro As… Hw            
##  5 AnPhA-S1… AnPhA   S116     01           85865 0.3: Intro As… Hw            
##  6 AnPhA-S1… AnPhA   S116     01           85865 1.1: Quiz      Qz            
##  7 AnPhA-S1… AnPhA   S116     01           85865 1.2: Quiz      Qz            
##  8 AnPhA-S1… AnPhA   S116     01           85865 1.3: Create a… Hw            
##  9 AnPhA-S1… AnPhA   S116     01           85865 1.3: Create a… Hw            
## 10 AnPhA-S1… AnPhA   S116     01           85865 1.4: Negative… Hw            
## # … with 1,046 more rows, and 4 more variables: FinalGradeCEMS <dbl>,
## #   Points_Possible <dbl>, Points_Earned <dbl>, Gender <chr>

7.9.2.3 right_join()

right_join(): perhaps the least helpful of the three, right_join() works the same as left_join(), but by retaining all of the rows in the “right” data frame, and joining matching rows in the “left” data frame (so, the opposite of left_join()).

## # A tibble: 39,593 x 21
##    course_id subject semester section student_id Gradebook_Item Grade_Category
##    <chr>     <chr>   <chr>    <chr>        <dbl> <chr>          <chr>         
##  1 FrScA-S1… <NA>    <NA>     <NA>         80624 <NA>           <NA>          
##  2 BioA-S11… <NA>    <NA>     <NA>         80623 <NA>           <NA>          
##  3 OcnA-S11… <NA>    <NA>     <NA>         82588 <NA>           <NA>          
##  4 AnPhA-S1… <NA>    <NA>     <NA>         80623 <NA>           <NA>          
##  5 AnPhA-S1… <NA>    <NA>     <NA>         80624 <NA>           <NA>          
##  6 AnPhA-S1… <NA>    <NA>     <NA>         80624 <NA>           <NA>          
##  7 AnPhA-T1… <NA>    <NA>     <NA>         80624 <NA>           <NA>          
##  8 BioA-S11… <NA>    <NA>     <NA>         80624 <NA>           <NA>          
##  9 BioA-T11… <NA>    <NA>     <NA>         80624 <NA>           <NA>          
## 10 PhysA-S1… <NA>    <NA>     <NA>         80624 <NA>           <NA>          
## # … with 39,583 more rows, and 14 more variables: FinalGradeCEMS <dbl>,
## #   Points_Possible <dbl>, Points_Earned <dbl>, Gender <chr>, q1 <dbl>,
## #   q2 <dbl>, q3 <dbl>, q4 <dbl>, q5 <dbl>, q6 <dbl>, q7 <dbl>, q8 <dbl>,
## #   q9 <dbl>, q10 <dbl>

If we wanted this to return exactly the same output as left_join() (and so to create a data frame that is identical to the dat data frame we created above), we could simply switch the order of the two data frames to be the opposite of those used for the left_join() above:

## # A tibble: 801 x 12
##    student_id course_id    q1    q2    q3    q4    q5    q6    q7    q8    q9
##         <dbl> <chr>     <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
##  1      85791 FrScA-S1…     3     3     3     3     4     3     3     3     2
##  2      87010 FrScA-S1…     5     3     3     5     4     4     3     5     2
##  3      87027 FrScA-S1…     5     5     4     4     4     5     4     5     4
##  4      85649 FrScA-S1…    NA    NA    NA    NA    NA    NA    NA    NA    NA
##  5      86216 BioA-S11…     5     3     4     4     5     4     3     5     4
##  6      68476 OcnA-S11…     4     4     2     2     3     4     4     4     4
##  7      68476 OcnA-S11…     4     4     4     4     4     4     4     4     4
##  8      87866 FrScA-T1…     5     4     3     5     4     4     3     3     3
##  9      64930 FrScA-T1…     4     3     3     4     4     4     3     4     4
## 10      86280 FrScA-S1…     4     3     2     4     4     4     4     4     3
## # … with 791 more rows, and 1 more variable: q10 <dbl>

Now that we’ve gone through the different types of joins available, we will return to our main focus: joining our course datasets together. While we didn’t do any data processing steps on it, we still have the course_minutes dataset in our environment from when we loaded it there earlier in the chapter. In the code chunk below, we will rename the necessary variables in that dataset so that it is ready to merge. Then, we will merge the course_minutes dataset, with its newly renamed variables student_id and course_id, with our dat dataset.

Note that they’re now combined, even though the course data had many more rows. The pre-survey data has been joined for each student-course combination. We have a pretty large data frame! Let’s take a quick look.

## # A tibble: 40,348 x 22
##    course_id subject semester section student_id Gradebook_Item Grade_Category
##    <chr>     <chr>   <chr>    <chr>        <dbl> <chr>          <chr>         
##  1 AnPhA-S1… AnPhA   S116     01           60186 POINTS EARNED… <NA>          
##  2 AnPhA-S1… AnPhA   S116     01           60186 WORK ATTEMPTED <NA>          
##  3 AnPhA-S1… AnPhA   S116     01           60186 0.1: Message … <NA>          
##  4 AnPhA-S1… AnPhA   S116     01           60186 0.2: Intro As… Hw            
##  5 AnPhA-S1… AnPhA   S116     01           60186 0.3: Intro As… Hw            
##  6 AnPhA-S1… AnPhA   S116     01           60186 1.1: Quiz      Qz            
##  7 AnPhA-S1… AnPhA   S116     01           60186 1.2: Quiz      Qz            
##  8 AnPhA-S1… AnPhA   S116     01           60186 1.3: Create a… Hw            
##  9 AnPhA-S1… AnPhA   S116     01           60186 1.3: Create a… Hw            
## 10 AnPhA-S1… AnPhA   S116     01           60186 1.4: Negative… Hw            
## # … with 40,338 more rows, and 15 more variables: FinalGradeCEMS <dbl>,
## #   Points_Possible <dbl>, Points_Earned <dbl>, Gender <chr>, q1 <dbl>,
## #   q2 <dbl>, q3 <dbl>, q4 <dbl>, q5 <dbl>, q6 <dbl>, q7 <dbl>, q8 <dbl>,
## #   q9 <dbl>, q10 <dbl>, TimeSpent <dbl>

It looks like we have 40348 observations from 22 variables.

7.9.3 Finding Distinct Cases at the Student-Level

If a student was enrolled in two courses, she will have a different final grade for each of those two courses. However, our data in its current form has many rows representing *each course. An easy way we can visually inspect to make sure every row is the same for the same student, by course is to use the glimpse() function. Try it below.

## Rows: 40,348
## Columns: 22
## $ course_id       <chr> "AnPhA-S116-01", "AnPhA-S116-01", "AnPhA-S116-01", "A…
## $ subject         <chr> "AnPhA", "AnPhA", "AnPhA", "AnPhA", "AnPhA", "AnPhA",…
## $ semester        <chr> "S116", "S116", "S116", "S116", "S116", "S116", "S116…
## $ section         <chr> "01", "01", "01", "01", "01", "01", "01", "01", "01",…
## $ student_id      <dbl> 60186, 60186, 60186, 60186, 60186, 60186, 60186, 6018…
## $ Gradebook_Item  <chr> "POINTS EARNED & TOTAL COURSE POINTS", "WORK ATTEMPTE…
## $ Grade_Category  <chr> NA, NA, NA, "Hw", "Hw", "Qz", "Qz", "Hw", "Hw", "Hw",…
## $ FinalGradeCEMS  <dbl> 86.3, 86.3, 86.3, 86.3, 86.3, 86.3, 86.3, 86.3, 86.3,…
## $ Points_Possible <dbl> 5, 30, 105, 140, 5, 5, 20, 50, 10, 50, 5, 5, 24, 10, …
## $ Points_Earned   <dbl> 4.05, 24.00, 71.67, 140.97, 5.00, 4.00, NA, 50.00, NA…
## $ Gender          <chr> "F", "F", "F", "F", "M", "F", "F", "F", "F", "F", "M"…
## $ q1              <dbl> 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,…
## $ q2              <dbl> 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,…
## $ q3              <dbl> 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,…
## $ q4              <dbl> 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,…
## $ q5              <dbl> 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,…
## $ q6              <dbl> 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,…
## $ q7              <dbl> 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,…
## $ q8              <dbl> 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,…
## $ q9              <dbl> 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,…
## $ q10             <dbl> 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,…
## $ TimeSpent       <dbl> 2087, 2087, 2087, 2087, 2087, 2087, 2087, 2087, 2087,…

You can also use View(dat) in order to view the data in RStudio’s viewer.

Visually inspecting the first several rows of data, we see that they all correspond to the same student for the same course. As we expected, the FinalGradeCEMs variable (representing students’ final grade) is also consistent across these rows.

Since we are not carrying out a finer-grained analysis using the Gradebook_Item, these duplicate rows are not necessary. We only want variables at the student level, and not at the level of different gradebook items. We can extract only the unique student-level data using the distinct() function. This function takes as arguments the name of the data frame and the name of the variables used to determine what counts as a unique case.

Imagine having a bucket of Halloween candy that has 100 pieces of candy. You know that these 100 pieces are really just a bunch of duplicate pieces from a relatively short list of candy brands. distinct() takes that bucket of 100 pieces and returns a bucket containing only one of each distinct piece.

Another thing to note about distinct() is that it will only return the variable(s) (it is possible to pass more than one variable to distinct()) you used to determine uniqueness, unless you include the argument .keep_all = TRUE. For the sake of making it simple to view the output, we will omit this argument for now.

Were we to run distinct(dat, Gradebook_Item), what do you think would be returned? Running the following code returns a one-column data frame that lists the names of every distinct gradebook item.

## # A tibble: 222 x 1
##    Gradebook_Item                                  
##    <chr>                                           
##  1 POINTS EARNED & TOTAL COURSE POINTS             
##  2 WORK ATTEMPTED                                  
##  3 0.1: Message Your Instructor                    
##  4 0.2: Intro Assignment - Discussion Board        
##  5 0.3: Intro Assignment - Submitting Files        
##  6 1.1: Quiz                                       
##  7 1.2: Quiz                                       
##  8 1.3: Create a Living Creature                   
##  9 1.3: Create a Living Creature - Discussion Board
## 10 1.4: Negative Feedback Loop Flowchart           
## # … with 212 more rows

You might be wondering whether some gradebook items have the same names across courses. We can return the unique combination of courses and gradebook items by simply adding another variable to distinct():

## # A tibble: 1,269 x 2
##    course_id     Gradebook_Item                                  
##    <chr>         <chr>                                           
##  1 AnPhA-S116-01 POINTS EARNED & TOTAL COURSE POINTS             
##  2 AnPhA-S116-01 WORK ATTEMPTED                                  
##  3 AnPhA-S116-01 0.1: Message Your Instructor                    
##  4 AnPhA-S116-01 0.2: Intro Assignment - Discussion Board        
##  5 AnPhA-S116-01 0.3: Intro Assignment - Submitting Files        
##  6 AnPhA-S116-01 1.1: Quiz                                       
##  7 AnPhA-S116-01 1.2: Quiz                                       
##  8 AnPhA-S116-01 1.3: Create a Living Creature                   
##  9 AnPhA-S116-01 1.3: Create a Living Creature - Discussion Board
## 10 AnPhA-S116-01 1.4: Negative Feedback Loop Flowchart           
## # … with 1,259 more rows

The data frame we get when we run the code chunk above yields a much longer (more observations) dataset. Thus, it looks like a lot of gradebook items were repeated across courses - likely across the different sections of the same course. If you’d like, you can continue to investigate this: we would be curious to hear what you find if you do!

Next, let’s use a similar process to find the unique values at the student level. Thus, instead of exploring unique gradebook items, we will explore unique students (still accounting for the course, as students could enroll in more than one course.) This time, we will add the keep_all = TRUE argument.

This is a much smaller data frame - with one row for each student in the course. Whereas our prior version of the dat dataset had over 40,000 rows, that prior version is only helpful if we wanted to do an analysis at the level of specific students’ grades for specific gradebook items. Our new dataset keeps only the unique combinations of student and course, leaving us with a more manageable number of observations: 603. Now that our data are ready to go, we can start to ask some questions of the data.

Let’s take one last step. Since we will be using the final grade variable in many of the figures and analyses that follow, let’s rename it using the {dplyr} rename() function to something that is a bit easier to type and remember than FinalGradeCEMS:

7.10 Analysis

In this section, we focus on some initial analyses in the form of visualizations and some models. We expand on these in Chapter 13. Before we start visualizing relationships between variables in our survey dataset, let’s introduce {ggplot2}, a visualization package we’ll be using in our walkthroughs.

7.10.1 About {ggplot2}

{ggplot2} is a package we’ll be using a lot for graphing our education datasets. {ggplot2} is designed to build graphs layer by layer, where each layer is a building block for your graph. Making graphs in layers is useful because we can think of building up our graphs in separate parts: the data comes first, then the x-axis and y-axis, and finally other components like text labels and graph shapes. When something goes wrong and your ggplot2 code returns an error, you can learn about what’s happening by removing one layer at a time and running it again until the code works properly. Once you know which line is causing the problem, you can focus on fixing it.

The first two lines of {ggplot2} code look similar for most graphs. The first line tells R which dataset to graph and which columns the x-axis and y-axis will represent. The second line tells R which shape to use when drawing the graph. You can tell R which shape to use in your graphs with a family of {ggplot2} functions that start with geom_. {ggplot2} has many graph shapes you can use, including points, bars, lines, and boxplots. Here’s a {ggplot2} example using a dataset of school mean test scores to graph a bar chart:

Example Plot

Figure 7.1: Example Plot

The data argument in the first line tells R we’ll be using the dataset called students. The aes argument tells R we’ll be using values from the school_id column for the x-axis and values from the mean_score column for the y-axis. In the second line, the geom_bar function tells R we’ll drawing the graph using the bar chart format. Each line of {ggplot2} code is connected by a + at the end to tell R the next line of code is an additional {ggplot2} layer to add.

Writing code is like writing essays. There’s a range of acceptable styles and certainly you can practice unusual ways of writing, but other people will find it harder to understand what you want to say. In this book, you’ll see variations in {ggplot2} style, but all within what we believe is the range of acceptable conventions. Here are some examples:

  • Piping data to ggplot() using %>% vs including it as an argument in ggplot()
  • Using ggtitle() for labels vs using labs()
  • Order of ggplot() levels

It’s ok if those terms are new to you. The main point is there are multiple ways to make the plot you want. You’ll see that in this book and in other peoples’ code. As you learn, we encourage you to practice empathy and think about how well your code conveys your ideas to other people, including yourself when you look at it many weeks from when you wrote it.

7.10.2 The Relationship between Time Spent on Course and Final Grade

One thing we might be wondering is how time spent on course is related to students’ final grade. Let’s make a plot to depict that relationship. Below, we’ll use geom_point instead of geom_bar.

Percentage Earned vs. Time Spent

Figure 7.2: Percentage Earned vs. Time Spent

Note: you may receive a warning that reads Warning message: Removed 5 rows containing missing values (geom_point). This is due to the NA values that were introduced through coercion earlier in this walkthrough, and are not a cause for alarm!

There appears to be some relationship. What if we added a line of best fit - a linear model? The code below is the same plot we just made, but it includes the addition of another layer called geom_smooth.

Adding a Line of Best Fit

Figure 7.3: Adding a Line of Best Fit

Looking at this plot, it appears that the more time students spent on the course, the higher that there final grade is.

What is the line doing in the upper right part of the graph? Based upon the trend that is observable in the data, the line of best fit predicts that students who spend a particular amount of time on the course earn greater than 100 for their final grade! Of course, this is not possible, and highlights the importance of understanding your data and carefully interpreting lines of best fit (and other, more sophisticated analyses) carefully, keeping that understanding and knowledge in mind as you present and make sense of the results.

7.10.3 Linear Model (Regression)

We can find out exactly what the relationship between these two variables is using a linear model. We discuss linear models in more detail in Chapter 10.

Let’s use this technique to model the relationship between the time spent on the course and students’ final grade. Here, we predict final_grade. Students’ final, reported grade is the dependent, or y-variable, and so we enter it first, after the lm() command and before the tilde (~) symbol. To the right of the tilde is one independent variable, TimeSpent, or the time that students spent on the course. We also pass, or provide, the data frame, dat. At this point, we’re ready to run the model. Let’s run this line of code and save the results to an object - we chose m_linear, but any name will work. We will then run the summary() function on the output.

## 
## Call:
## lm(formula = final_grade ~ TimeSpent, data = dat)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -67.14  -7.80   4.72  14.47  30.32 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 6.58e+01   1.49e+00   44.13   <2e-16 ***
## TimeSpent   6.08e-03   6.48e-04    9.38   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 20.7 on 571 degrees of freedom
##   (30 observations deleted due to missingness)
## Multiple R-squared:  0.134,  Adjusted R-squared:  0.132 
## F-statistic:   88 on 1 and 571 DF,  p-value: <2e-16

Another way that we can generate table output is with a function from the {sjPlot} package, tab_model(). When you run this code, you should see the results pop up in the “Viewer” pane of RStudio. If you haven’t changed the default settings, this will be in the lower right quadrant of your screen.

Table 7.1
  final grade
Predictors Estimates CI p
(Intercept) 65.81 62.88 – 68.74 <0.001
TimeSpent 0.01 0.00 – 0.01 <0.001
Observations 573
R2 / R2 adjusted 0.134 / 0.132

This will work well for R Markdown documents (or simply to interpret the model in R). If you want to save the model for use in a Word document, the {apaTables} (https://cran.r-project.org/web/packages/apaTables/vignettes/apaTables.html) package may be helpful. To save a table in Word format, just pass the name of the regression model to a function from the apaTables package, like we did with the tab_model() function. Then, you can save the output to a Word document, simply by adding a filename argument:

You might be wondering what else the {apaTables} package does. We encourage you to read more about the package here: https://cran.r-project.org/web/packages/apaTables/index.html. The vignette is especially helpful. One function that may be useful for writing manuscripts is the following function for creating correlation tables. This function takes, as an input, a data frame with the variables for which you wish to calculate correlations.

Before we proceed to the next code chunk, let’s talk about some functions we’ll be using a lot in this book. filter(), group_by(), and summarize() are functions in the {dplyr} package that you will see a lot in upcoming chapters. You got a preview of these functions earlier in this chapter, and now that you’ve seen how they are used, we want to provide clear definitions for each of these functions.

  • filter() removes rows from the dataset that don’t match a criteria. Use it for tasks like only keeping records for students in the fifth grade
  • group_by() groups records together so you can perform operations on those groups instead of on the entire dataset. Use it for tasks like getting the mean test score of each school instead of a whole school district
  • summarize() and summarise() reduce your dataset down to a summary statistic. Use it for tasks like turning a dataset of student test scores into a dataset of grade levels and their mean test score

Now let’s use these {dplyr} functions on our survey analysis. We will create the same measures (based on the survey items) that we used earlier to understand how they relate to one another.

## # A tibble: 515 x 4
## # Groups:   student_id [515]
##    student_id   int    pc    uv
##         <dbl> <dbl> <dbl> <dbl>
##  1      43146  5     4.5   4.33
##  2      44638  4.2   3.5   4   
##  3      47448  5     4     3.67
##  4      47979  5     3.5   5   
##  5      48797  3.8   3.5   3.5 
##  6      49147  4.25  3.73  3.71
##  7      51943  4.6   4     4   
##  8      52326  5     3.5   5   
##  9      52446  3     3     3.33
## 10      53248  4     3     3.33
## # … with 505 more rows

Now that we’ve prepared the survey responses, we can use the apa.cor.table() function:

## 
## 
## Means, standard deviations, and correlations with confidence intervals
##  
## 
##   Variable      M        SD       1           2          3         
##   1. student_id 85966.07 10809.12                                  
##                                                                    
##   2. int        4.22     0.59     .00                              
##                                   [-.08, .09]                      
##                                                                    
##   3. pc         3.60     0.64     .04         .59**                
##                                   [-.05, .13] [.53, .64]           
##                                                                    
##   4. uv         3.71     0.71     .02         .57**      .50**     
##                                   [-.06, .11] [.51, .62] [.43, .56]
##                                                                    
## 
## Note. M and SD are used to represent mean and standard deviation, respectively.
## Values in square brackets indicate the 95% confidence interval.
## The confidence interval is a plausible range of population correlations 
## that could have caused the sample correlation (Cumming, 2014).
## * indicates p < .05. ** indicates p < .01.
## 

The time spent variable is on a very large scale (minutes); what if we transformed it to represent the number of hours that students spent on the course? Let’s use the mutate() function we used earlier. We’ll end the variable name in _hours, to represent what this variable means.

Table 7.2
  final grade
Predictors Estimates CI p
(Intercept) 65.81 62.88 – 68.74 <0.001
TimeSpent_hours 0.36 0.29 – 0.44 <0.001
Observations 573
R2 / R2 adjusted 0.134 / 0.132

The scale still does not seem quite right. What if we standardized the variable to have a mean of zero and a standard deviation of one?

Table 7.3
  final grade
Predictors Estimates CI p
(Intercept) 76.75 75.05 – 78.45 <0.001
TimeSpent_std 8.24 6.51 – 9.96 <0.001
Observations 573
R2 / R2 adjusted 0.134 / 0.132

When we look at this output, it seems to make more sense. However, there is a different interpretation now for the time spent variable: for every one standard deviation increase in the amount of time spent on the course, students’ final grades increases by 8.24, or around eight percentage points.

7.11 Results

Let’s extend our regression model and consider the following to be the final model in this sequence of models: What other variables may matter? Perhaps there are differences based on the subject of the course. We can add subject as a variable easily, as follows:

We can use tab_model() once again to view the results:

Table 7.4
  final grade
Predictors Estimates CI p
(Intercept) 70.19 66.76 – 73.61 <0.001
TimeSpent_std 9.63 7.90 – 11.37 <0.001
subject [BioA] -1.56 -8.64 – 5.52 0.665
subject [FrScA] 11.73 7.38 – 16.08 <0.001
subject [OcnA] 1.10 -3.96 – 6.16 0.670
subject [PhysA] 16.04 10.00 – 22.07 <0.001
Observations 573
R2 / R2 adjusted 0.213 / 0.206

It looks like subject FrSc - forensic science - and subject Ocn - oceanography - are associated with a higher final grade. This indicates that students in those two classes earned higher grades than students in other science classes in this dataset.

7.12 Conclusion

In this walkthrough, we focused on taking unprocessed, or raw data, and loading, viewing, and then processing it through a series of steps. The result was a data set which we could use to create visualizations and a simple (but powerful!) linear model, also known as a regression model. We found that the time that students spent on the course was positively (and statistically significantly) related to students’ final grades, and that there appeared to be differences by subject. While we focused on using this model in a traditional, explanatory sense, it could also potentially be used for predictive analytics, in that knowing how long students spent on the course and what subject their course is could be used to estimate what that students’ final grade might be. We focus on uses of predictive models further in Chapter 14.

In the follow-up to this walkthrough (see Chapter 13), we will focus on visualizing and then modeling the data using an advanced methodological technique, multi-level models, using the data we prepared as a part of this data processing pipeline used in this chapter.