Analytics Types & Visualization

Learning Analytics — Analytics & Visualization (Required)

Author

Caitlin Shelton

Published

June 13, 2001

Learning objectives

By the end of this file, you will be able to:

  • Simulate and save an educational dataset in R
  • Apply descriptive analytics using colMeans() and rowMeans()
  • Reshape data from wide to long format using pivot_longer()
  • Create and interpret scatter plots, bar plots, line plots, and histograms
  • Compute and interpret correlation between two variables
  • Apply the analytics type (descriptive, diagnostic, predictive) to real questions

The analytics types — a reminder

Before coding, connect each technique to the type of question it answers:

Analytics type Question Technique used in this file
Descriptive What happened? Summary stats, bar plot, histogram
Diagnostic Why did it happen? Scatter plot, correlation
Predictive What will happen next? Regression line, risk flagging

Keep this table in mind as you work through the exercises below. Every output you produce should be connected to one of these questions.

Part 1 · Creating and saving a simulated dataset

Instead of loading existing data, we will create our own simulated dataset. This teaches you how data is structured in R — useful when you need to build a small dataset from scratch for testing or teaching.

Creating the dataset

# set.seed() makes the random data reproducible —
# everyone running this code gets the same values
set.seed(42)

data_lms <- data.frame(
  Student_ID = paste("Student", 1:40, sep = "_"),
  Week_1  = sample(6:20, 40, replace = TRUE),
  Week_2  = sample(6:20, 40, replace = TRUE),
  Week_3  = sample(6:20, 40, replace = TRUE),
  Week_4  = sample(6:20, 40, replace = TRUE),
  Week_5  = sample(6:20, 40, replace = TRUE),
  Week_6  = sample(6:20, 40, replace = TRUE),
  Week_7  = sample(6:20, 40, replace = TRUE),
  Week_8  = sample(6:20, 40, replace = TRUE),
  Week_9  = sample(6:20, 40, replace = TRUE),
  Week_10 = sample(6:20, 40, replace = TRUE),
  Week_11 = sample(6:20, 40, replace = TRUE),
  Week_12 = sample(6:20, 40, replace = TRUE),
  Week_13 = sample(6:20, 40, replace = TRUE),
  Week_14 = sample(6:20, 40, replace = TRUE),
  Week_15 = sample(6:20, 40, replace = TRUE),
  Week_16 = sample(6:20, 40, replace = TRUE)
)

# Inspect the first few rows
head(data_lms)

Question: What does sample(6:20, 40, replace = TRUE) do? What would change if you set replace = FALSE? As always, use your own words to answer the question.

  • What this means is that you are randomly sampling 40 from a set of 15. Including TRUE in the statement means that you will get 40 items, but because the pool is less than 40 there will be repeats. Including FALSE in the statement will give you an error because you cannot pull 40 unique values from a pool of 15.

Saving the dataset

# Save as a CSV file in your project folder
write.csv(data_lms, "data_lms.csv", row.names = FALSE)

# Confirm it saved — check your Files pane for the new file
getwd()
[1] "/cloud/project/CUED7540_LearningAnalytics"

Question: Why is it important to be able to create and save datasets manually, rather than only working with provided data?

  • While you can work with provided data, being able to create and save datasets as you work allows you to do more with the information. You are not confided by data provided. You can clean and work with the datasets that you created which will ultimately help as you work with the data.

Part 2 · Descriptive analytics — what happened?

Summary statistics

# Summary of all weekly columns (excluding Student_ID column)
summary_stats <- summary(data_lms[, -1])
summary_stats
     Week_1          Week_2          Week_3          Week_4     
 Min.   : 6.00   Min.   : 6.00   Min.   : 6.00   Min.   : 6.00  
 1st Qu.: 9.00   1st Qu.: 8.00   1st Qu.: 9.75   1st Qu.:12.00  
 Median :13.00   Median :10.50   Median :12.50   Median :14.50  
 Mean   :12.32   Mean   :10.75   Mean   :12.53   Mean   :14.28  
 3rd Qu.:15.00   3rd Qu.:13.00   3rd Qu.:16.00   3rd Qu.:18.00  
 Max.   :20.00   Max.   :20.00   Max.   :19.00   Max.   :20.00  
     Week_5          Week_6          Week_7          Week_8     
 Min.   : 6.00   Min.   : 6.00   Min.   : 6.00   Min.   : 6.00  
 1st Qu.: 8.50   1st Qu.: 9.00   1st Qu.: 8.75   1st Qu.:10.75  
 Median :13.50   Median :15.00   Median :14.00   Median :13.50  
 Mean   :13.18   Mean   :13.22   Mean   :13.60   Mean   :13.05  
 3rd Qu.:17.00   3rd Qu.:17.00   3rd Qu.:18.25   3rd Qu.:16.00  
 Max.   :20.00   Max.   :20.00   Max.   :20.00   Max.   :20.00  
     Week_9         Week_10         Week_11         Week_12     
 Min.   : 6.00   Min.   : 6.00   Min.   : 6.00   Min.   : 6.00  
 1st Qu.:10.00   1st Qu.: 9.00   1st Qu.:10.75   1st Qu.: 8.00  
 Median :14.00   Median :13.00   Median :14.00   Median :12.00  
 Mean   :13.05   Mean   :12.75   Mean   :13.47   Mean   :12.12  
 3rd Qu.:16.00   3rd Qu.:16.00   3rd Qu.:17.00   3rd Qu.:15.00  
 Max.   :20.00   Max.   :20.00   Max.   :20.00   Max.   :19.00  
    Week_13         Week_14         Week_15         Week_16     
 Min.   : 6.00   Min.   : 6.00   Min.   : 6.00   Min.   : 6.00  
 1st Qu.: 9.75   1st Qu.:10.75   1st Qu.:10.75   1st Qu.:10.00  
 Median :14.00   Median :14.00   Median :15.00   Median :15.00  
 Mean   :12.90   Mean   :13.70   Mean   :13.75   Mean   :13.65  
 3rd Qu.:16.00   3rd Qu.:17.25   3rd Qu.:17.00   3rd Qu.:17.00  
 Max.   :20.00   Max.   :20.00   Max.   :20.00   Max.   :20.00

Question: What insights do you gain from the summary? Pick one week and describe what the min, median, and max values tell you about student engagement that week.

  • This allows you to compare and contrast the values between the different weeks. Looking at Week 16, the lowest score was 6 and the highest was 20. The average score, mean, was 13.65. With the median score being 15, that is higher than average which indicates more student engagement.

Average time spent per week (colMeans)

# Select only the Week columns explicitly using grep()
# This protects against any extra columns added later (Semester_Average etc.)
# that would break names(average_time) if included accidentally
week_cols    <- grep("^Week_", names(data_lms), value = TRUE)
average_time <- colMeans(data_lms[, week_cols])
average_time
 Week_1  Week_2  Week_3  Week_4  Week_5  Week_6  Week_7  Week_8  Week_9 Week_10 
 12.325  10.750  12.525  14.275  13.175  13.225  13.600  13.050  13.050  12.750 
Week_11 Week_12 Week_13 Week_14 Week_15 Week_16 
 13.475  12.125  12.900  13.700  13.750  13.650

Question: If some weeks show notably higher or lower average time, what actions might an instructor take?

  • The weeks that have higher engagement time show that hopefully the material is interesting to the students, so they spend more time with it. It could be that those weeks simply have more work built into them though, which means the students have to spend more time working on it. The flip side is also true for lower engagement times. I would expect there to be higher times during midterm and finals weeks. As an instructor, I would look at what all was built into each week’s work to ensure things are balanced.

Each student’s semester average (rowMeans)

# rowMeans() calculates the mean across columns for each row (each student)
data_lms$Semester_Average <- rowMeans(data_lms[, 2:17])

head(data_lms |> select(Student_ID, Semester_Average))

Task: Calculate the average time spent for only Weeks 1–5 and save it as early_semester_average. Add it to the data frame.

# YOUR CODE HERE
# Hint: weeks 1–5 are columns 2–6 in the data frame.
# Follow the same pattern as the row-means chunk above,
# but change the column range to cover only the first 5 weeks.
data_lms$early_semester_average <- rowMeans(data_lms [, 2:6])

head(data_lms |> select(Student_ID, early_semester_average))

Question: How could the early semester average help an instructor identify at-risk students before midterm?

  • As an advisor, I see this all the time. If faculty members pay attention to the student progress early in the semester, they can submit early alerts which help us support the at risk students before they get too deeply in the hole.

Part 3 · Visualization — bar plot and line plot

Prepare data for plotting

# Confirm average_time exists and has names before reshaping
# This prevents the "zero-length variable name" error
stopifnot(
  "Run the col-means chunk first" = exists("average_time"),
  "average_time has no names"     = !is.null(names(average_time)),
  "average_time is empty"         = length(average_time) > 0
)

average_time_table <- data.frame(
  Week               = factor(names(average_time), levels = names(average_time)),
  Average_Time_Spent = average_time
)

# Quick check — should show 16 rows, one per week
nrow(average_time_table)
[1] 16
head(average_time_table)

Bar plot — average time per week

ggplot(average_time_table, aes(x = Week, y = Average_Time_Spent)) +
  geom_bar(stat = "identity", fill = "#1D9E75", color = "white") +
  labs(
    title = "Average Time Spent per Week",
    x = "Week",
    y = "Average Hours"
  ) +
  theme_minimal() +
  theme(
    plot.title  = element_text(size = 16, face = "bold", hjust = 0.5),
    axis.text.x = element_text(angle = 45, hjust = 1)
  )

Average LMS time spent per week across all 40 students

Line plot — trend over time

ggplot(average_time_table, aes(x = Week, y = Average_Time_Spent, group = 1)) +
  geom_line(color = "#185FA5", linewidth = 1.2) +
  geom_point(color = "#185FA5", size = 3) +
  labs(
    title = "Trend of Average Time Spent per Week",
    x = "Week",
    y = "Average Hours"
  ) +
  theme_minimal() +
  theme(
    plot.title  = element_text(size = 16, face = "bold", hjust = 0.5),
    axis.text.x = element_text(angle = 45, hjust = 1)
  )

Trend of average LMS time across the semester

Question: What differences do you notice between the bar plot and the line plot? Which is more effective for showing a trend and why? Use your own words.

  • One area is the difference between the average hours highlighted. The bar plot starts from zero whereas the line plot starts with 11. I personally think the line plot is more effective for showing a trend. It allows you to see patterns a bit more clearly, notably growth/decline.

Line plot — individual students

# Reshape from wide to long format for individual student lines
data_long <- data_lms |>
  pivot_longer(
    cols      = starts_with("Week"),
    names_to  = "Week",
    values_to = "TimeSpent"
  )

ggplot(data_long, aes(x = Week, y = TimeSpent,
                      group = Student_ID, color = Student_ID)) +
  geom_line(alpha = 0.5) +
  labs(
    title = "Weekly Time Spent by Each Student",
    x = "Week",
    y = "Hours"
  ) +
  theme_minimal() +
  theme(
    plot.title     = element_text(size = 14, face = "bold", hjust = 0.5),
    axis.text.x    = element_text(angle = 45, hjust = 1),
    legend.position = "none"
  )

Weekly LMS time for all 40 students

Question: What patterns do you notice when looking at all 40 students at once? Is this visualization easy to interpret? Why or why not?

  • I’ll be honest, it is not easy to look at this visualization to notice any sort of patterns. It is quite overwhelming to see all 40 students at once and follow along with what line correlates with which student.

Line plot — selected students only

Task: Choose 5 students you want to compare and update the code below.

# YOUR CODE HERE
# Step 1: Choose 5 Student_IDs from the data and filter for them.
#         Student IDs are in the format "Student_1", "Student_2", etc.
#         Pick students whose patterns you find interesting to compare —
#         for example, mix high and low average engagement.
#
# Step 2: Reshape with pivot_longer() — same as the lineplot-all chunk above.
#
# Step 3: Plot with ggplot() — copy the structure from lineplot-all
#         and adjust the title and legend position.

library(dplyr)
selected_students <- data_lms%>%
  filter(Student_ID %in% c("Student_1","Student_4","Student_13","Student_25","Student_32"))

data_long <- data_lms |>
  pivot_longer(
    cols = starts_with("Week"),
    names_to = "Week",
    values_to = "TimeSpent"
  )

ggplot(data_long, aes(x = Week, y = TimeSpent,
                      group = Student_ID, color = Student_ID)) +
  geom_line() +
  geom_point() +
  labs (
    title = "Weekly LMS Time for Selected Students",
    x = "Week",
    y = "Engagement"
  ) +
  theme_minimal() +
  theme(
    plot.title = element_text(size = 14, face = "bold", hjust = 0.5),
    axis.text.x = element_text(angle = 45, hjust = 1),
    legend.position = "none"
    )

Weekly LMS time for selected students

Question: What insights do you gain from this focused view? What design decisions did you make in choosing these five students?

  • Truthfully, there is an error somewhere with my table. It is not filtering based on the individual five students I selected, so it is not making it easy to gain anything from the attempted focus view. Additionally, my weeks are not showing up correctly in order.

Histogram — semester averages

ggplot(data_lms, aes(x = Semester_Average)) +
  geom_histogram(binwidth = 1, fill = "#378ADD", color = "white") +
  labs(
    title = "Distribution of Semester Average Time Spent",
    x = "Semester Average (hours/week)",
    y = "Number of Students"
  ) +
  theme_minimal() +
  theme(plot.title = element_text(size = 14, face = "bold", hjust = 0.5))

Distribution of semester averages across 40 students

Part 4 · Diagnostic analytics — why did it happen?

Now we switch to the sci-online-classes dataset to explore the relationship between time spent and final grades.

# Load the dataset used in the previous module
# Make sure sci-online-classes.csv is in your data folder
data_sci <- read_csv("data/sci-online-classes.csv") |>
  clean_names()

glimpse(data_sci)
Rows: 603
Columns: 30
$ student_id            <dbl> 43146, 44638, 47448, 47979, 48797, 51943, 52326,…
$ course_id             <chr> "FrScA-S216-02", "OcnA-S116-01", "FrScA-S216-01"…
$ total_points_possible <dbl> 3280, 3531, 2870, 4562, 2207, 4208, 4325, 2086, …
$ total_points_earned   <dbl> 2220, 2672, 1897, 3090, 1910, 3596, 2255, 1719, …
$ percentage_earned     <dbl> 0.6768293, 0.7567261, 0.6609756, 0.6773345, 0.86…
$ subject               <chr> "FrScA", "OcnA", "FrScA", "OcnA", "PhysA", "FrSc…
$ semester              <chr> "S216", "S116", "S216", "S216", "S116", "S216", …
$ section               <chr> "02", "01", "01", "01", "01", "03", "01", "01", …
$ gradebook_item        <chr> "POINTS EARNED & TOTAL COURSE POINTS", "ATTEMPTE…
$ grade_category        <lgl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, …
$ final_grade_cems      <dbl> 93.45372, 81.70184, 88.48758, 81.85260, 84.00000…
$ points_possible       <dbl> 5, 10, 10, 5, 438, 5, 10, 10, 443, 5, 12, 10, 5,…
$ points_earned         <dbl> NA, 10.00, NA, 4.00, 399.00, NA, NA, 10.00, 425.…
$ gender                <chr> "M", "F", "M", "M", "F", "F", "M", "F", "F", "M"…
$ q1                    <dbl> 5, 4, 5, 5, 4, NA, 5, 3, 4, NA, NA, 4, 3, 5, NA,…
$ q2                    <dbl> 4, 4, 4, 5, 3, NA, 5, 3, 3, NA, NA, 5, 3, 3, NA,…
$ q3                    <dbl> 4, 3, 4, 3, 3, NA, 3, 3, 3, NA, NA, 3, 3, 5, NA,…
$ q4                    <dbl> 5, 4, 5, 5, 4, NA, 5, 3, 4, NA, NA, 5, 3, 5, NA,…
$ q5                    <dbl> 5, 4, 5, 5, 4, NA, 5, 3, 4, NA, NA, 5, 4, 5, NA,…
$ q6                    <dbl> 5, 4, 4, 5, 4, NA, 5, 4, 3, NA, NA, 5, 3, 5, NA,…
$ q7                    <dbl> 5, 4, 4, 4, 4, NA, 4, 3, 3, NA, NA, 5, 3, 5, NA,…
$ q8                    <dbl> 5, 5, 5, 5, 4, NA, 5, 3, 4, NA, NA, 4, 3, 5, NA,…
$ q9                    <dbl> 4, 4, 3, 5, NA, NA, 5, 3, 2, NA, NA, 5, 2, 2, NA…
$ q10                   <dbl> 5, 4, 5, 5, 3, NA, 5, 3, 5, NA, NA, 4, 4, 5, NA,…
$ time_spent            <dbl> 1555.1667, 1382.7001, 860.4335, 1598.6166, 1481.…
$ time_spent_hours      <dbl> 25.91944500, 23.04500167, 14.34055833, 26.643610…
$ time_spent_std        <dbl> -0.18051496, -0.30780313, -0.69325954, -0.148446…
$ int                   <dbl> 5.0, 4.2, 5.0, 5.0, 3.8, 4.6, 5.0, 3.0, 4.2, NA,…
$ pc                    <dbl> 4.50, 3.50, 4.00, 3.50, 3.50, 4.00, 3.50, 3.00, …
$ uv                    <dbl> 4.333333, 4.000000, 3.666667, 5.000000, 3.500000…
Note

This is the same dataset from previous module. We are reloading it here because the LMS time data (Parts 1–3) and the sci-online-classes data (Part 4) are separate files. Reloading makes this file self-contained.

Scatter plot with regression line

ggplot(data_sci,
       aes(x = time_spent_hours, y = final_grade_cems)) +
  geom_point(color = "#185FA5", size = 2.5, alpha = 0.6) +
  geom_smooth(method = "lm", color = "#993C1D", se = TRUE) +
  labs(
    title = "Time Spent vs. Final Grade",
    x = "Time Spent on LMS (hours)",
    y = "Final Grade"
  ) +
  theme_minimal() +
  theme(plot.title = element_text(size = 14, face = "bold", hjust = 0.5))

Relationship between time spent and final grade

Question: Based on the scatter plot, what do you expect the relationship between time spent and final grades to be? Write your hypothesis before looking at the correlation.

  • I always expect to be a more time spent on the LMS to reflect higher grades in the course.

Correlation

# cor() computes the Pearson correlation coefficient
# use = "complete.obs" ignores rows with missing data
correlation <- cor(data_sci$time_spent_hours,
                   data_sci$final_grade_cems,
                   use = "complete.obs")

correlation
[1] 0.3654121
TipInterpreting correlation
  • Values close to +1: strong positive relationship (more time → higher grade)
  • Values close to -1: strong negative relationship
  • Values close to 0: little or no linear relationship
  • This is NOT a statistics course — focus on interpreting what this number means for learners, not on p-values.

Question: With both the scatter plot and the correlation value in front of you, what can you say about the relationship between time spent and final grades? What would you recommend to an instructor based on this finding?

  • I always am a little astonished that I seem to be wrong in thinking more time on the LMS means longer engagement on the platform means students will have higher grades. It actually appears that lower time spent does make for an above average grade. One thing I may wonder is while students spend less time, quite possibly they are more focused in that window than those that spend prolonged periods of time in that system. Students are being more active in their learning and therefore retaining the material better in these shorter LMS periods.

Practice — grouped summary by subject

Task: Using data_sci, calculate the mean final_grade_cems and mean time_spent_hours grouped by subject. Arrange by mean grade descending. Which subject has the highest average grade? Is it also the subject with the most time spent?

TipHint

You have used group_by() and summarise() in the previous file. Apply the same pattern here with a different grouping variable. If you need a column name reminder, run names(data_sci) in the Console.

# YOUR CODE HERE
# Steps: group_by(subject) |> summarise(mean_grade = ..., mean_time = ...) |> arrange(desc(...))

library(dplyr)

subject_summary <- data_sci %>%
  group_by(subject) %>%
  summarise(mean_grade = mean(final_grade_cems, na.rm = TRUE),
    mean_time = mean(time_spent_hours, na.rm = TRUE)) %>%
  arrange(desc(mean_grade))

print(subject_summary)
# A tibble: 5 × 3
  subject mean_grade mean_time
  <chr>        <dbl>     <dbl>
1 PhysA         83.7      23.7
2 FrScA         80.6      25.7
3 AnPhA         75.1      40.1
4 OcnA          73.4      33.1
5 BioA          65.1      21.3

Question: Does the subject with the highest average grade also have the most time spent? What might explain any differences you find?

  • No, the subject with the highest average does not have the most time spent. It actually has one of the lower. One difference could be in relation to how well the students may know the subject matter and may mean there is less time spent on this subject material.

Part 5 · Box plot

A box plot shows the distribution of a variable across categories — useful for comparing groups and spotting outliers.

ggplot(data_sci, aes(x = gender, y = final_grade_cems, fill = gender)) +
  geom_boxplot(color = "gray30",
               outlier.colour = "#993C1D",
               outlier.shape  = 16,
               outlier.size   = 2) +
  scale_fill_manual(values = c("F" = "#E1F5EE", "M" = "#E6F1FB")) +
  labs(
    title = "Final Grade Distribution by Gender",
    x     = "Gender",
    y     = "Final Grade"
  ) +
  theme_minimal() +
  theme(
    plot.title     = element_text(size = 14, face = "bold", hjust = 0.5),
    legend.position = "none"
  )

Final grade distribution by gender

Question: What does the box plot tell you about the distribution of final grades by gender? Are there differences worth investigating?

  • As one who has never seen a box plot before, I had to do some Googling to get some ideas on how to interpret them. This box plot shows that all grades regardless of gender fell below the 50 percent mark. The females seem to be clustered in the zero to 25 range while the males seem to be a bit more spread out. I do not think there are any differences between the two genders that are worth investigating.

Final reflection

After completing both the LMS time analysis and the sci-online-classes analysis, reflect on the following:

Question: How could these analytics techniques be applied in a real classroom or course design context? Describe one specific scenario — from your track (K–12 or ID/higher ed) — where the combination of a bar plot, line plot, and correlation would help an educator or designer make a better decision.

  • From a higher ed perspective, I think that bar and line plots can be extremely beneficial to individual faculty members who could use them to track success rates for individual assignments up to department leaders who could assess overall course rates. To be specific, a department dean could use a bar plot to look at success rates in a specific course for the entire school. A bar plot could show comparative rates based on modality, part of semester, time of day, or other endless opportunities.

Render & submit

Step 1 — Add your name

Change the author: field in the YAML header at the top to your name.

Step 2 — Render

Click Render in the toolbar. A formatted HTML page will appear in your Viewer tab or a new browser window. Check the Console for any error messages if the render fails.

Step 3 — Publish

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This document shows three levels of analytics work: descriptive (summary statistics and bar plots), trend analysis (line plots), and diagnostic (scatter plot and correlation). Together they demonstrate a complete analytical workflow that is worth showcasing in a professional portfolio.

Share your published link with your instructor once you have rendered and published. Post in the course discussion board if you run into any technical issues.