Introduction

1. Overview

This Week 06 tutorial builds on our previous data analytics foundations and focuses on the critical first step of any analysis: Data Screening. Before running statistical models, we must ensure our data is clean, accurate, and meets necessary assumptions. This tutorial upgrades the lecture concepts from 06_datascreen_1.rmd into hands-on, code-first workflows:

Accuracy Checks: Identifying and fixing typos, out-of-range values, and coding errors.
Missing Data: Understanding types of missingness (MCAR, MNAR) and handling them appropriately (deletion vs. imputation).
Outlier Detection: Using univariate (Z-scores) and multivariate (Mahalanobis distance) methods.
Assumptions: A brief introduction to what we prepare for (Normality, Linearity, etc.).

Reference: This tutorial draws heavily from Field, Miles, and Field [1], Discovering Statistics Using R, particularly the chapters on data screening and cleaning, with IEEE-style citations throughout.

Upgrade note: This hands-on tutorial extends the Week 06 lecture slides in 06_datascreen_1.rmd with code-first workflows, beginner-friendly explanations, and theoretical grounding from Field et al. [1].

For Beginners: Quick Start

How to run code:
- RStudio: place cursor in a chunk, press Ctrl+Enter (Cmd+Enter on Mac) to run; use Knit to render the full document.
- VS Code: highlight lines and press Ctrl+Enter, or click the Run button above a chunk.
Installing packages: if you see “there is no package called ‘X’”, run install.packages("X") once, then library(X).
If stuck: restart R (RStudio: Session → Restart R), then re-run chunks from the top (setup first).
Reading errors: focus on the last lines of the message; they usually state the actual problem (e.g., object not found, package missing, misspelled column).

2. Learning Objectives

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

Perform accuracy checks on categorical and continuous variables.
Diagnose types of missing data (MCAR vs. MNAR).
Implement strategies for handling missing data, including listwise deletion and multiple imputation with mice.
Detect and handle univariate outliers using Z-scores (cutoff \(\pm 3.29\)).
Detect and handle multivariate outliers using Mahalanobis distance.

3. Required Packages

# Install if needed
# install.packages(c("tidyverse", "rio", "mice", "VIM", "knitr", "kableExtra", "ggplot2", "gridExtra"))

library(tidyverse)
library(ggplot2)  # For data visualization
library(gridExtra) # For arranging multiple plots
library(rio)      # For data import
library(mice)     # For multiple imputation
library(VIM)      # For visualizing missing data
library(knitr)
library(kableExtra)

cat("\n=== REPRODUCIBLE SEED INFORMATION ===")

## 
## === REPRODUCIBLE SEED INFORMATION ===

cat("\nGenerator Name: Week06 Data Screening - ANLY500")

## 
## Generator Name: Week06 Data Screening - ANLY500

cat("\nMD5 Hash:", gen$get_hash())

## 
## MD5 Hash: 4476fe6d5a95542e0ac57b95797b6709

cat("\nAvailable Seeds:", paste(seeds[1:5], collapse = ", "), "...\n\n")

## 
## Available Seeds: -803686227, -78650771, -915116207, -338502455, 574023479 ...

Part 1: Data Screening Principles

1.1 What is Data Screening?

Data screening is the process of inspecting a dataset for errors, missing values, and outliers before analysis. As Field et al. note, screening is crucial because issues like outliers can “bias the mean and inflate the standard deviation” [1], and missing data can arise from various sources (e.g., participants accidentally missing questions) [1]. Field explicitly refers to Tabachnick and Fidell as the “definitive guide to screening data” [1].

1.2 The “Garbage In, Garbage Out” Rule

Data screening is a key facet of any analysis. If the data is incorrect, the output will be useless. Screening ensures results are interpretable and valid. Our checks should always include:

Accuracy: Is the data correct? (e.g., “Age” shouldn’t be 200).
Missing Data: Is the data complete? (e.g., Did someone skip questions?).
Outliers: Are there extreme values? (e.g., A millionaire in a study of student income).
Assumptions: Does the data fit the rules of our statistical test? (e.g., Is it a bell curve?).

An Important Note on Significance

Normally, our \(\alpha\) value is set to 0.05 (Type 1 Error), meaning we use \(p < .05\) as a criterion for statistical significance. However, in data screening, we want to use a stricter criterion to avoid over-cleaning or incorrectly flagging data. Therefore, we use \(p < .001\) to denote problematic issues [1].

1.3 The Order of Operations

We follow this specific order because each step can affect the next:

Accuracy Check: If you correct errors, they may become missing data points.
Missing Data Check: If you replace missing data, they may become outliers.
Outliers Check: If you exclude outliers, this may change assumption interpretations (e.g., normality).
Assumptions: Finally, check assumptions for the specific analysis to be performed.

Part 2: Accuracy Checks

We will use a dataset that examines the resiliency (RS columns) of teenagers after a natural disaster. While we haven’t covered specific analyses yet, we can screen this data overall.

# Import the dataset
# Note: Ensure "data/data_screening.csv" exists in your working directory or adjust the path
# If the file is not available, we will simulate a similar structure for this tutorial
if(file.exists("data/data_screening.csv")) {
  master <- import("data/data_screening.csv")
} else {
  # Simulation for tutorial purposes if file is missing
  set.seed(seeds[2])
  n <- 100
  master <- data.frame(
    Sex = sample(c(1, 2, 3), n, replace = TRUE, prob = c(0.45, 0.45, 0.1)), # 3 is typo
    SES = sample(c(1, 2, 3), n, replace = TRUE),
    Grade = sample(8:14, n, replace = TRUE), # >12 is typo
    Absences = sample(0:20, n, replace = TRUE), # >15 is typo
    RS1 = sample(1:7, n, replace = TRUE),
    RS2 = sample(1:7, n, replace = TRUE),
    RS3 = sample(c(1:7, 99), n, replace = TRUE, prob = c(rep(0.14, 7), 0.02)) # 99 is outlier/typo
  )
  # Introduce some missingness
  master[sample(1:n, 10), "RS1"] <- NA
  master[sample(1:n, 5), "SES"] <- NA
}

str(master)

## 'data.frame':    137 obs. of  20 variables:
##  $ Sex     : int  1 1 1 1 1 1 1 1 1 1 ...
##  $ Age     : int  17 16 13 15 16 15 12 14 13 18 ...
##  $ SES     : int  2 3 2 3 2 3 3 3 1 3 ...
##  $ Grade   : int  11 7 5 6 11 7 4 6 4 9 ...
##  $ Absences: int  2 2 2 2 6 2 1 2 2 5 ...
##  $ RS1     : int  6 7 5 5 7 7 1 2 6 7 ...
##  $ RS2     : int  4 1 NA 5 4 7 6 3 6 6 ...
##  $ RS3     : int  2 1 5 5 4 7 NA 2 7 5 ...
##  $ RS4     : int  2 5 7 7 7 7 1 3 6 NA ...
##  $ RS5     : int  4 7 4 5 4 7 4 2 1 6 ...
##  $ RS6     : int  7 7 6 6 4 7 7 3 4 6 ...
##  $ RS7     : int  7 7 7 5 7 7 7 3 6 10 ...
##  $ RS8     : int  4 7 6 7 7 7 NA 3 6 7 ...
##  $ RS9     : int  5 4 6 6 4 7 NA 2 2 7 ...
##  $ RS10    : int  7 7 7 7 7 7 4 2 5 7 ...
##  $ RS11    : int  4 1 NA 6 7 7 3 3 6 5 ...
##  $ RS12    : int  7 7 5 6 4 7 7 3 6 6 ...
##  $ RS13    : int  4 4 7 6 7 7 7 2 6 6 ...
##  $ RS14    : int  7 7 6 6 4 7 7 3 2 6 ...
##  $ Health  : int  6 6 2 2 6 4 3 6 1 5 ...

2.1 Categorical Variables

We need to check for factor variables incorrectly imported as numbers and out-of-range values. Let’s check Sex and SES.

Visualizing the Problem

Before fixing, let’s visualize the Sex variable to see the error. We expect only two categories (e.g., 1 and 2), but a third bar might appear.

p1 <- ggplot(master, aes(x = factor(Sex))) +
  geom_bar(fill = "steelblue", color = "black") +
  labs(title = "Before Cleaning: Sex",
       subtitle = "Note the invalid category '3'",
       x = "Sex Code",
       y = "Count") +
  theme_minimal()

p1

Interpretation: You can clearly see a bar for “3”. If our codebook says 1=Women and 2=Men, then “3” is a typo! This visual confirmation is faster than reading raw tables.

Checking Tables

notypos <- master # Create a copy to update
apply(notypos[ , c("Sex", "SES")], 2, table)

##   Sex SES
## 1  64   9
## 2  72  56
## 3   1  72

Explanation: - apply(X, 2, table): This function takes our data (X), looks at columns (2), and runs the table() function on each one. - It’s a quick way to get counts for multiple columns at once.

Fixing the Issue

We can fix this by using factor() and excluding the bad label. Values not listed in levels will automatically become NA.

## Fix categorical labels and drop typos
notypos$Sex <- factor(notypos$Sex, 
                     levels = c(1,2), # We intentionally omit 3
                     labels = c("Women", "Men"))

notypos$SES <- factor(notypos$SES, 
                     levels = c(1,2, 3),
                     labels = c("Low", "Medium", "High"))

# Let's verify with a plot
p2 <- ggplot(notypos, aes(x = Sex)) +
  geom_bar(fill = "forestgreen", color = "black") +
  labs(title = "After Cleaning: Sex",
       subtitle = "Invalid categories removed (became NA)",
       x = "Sex",
       y = "Count") +
  theme_minimal()

grid.arrange(p1, p2, ncol = 2)

Visual Check: The “Before” plot shows the error (3). The “After” plot shows only valid categories (Women, Men). The typos didn’t disappear; they became NA (missing values), which we will deal with later.

2.2 Continuous Variables

Use summary() to check min/max values. For example, if the RS scale runs from 1 to 7, any value outside this range (like 99) is a typo.

summary(notypos)

##     Sex          Age            SES         Grade           Absences     
##  Women:64   Min.   :11.00   Low   : 9   Min.   : 1.000   Min.   : 1.000  
##  Men  :72   1st Qu.:13.00   Medium:56   1st Qu.: 4.000   1st Qu.: 2.000  
##  NA's : 1   Median :15.50   High  :72   Median : 6.000   Median : 2.000  
##             Mean   :15.05               Mean   : 5.883   Mean   : 3.358  
##             3rd Qu.:17.00               3rd Qu.: 8.000   3rd Qu.: 5.000  
##             Max.   :18.00               Max.   :35.000   Max.   :35.000  
##             NA's   :5                                                    
##       RS1             RS2             RS3             RS4            RS5       
##  Min.   :1.000   Min.   :1.000   Min.   : 1.00   Min.   :1.00   Min.   :1.000  
##  1st Qu.:4.000   1st Qu.:4.000   1st Qu.: 3.00   1st Qu.:3.00   1st Qu.:3.000  
##  Median :5.000   Median :5.000   Median : 4.00   Median :5.00   Median :4.000  
##  Mean   :4.858   Mean   :4.962   Mean   : 4.42   Mean   :4.55   Mean   :4.448  
##  3rd Qu.:6.000   3rd Qu.:6.000   3rd Qu.: 6.00   3rd Qu.:7.00   3rd Qu.:6.750  
##  Max.   :7.000   Max.   :7.000   Max.   :18.00   Max.   :7.00   Max.   :7.000  
##  NA's   :3       NA's   :5       NA's   :6       NA's   :6      NA's   :3      
##       RS6         RS7              RS8             RS9             RS10      
##  Min.   :1   Min.   : 1.000   Min.   :1.000   Min.   :1.000   Min.   :1.000  
##  1st Qu.:4   1st Qu.: 4.000   1st Qu.:3.000   1st Qu.:4.000   1st Qu.:4.000  
##  Median :5   Median : 5.000   Median :5.000   Median :5.000   Median :5.500  
##  Mean   :5   Mean   : 5.082   Mean   :4.764   Mean   :4.692   Mean   :5.313  
##  3rd Qu.:7   3rd Qu.: 7.000   3rd Qu.:7.000   3rd Qu.:6.000   3rd Qu.:7.000  
##  Max.   :7   Max.   :10.000   Max.   :7.000   Max.   :7.000   Max.   :7.000  
##  NA's   :7   NA's   :3        NA's   :10      NA's   :7       NA's   :3      
##       RS11            RS12            RS13             RS14     
##  Min.   :1.000   Min.   :1.000   Min.   : 1.000   Min.   :1.00  
##  1st Qu.:3.000   1st Qu.:5.000   1st Qu.: 4.000   1st Qu.:4.00  
##  Median :5.000   Median :6.000   Median : 6.000   Median :5.00  
##  Mean   :4.641   Mean   :5.552   Mean   : 5.507   Mean   :4.97  
##  3rd Qu.:6.500   3rd Qu.:7.000   3rd Qu.: 7.000   3rd Qu.:7.00  
##  Max.   :7.000   Max.   :7.000   Max.   :15.000   Max.   :7.00  
##  NA's   :6       NA's   :3       NA's   :3        NA's   :5     
##      Health     
##  Min.   :1.000  
##  1st Qu.:2.000  
##  Median :4.000  
##  Mean   :3.839  
##  3rd Qu.:6.000  
##  Max.   :7.000  
##

Visualizing Continuous Errors

Let’s look at RS3. We suspect a typo (99).

# Histogram to see distribution shape
p3 <- ggplot(notypos, aes(x = RS3)) +
  geom_histogram(fill = "orange", color = "black", bins = 30) +
  labs(title = "Histogram of RS3",
       subtitle = "Note the gap and value near 100",
       x = "RS3 Score", y = "Frequency") +
  theme_minimal()

# Boxplot to see outliers clearly
p4 <- ggplot(notypos, aes(y = RS3)) +
  geom_boxplot(fill = "orange", alpha = 0.5) +
  labs(title = "Boxplot of RS3",
       subtitle = "The dot at top is the extreme value",
       y = "RS3 Score") +
  theme_minimal()

grid.arrange(p3, p4, ncol = 2)

Interpretation: - Histogram (Left): Most data is clustered 0-10. There is a tiny bar near 100. This is suspicious. - Boxplot (Right): The box is “squashed” at the bottom, and a single dot is way up at 100. This confirms we have an out-of-range value that needs fixing.

Fixing Issues

How do we fix these? 1. Find the original data and figure out what the point should be. 2. Delete that data point (set to NA) but not the entire participant.

Example: Using Logical Subsetting Suppose Grade cannot be > 12 and Absences cannot be > 15.

# Check Grade
summary(notypos$Grade)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   1.000   4.000   6.000   5.883   8.000  35.000

# Code Explanation: "In the Grade column, find values > 12, and set them to NA"
notypos$Grade[ notypos$Grade > 12 ] <- NA 
summary(notypos$Grade)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
##   1.000   4.000   6.000   5.669   8.000  11.000       1

# Check Absences
summary(notypos$Absences)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   1.000   2.000   2.000   3.358   5.000  35.000

notypos$Absences[ notypos$Absences > 15 ] <- NA
summary(notypos$Absences)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
##   1.000   2.000   2.000   3.125   5.000   7.000       1

Example: Multiple Columns If multiple columns (e.g., RS items) have the same range (1-7), we can clean them all at once.

# Assuming RS columns are from column 5 onwards (adjust indices as needed)
# In our simulated data, RS columns are 5, 6, 7
rs_cols <- grep("RS", names(notypos))

# Check before
summary(notypos[ , rs_cols])

##       RS1             RS2             RS3             RS4            RS5       
##  Min.   :1.000   Min.   :1.000   Min.   : 1.00   Min.   :1.00   Min.   :1.000  
##  1st Qu.:4.000   1st Qu.:4.000   1st Qu.: 3.00   1st Qu.:3.00   1st Qu.:3.000  
##  Median :5.000   Median :5.000   Median : 4.00   Median :5.00   Median :4.000  
##  Mean   :4.858   Mean   :4.962   Mean   : 4.42   Mean   :4.55   Mean   :4.448  
##  3rd Qu.:6.000   3rd Qu.:6.000   3rd Qu.: 6.00   3rd Qu.:7.00   3rd Qu.:6.750  
##  Max.   :7.000   Max.   :7.000   Max.   :18.00   Max.   :7.00   Max.   :7.000  
##  NA's   :3       NA's   :5       NA's   :6       NA's   :6      NA's   :3      
##       RS6         RS7              RS8             RS9             RS10      
##  Min.   :1   Min.   : 1.000   Min.   :1.000   Min.   :1.000   Min.   :1.000  
##  1st Qu.:4   1st Qu.: 4.000   1st Qu.:3.000   1st Qu.:4.000   1st Qu.:4.000  
##  Median :5   Median : 5.000   Median :5.000   Median :5.000   Median :5.500  
##  Mean   :5   Mean   : 5.082   Mean   :4.764   Mean   :4.692   Mean   :5.313  
##  3rd Qu.:7   3rd Qu.: 7.000   3rd Qu.:7.000   3rd Qu.:6.000   3rd Qu.:7.000  
##  Max.   :7   Max.   :10.000   Max.   :7.000   Max.   :7.000   Max.   :7.000  
##  NA's   :7   NA's   :3        NA's   :10      NA's   :7       NA's   :3      
##       RS11            RS12            RS13             RS14     
##  Min.   :1.000   Min.   :1.000   Min.   : 1.000   Min.   :1.00  
##  1st Qu.:3.000   1st Qu.:5.000   1st Qu.: 4.000   1st Qu.:4.00  
##  Median :5.000   Median :6.000   Median : 6.000   Median :5.00  
##  Mean   :4.641   Mean   :5.552   Mean   : 5.507   Mean   :4.97  
##  3rd Qu.:6.500   3rd Qu.:7.000   3rd Qu.: 7.000   3rd Qu.:7.00  
##  Max.   :7.000   Max.   :7.000   Max.   :15.000   Max.   :7.00  
##  NA's   :6       NA's   :3       NA's   :3        NA's   :5

# Apply fix: any value > 7 in these columns becomes NA
notypos[ , rs_cols][ notypos[ , rs_cols] > 7 ] <- NA

# Check after
summary(notypos[ , rs_cols])

##       RS1             RS2             RS3             RS4            RS5       
##  Min.   :1.000   Min.   :1.000   Min.   :1.000   Min.   :1.00   Min.   :1.000  
##  1st Qu.:4.000   1st Qu.:4.000   1st Qu.:3.000   1st Qu.:3.00   1st Qu.:3.000  
##  Median :5.000   Median :5.000   Median :4.000   Median :5.00   Median :4.000  
##  Mean   :4.858   Mean   :4.962   Mean   :4.315   Mean   :4.55   Mean   :4.448  
##  3rd Qu.:6.000   3rd Qu.:6.000   3rd Qu.:6.000   3rd Qu.:7.00   3rd Qu.:6.750  
##  Max.   :7.000   Max.   :7.000   Max.   :7.000   Max.   :7.00   Max.   :7.000  
##  NA's   :3       NA's   :5       NA's   :7       NA's   :6      NA's   :3      
##       RS6         RS7             RS8             RS9             RS10      
##  Min.   :1   Min.   :1.000   Min.   :1.000   Min.   :1.000   Min.   :1.000  
##  1st Qu.:4   1st Qu.:4.000   1st Qu.:3.000   1st Qu.:4.000   1st Qu.:4.000  
##  Median :5   Median :5.000   Median :5.000   Median :5.000   Median :5.500  
##  Mean   :5   Mean   :5.008   Mean   :4.764   Mean   :4.692   Mean   :5.313  
##  3rd Qu.:7   3rd Qu.:7.000   3rd Qu.:7.000   3rd Qu.:6.000   3rd Qu.:7.000  
##  Max.   :7   Max.   :7.000   Max.   :7.000   Max.   :7.000   Max.   :7.000  
##  NA's   :7   NA's   :5       NA's   :10      NA's   :7       NA's   :3      
##       RS11            RS12            RS13            RS14     
##  Min.   :1.000   Min.   :1.000   Min.   :1.000   Min.   :1.00  
##  1st Qu.:3.000   1st Qu.:5.000   1st Qu.:4.000   1st Qu.:4.00  
##  Median :5.000   Median :6.000   Median :6.000   Median :5.00  
##  Mean   :4.641   Mean   :5.552   Mean   :5.364   Mean   :4.97  
##  3rd Qu.:6.500   3rd Qu.:7.000   3rd Qu.:7.000   3rd Qu.:7.00  
##  Max.   :7.000   Max.   :7.000   Max.   :7.000   Max.   :7.00  
##  NA's   :6       NA's   :3       NA's   :5       NA's   :5

Part 3: Missing Data

Use summary() or apply() to count NA values.

apply(notypos, 2, function(x) { sum(is.na(x)) })

##      Sex      Age      SES    Grade Absences      RS1      RS2      RS3 
##        1        5        0        1        1        3        5        7 
##      RS4      RS5      RS6      RS7      RS8      RS9     RS10     RS11 
##        6        3        7        5       10        7        3        6 
##     RS12     RS13     RS14   Health 
##        3        5        5        0

3.1 Diagnosing Missingness

Understanding why data is missing is crucial [1]:

MCAR (Missing Completely at Random):
- Analogy: You are carrying a tray of blood samples and trip, breaking random vials. The missingness has nothing to do with the patient’s health.
- Handling: Safe to replace or ignore.
MNAR (Missing Not at Random):
- Analogy: Patients with very high blood pressure refuse to have it measured because they are scared. The missingness is related to the health outcome.
- Handling: Dangerous to replace. Excluding might be safer.

Quick Fix: For simple statistics, you can often use na.rm = TRUE (e.g., mean(x, na.rm = TRUE)) to ignore missing values without permanently deleting them [1].

3.2 Visualizing Missing Data

The VIM package helps visualize patterns.

aggr(notypos, numbers = TRUE, prop = FALSE)

Interpretation: - Left Bar Chart: Shows the proportion of missing data in each variable. - Right Grid: Shows the combinations of missingness. Blue is observed, Red is missing. - If you see red blocks lining up across multiple variables, it means people who missed Question A also tended to miss Question B.

3.3 Handling Missing Data

By Rows (Participants)

Check the percentage of missing data per participant.

# Create a custom function to calculate % missing
percentmiss <- function(x){ sum(is.na(x))/length(x) * 100 }

# Apply it to rows (margin = 1)
missing <- apply(notypos, 1, percentmiss)
table(missing)

## missing
##   0   5  10  15  20  70 
## 108  17   4   4   1   3

We can create subsets: - Replaceable: Participants with \(\le 5\%\) missing data. - Not Replaceable: Participants with \(> 5\%\) missing data (often excluded or analyzed separately).

replace_rows <- subset(notypos, missing <= 5)
noreplace_rows <- subset(notypos, missing > 5)

cat("Original N:", nrow(notypos), "\n")

## Original N: 137

cat("Rows to replace:", nrow(replace_rows), "\n")

## Rows to replace: 125

cat("Rows dropped/kept separate:", nrow(noreplace_rows), "\n")

## Rows dropped/kept separate: 12

Multiple Imputation with `mice`

We do not replace missing data for categorical/demographic variables (Sex, SES, Grade). We use them to help estimate missing values in other variables.

What is MICE? Multivariate Imputation by Chained Equations. It creates multiple “complete” datasets by guessing missing values based on relationships with other variables. It’s better than just plugging in the mean because it preserves the variance in the data.

# Run mice on our replaceable rows
# printFlag = FALSE keeps the output clean
temp_no_miss <- mice(replace_rows, printFlag = FALSE, seed = 123)

Now, complete the dataset (pick one of the imputations, e.g., #1).

nomiss <- complete(temp_no_miss, 1)
all_columns <- nomiss # This is our clean dataset

Visual Verification: Did Imputation Change Data Shape?

It is critical to verify that imputing data didn’t distort our variables. The distribution should look roughly the same before and after.

# Combine data for plotting
before <- data.frame(Value = replace_rows$RS1, Type = "Original (with NA)")
after <- data.frame(Value = all_columns$RS1, Type = "Imputed (Complete)")
comparison <- rbind(before, after)

ggplot(comparison, aes(x = Value, fill = Type)) +
  geom_density(alpha = 0.5) +
  labs(title = "Density Plot: RS1 Before vs. After Imputation",
       subtitle = "Curves should be similar. Drastic changes indicate bad imputation.",
       x = "RS1 Score",
       y = "Density") +
  theme_minimal() +
  scale_fill_manual(values = c("blue", "red"))

Interpretation: If the Red and Blue curves overlap significantly, your imputation is good! It means you filled in the holes without changing the “story” of the data.

Part 4: Outliers

Definition: A case with an extreme value on one or multiple variables. Why remove them? The mean is sensitive to outliers. We use a strict criterion (\(p < .001\)) to remove only very extreme scores.

4.1 Univariate Outliers (Z-scores)

For a single variable, we can use Z-scores. - Concept: A Z-score tells you how many standard deviations a score is from the mean. - \(Z = 0\): Exactly average. - \(Z = +1\): One standard deviation above average. - \(Z = +3.29\): Extremely high (less than 0.1% chance). - Criterion: \(Z > 3.29\) or \(Z < -3.29\) (corresponding to \(p < .001\)) [1].

# Calculate Z-scores for RS1 (as an example)
# scale() function calculates Z-scores
all_columns$RS1_z <- scale(all_columns$RS1)

# Check for outliers
summary(all_columns$RS1_z)

##        V1          
##  Min.   :-2.15130  
##  1st Qu.:-0.50153  
##  Median : 0.04839  
##  Mean   : 0.00000  
##  3rd Qu.: 1.14824  
##  Max.   : 1.14824

Visualizing Z-scores

ggplot(all_columns, aes(x = RS1_z)) +
  geom_histogram(bins = 20, fill = "purple", color = "black") +
  geom_vline(xintercept = c(-3.29, 3.29), linetype = "dashed", color = "red", size = 1) +
  labs(title = "Histogram of Z-scores (RS1)",
       subtitle = "Red dashed lines indicate the +/- 3.29 cutoff",
       x = "Z-score",
       y = "Count") +
  theme_minimal()

Interpretation: Any bars outside the red dashed lines represent outliers that should be removed or investigated.

4.2 Multivariate Outliers: Mahalanobis Distance

For multiple continuous variables, we measure the distance of a case from the centroid (mean of means).

Concept: Imagine a cloud of points in 3D space. The “centroid” is the middle of the cloud. Mahalanobis distance measures how far a point is from this middle, accounting for the shape of the cloud.

Calculation

# Select only continuous variables for outlier check
# Let's use RS1, RS2, RS3, and Absences
cont_vars <- all_columns %>% select(RS1, RS2, RS3, Absences)

# Calculate distance
mahal <- mahalanobis(cont_vars,
                    colMeans(cont_vars, na.rm=TRUE),
                    cov(cont_vars, use ="pairwise.complete.obs"))

Cutoff and Elimination

Cutoff: \(\chi^2\) (Chi-square) distribution with \(df =\) number of variables, at \(\alpha < .001\).

cutoff <- qchisq(1 - .001, ncol(cont_vars))

cat("Degrees of Freedom:", ncol(cont_vars), "\n")

## Degrees of Freedom: 4

cat("Cutoff Value:", cutoff, "\n")

## Cutoff Value: 18.46683

# Check how many outliers
# FALSE means NOT an outlier (Good), TRUE means outlier (Bad)
summary(mahal < cutoff)

##    Mode    TRUE 
## logical     125

4.3 Visualizing Outliers

Let’s plot the Mahalanobis distances to see who the “troublemakers” are.

# Create a data frame for plotting
outlier_plot <- data.frame(
  ID = 1:length(mahal),
  Distance = mahal,
  Outlier = mahal > cutoff
)

ggplot(outlier_plot, aes(x = ID, y = Distance, color = Outlier)) +
  geom_point(size = 3, alpha = 0.7) +
  geom_hline(yintercept = cutoff, linetype = "dashed", color = "red") +
  geom_text(aes(label = ifelse(Outlier, ID, "")), vjust = -0.5, show.legend = FALSE) +
  labs(title = "Mahalanobis Distances",
       subtitle = paste("Points above the red line (Cutoff =", round(cutoff, 2), ") are multivariate outliers"),
       y = "Distance (D^2)",
       x = "Participant ID") +
  theme_minimal() +
  scale_color_manual(values = c("black", "red"))

Interpretation: - Points below the red line are safe. - Points above the red line are multivariate outliers. We’ve labeled their IDs so you can find them!

Final Removal

# Eliminate outliers
noout <- subset(all_columns, mahal < cutoff)

cat("\nDimensions before outlier removal:", dim(all_columns)[1], "\n")

## 
## Dimensions before outlier removal: 125

cat("Dimensions after outlier removal:", dim(noout)[1], "\n")

## Dimensions after outlier removal: 125

Summary

In this tutorial, we have covered the essential first steps of data analysis: 1. Accuracy: Checked for and fixed typos and impossible values. 2. Missing Data: Identified missingness patterns and used multiple imputation. 3. Outliers: Applied a strict statistical criterion (\(p < .001\)) to identify univariate and multivariate outliers.

Your dataset noout is now screened and ready for assumption checking and analysis!

References

[1] A. Field, J. Miles, and Z. Field, Discovering Statistics Using R. London: SAGE Publications, 2012.

Week 06: R for Data Analytics (Data Screening Part 1)

Ziyuan Huang

Last Updated: December 18, 2025

Introduction

1. Overview

For Beginners: Quick Start

2. Learning Objectives

3. Required Packages

Part 1: Data Screening Principles

1.1 What is Data Screening?

1.2 The “Garbage In, Garbage Out” Rule

An Important Note on Significance

1.3 The Order of Operations

Part 2: Accuracy Checks

2.1 Categorical Variables

Visualizing the Problem

Checking Tables

Fixing the Issue

2.2 Continuous Variables

Visualizing Continuous Errors

Fixing Issues

Part 3: Missing Data

3.1 Diagnosing Missingness

3.2 Visualizing Missing Data

3.3 Handling Missing Data

By Rows (Participants)

Multiple Imputation with `mice`

Visual Verification: Did Imputation Change Data Shape?

Part 4: Outliers

4.1 Univariate Outliers (Z-scores)

Visualizing Z-scores

4.2 Multivariate Outliers: Mahalanobis Distance

Calculation

Cutoff and Elimination

4.3 Visualizing Outliers

Final Removal

Summary

References

Week 06: R for Data Analytics (Data Screening Part 1)

Ziyuan Huang

Last Updated: December 18, 2025

Introduction

1. Overview

For Beginners: Quick Start

2. Learning Objectives

3. Required Packages

Part 1: Data Screening Principles

1.1 What is Data Screening?

1.2 The “Garbage In, Garbage Out” Rule

An Important Note on Significance

1.3 The Order of Operations

Part 2: Accuracy Checks

2.1 Categorical Variables

Visualizing the Problem

Checking Tables

Fixing the Issue

2.2 Continuous Variables

Visualizing Continuous Errors

Fixing Issues

Part 3: Missing Data

3.1 Diagnosing Missingness

3.2 Visualizing Missing Data

3.3 Handling Missing Data

By Rows (Participants)

Multiple Imputation with mice

Visual Verification: Did Imputation Change Data Shape?

Part 4: Outliers

4.1 Univariate Outliers (Z-scores)

Visualizing Z-scores

4.2 Multivariate Outliers: Mahalanobis Distance

Calculation

Cutoff and Elimination

4.3 Visualizing Outliers

Final Removal

Summary

References

Multiple Imputation with `mice`