Lab Overview

Time: ~30 minutes

Goal: Practice one-way ANOVA analysis from start to finish using real public health data

Learning Objectives:

Understand when and why to use ANOVA instead of multiple t-tests
Set up hypotheses for ANOVA
Conduct and interpret the F-test
Perform post-hoc tests when appropriate
Check ANOVA assumptions
Calculate and interpret effect size (η²)

Structure:

Part A: Guided Example (follow along)
Part B: Your Turn (independent practice)

Submission: Upload your completed .Rmd file and published to Brightspace by the end of class.

PART A: GUIDED EXAMPLE

Example: Blood Pressure and BMI Categories

Research Question: Is there a difference in mean systolic blood pressure (SBP) across three BMI categories (Normal weight, Overweight, Obese)?

Why ANOVA? We have one continuous outcome (SBP) and one categorical predictor with THREE groups (BMI category). Using multiple t-tests would inflate our Type I error rate.

Step 1: Setup and Data Preparation

# Load necessary libraries
library(tidyverse)   # For data manipulation and visualization
library(knitr)       # For nice tables
library(car)         # For Levene's test
library(NHANES)      # NHANES dataset

# Load the NHANES data
data(NHANES)

Create analysis dataset:

# Set seed for reproducibility
set.seed(553)

# Create BMI categories and prepare data
bp_bmi_data <- NHANES %>%
  filter(Age >= 18 & Age <= 65) %>%  # Adults 18-65
  filter(!is.na(BPSysAve) & !is.na(BMI)) %>%
  mutate(
    bmi_category = case_when(
      BMI < 25 ~ "Normal",
      BMI >= 25 & BMI < 30 ~ "Overweight",
      BMI >= 30 ~ "Obese",
      TRUE ~ NA_character_
    ),
    bmi_category = factor(bmi_category, 
                         levels = c("Normal", "Overweight", "Obese"))
  ) %>%
  filter(!is.na(bmi_category)) %>%
  select(ID, Age, Gender, BPSysAve, BMI, bmi_category)

# Display first few rows
head(bp_bmi_data) %>% 
  kable(caption = "Blood Pressure and BMI Dataset (first 6 rows)")

Blood Pressure and BMI Dataset (first 6 rows)
ID	Age	Gender	BPSysAve	BMI	bmi_category
51624	34	male	113	32.22	Obese
51624	34	male	113	32.22	Obese
51624	34	male	113	32.22	Obese
51630	49	female	112	30.57	Obese
51647	45	female	118	27.24	Overweight
51647	45	female	118	27.24	Overweight

# Check sample sizes
table(bp_bmi_data$bmi_category)

## 
##     Normal Overweight      Obese 
##       1939       1937       2150

Interpretation: We have 6026 adults with complete BP and BMI data across three BMI categories.

Step 2: Descriptive Statistics

# Calculate summary statistics by BMI category
summary_stats <- bp_bmi_data %>%
  group_by(bmi_category) %>%
  summarise(
    n = n(),
    Mean = mean(BPSysAve),
    SD = sd(BPSysAve),
    Median = median(BPSysAve),
    Min = min(BPSysAve),
    Max = max(BPSysAve)
  )

summary_stats %>% 
  kable(digits = 2, 
        caption = "Descriptive Statistics: Systolic BP by BMI Category")

Descriptive Statistics: Systolic BP by BMI Category
bmi_category	n	Mean	SD	Median	Min	Max
Normal	1939	114.23	15.01	113	78	221
Overweight	1937	118.74	13.86	117	83	186
Obese	2150	121.62	15.27	120	82	226

Observation: The mean SBP appears to increase from Normal (114.2) to Overweight (118.7) to Obese (121.6).

But is this difference statistically significant?

Step 3: Visualize the Data

# Create boxplots with individual points
ggplot(bp_bmi_data, 
  aes(x = bmi_category, y = BPSysAve, fill = bmi_category)) +
  geom_boxplot(alpha = 0.7, outlier.shape = NA) +
  geom_jitter(width = 0.2, alpha = 0.1, size = 0.5) +
  scale_fill_brewer(palette = "Set2") +
  labs(
    title = "Systolic Blood Pressure by BMI Category",
    subtitle = "NHANES Data, Adults aged 18-65",
    x = "BMI Category",
    y = "Systolic Blood Pressure (mmHg)",
    fill = "BMI Category"
  ) +
  theme_minimal(base_size = 12) +
  theme(legend.position = "none")

What the plot tells us:

There appears to be a trend: higher BMI categories have higher median SBP
The boxes overlap, but the obese group appears shifted upward
Variability (box heights) looks similar across groups

Step 4: Set Up Hypotheses

Null Hypothesis (H₀): μ_Normal = μ_Overweight = μ_Obese
(All three population means are equal)

Alternative Hypothesis (H₁): At least one population mean differs from the others

Significance level: α = 0.05

Step 5: Fit the ANOVA Model

# Fit the one-way ANOVA model
anova_model <- aov(BPSysAve ~ bmi_category, data = bp_bmi_data)

# Display the ANOVA table
summary(anova_model)

##                Df  Sum Sq Mean Sq F value Pr(>F)    
## bmi_category    2   56212   28106   129.2 <2e-16 ***
## Residuals    6023 1309859     217                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Interpretation:

F-statistic: 129.24
Degrees of freedom: df₁ = 2 (k-1 groups), df₂ = 6023 (n-k)
p-value: < 2e-16 (very small)
Decision: Since p < 0.05, we reject H₀
Conclusion: There is statistically significant evidence that mean systolic BP differs across at least two BMI categories.

Step 6: Post-Hoc Tests (Tukey HSD)

Why do we need this? The F-test tells us that groups differ, but not which groups differ. Tukey’s Honest Significant Difference controls the family-wise error rate for multiple pairwise comparisons.

# Conduct Tukey HSD test
tukey_results <- TukeyHSD(anova_model)
print(tukey_results)

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = BPSysAve ~ bmi_category, data = bp_bmi_data)
## 
## $bmi_category
##                       diff      lwr      upr p adj
## Overweight-Normal 4.507724 3.397134 5.618314     0
## Obese-Normal      7.391744 6.309024 8.474464     0
## Obese-Overweight  2.884019 1.801006 3.967033     0

# Visualize the confidence intervals
plot(tukey_results, las = 0)

Interpretation:

Comparison	Mean Diff	95% CI	p-value	Significant?
Overweight - Normal	4.51	[3.4, 5.62]	1.98e-13	Yes
Obese - Normal	7.39	[6.31, 8.47]	< 0.001	Yes
Obese - Overweight	2.88	[1.8, 3.97]	1.38e-09	Yes

Conclusion: All three pairwise comparisons are statistically significant. Obese adults have higher SBP than overweight adults, who in turn have higher SBP than normal-weight adults.

Step 7: Calculate Effect Size

# Extract sum of squares from ANOVA table
anova_summary <- summary(anova_model)[[1]]

ss_treatment <- anova_summary$`Sum Sq`[1]
ss_total <- sum(anova_summary$`Sum Sq`)

# Calculate eta-squared
eta_squared <- ss_treatment / ss_total

cat("Eta-squared (η²):", round(eta_squared, 4), "\n")

## Eta-squared (η²): 0.0411

cat("Percentage of variance explained:", round(eta_squared * 100, 2), "%")

## Percentage of variance explained: 4.11 %

Interpretation: BMI category explains 4.11% of the variance in systolic BP.

Effect size guidelines: Small (0.01), Medium (0.06), Large (0.14)
Our effect: Small

While statistically significant, the practical effect is modest—BMI category alone doesn’t explain most of the variation in blood pressure.

Step 8: Check Assumptions

ANOVA Assumptions:

Independence: Observations are independent (assumed based on study design)
Normality: Residuals are approximately normally distributed
Homogeneity of variance: Equal variances across groups

# Create diagnostic plots
par(mfrow = c(2, 2))
plot(anova_model)

par(mfrow = c(1, 1))

Diagnostic Plot Interpretation:

Residuals vs Fitted: Points show random scatter around zero with no clear pattern → Good!
Q-Q Plot: Points follow the diagonal line reasonably well → Normality assumption is reasonable
Scale-Location: Red line is relatively flat → Equal variance assumption is reasonable
Residuals vs Leverage: No points beyond Cook’s distance lines → No highly influential outliers

# Levene's test for homogeneity of variance
levene_test <- leveneTest(BPSysAve ~ bmi_category, data = bp_bmi_data)
print(levene_test)

## Levene's Test for Homogeneity of Variance (center = median)
##         Df F value  Pr(>F)  
## group    2  2.7615 0.06328 .
##       6023                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Levene’s Test Interpretation:

p-value: 0.0633
If p < 0.05, we would reject equal variances
Here: Equal variance assumption is met

Overall Assessment: With n > 2000, ANOVA is robust to minor violations. Our assumptions are reasonably satisfied.

Step 9: Report Results

Example Results Section:

We conducted a one-way ANOVA to examine whether mean systolic blood pressure (SBP) differs across BMI categories (Normal, Overweight, Obese) among 6,026 adults aged 18-65 from NHANES. Descriptive statistics showed mean SBP of 114.2 mmHg (SD = 15) for normal weight, 118.7 mmHg (SD = 13.9) for overweight, and 121.6 mmHg (SD = 15.3) for obese individuals.

The ANOVA revealed a statistically significant difference in mean SBP across BMI categories, F(2, 6023) = 129.24, p < 0.001. Tukey’s HSD post-hoc tests indicated that all pairwise comparisons were significant (p < 0.05): obese adults had on average 7.4 mmHg higher SBP than normal-weight adults, and 2.9 mmHg higher than overweight adults.

The effect size (η² = 0.041) indicates that BMI category explains 4.1% of the variance in systolic blood pressure, representing a small practical effect. These findings support the well-established relationship between higher BMI and elevated blood pressure, though other factors account for most of the variation in SBP.

PART B: YOUR TURN - INDEPENDENT PRACTICE

Practice Problem: Physical Activity and Depression

Research Question: Is there a difference in the number of days with poor mental health across three physical activity levels (None, Moderate, Vigorous)?

Your Task: Complete the same 9-step analysis workflow you just practiced, but now on a different outcome and predictor.

Step 1: Data Preparation

# Prepare the dataset
set.seed(553)

mental_health_data <- NHANES %>%
  filter(Age >= 18) %>%
  filter(!is.na(DaysMentHlthBad) & !is.na(PhysActive)) %>%
  mutate(
    activity_level = case_when(
      PhysActive == "No" ~ "None",
      PhysActive == "Yes" & !is.na(PhysActiveDays) & PhysActiveDays < 3 ~ "Moderate",
      PhysActive == "Yes" & !is.na(PhysActiveDays) & PhysActiveDays >= 3 ~ "Vigorous",
      TRUE ~ NA_character_
    ),
    activity_level = factor(activity_level, 
                           levels = c("None", "Moderate", "Vigorous"))
  ) %>%
  filter(!is.na(activity_level)) %>%
  select(ID, Age, Gender, DaysMentHlthBad, PhysActive, activity_level)

# YOUR TURN: Display the first 6 rows and check sample sizes

# Display first few rows
head(mental_health_data) %>% 
  kable(caption = "Mental Health and Physical Activity Levels (first 6 rows)")

Mental Health and Physical Activity Levels (first 6 rows)
ID	Age	Gender	DaysMentHlthBad	PhysActive	activity_level
51624	34	male	15	No	None
51624	34	male	15	No	None
51624	34	male	15	No	None
51630	49	female	10	No	None
51647	45	female	3	Yes	Vigorous
51647	45	female	3	Yes	Vigorous

# Check sample sizes
table(mental_health_data$activity_level)

## 
##     None Moderate Vigorous 
##     3139      768     1850

YOUR TURN - Answer these questions:

How many people are in each physical activity group?
- None: 3139 people are in none physical activity group.
- Moderate: 768 people are in moderate physical activity group.
- Vigorous: 1850 people are in Vigorous physical activity group.

Step 2: Descriptive Statistics

# YOUR TURN: Calculate summary statistics by activity level
# Hint: Follow the same structure as the guided example
# Variables to summarize: n, Mean, SD, Median, Min, Max

YOUR TURN - Interpret:

Which group has the highest mean number of bad mental health days?
Which group has the lowest?

Step 3: Visualization

# YOUR TURN: Create boxplots comparing DaysMentHlthBad across activity levels
# Hint: Use the same ggplot code structure as the example
# Change variable names and labels appropriately
# Create boxplots with individual points
ggplot(mental_health_data, 
  aes(x = activity_level, y = DaysMentHlthBad, fill = activity_level)) +
  geom_boxplot(alpha = 0.7, outlier.shape = NA) +
  geom_jitter(width = 0.2, alpha = 0.1, size = 0.5) +
  scale_fill_brewer(palette = "Set2") +
  labs(
    title = "Mental Health Condition by Activity Level",
    subtitle = "NHANES Data, Adults aged 18-65",
    x = "Activity Level",
    y = "Bad Mental Health",
    fill = "activity_level"
  ) +
  theme_minimal(base_size = 12) +
  theme(legend.position = "none")

YOUR TURN - Describe what you see:

Do the groups appear to differ?

Yes, the groups show noticeable differences. From the boxplots and point distributions, we can see that people with no physical activity tend to report more bad mental health days with the higher values.Compared to none and moderate, vigorous group shows the lowest central tendency with lower median and tighter compact distribution, with more observations clustered near zero- lesser variability. The median is almost close to zero with extremely short Q1 for all three groups. As physical activity increases, we can see downward trend in days of bad mental health.

Are the variances similar across groups? No, the variances are not similar across groups. The “None” and “moderate” group has greater variability, with a wider box (IQRs). Vigorous groups has cluster more tightly, suggesting less variation in bad mental health days. So, variances are not equal as it seem to be decreasing with the increasing activity level. —

Step 4: Set Up Hypotheses

YOUR TURN - Write the hypotheses:

Null Hypothesis (H₀): μ_none = μ_moderate = μ_vigorous
(All three activity levels have the same mean number of bad mental health days.)

Alternative Hypothesis (H₁): At least one population group mean differs from the others. (There is significant difference in the means of least one group.)

Significance level: α = 0.05

Step 5: Fit the ANOVA Model

# YOUR TURN: Fit the ANOVA model
# Outcome: DaysMentHlthBad
# Predictor: activity_level
# Fit the one-way ANOVA model
anova_model <- aov(DaysMentHlthBad ~ activity_level, data = mental_health_data)

# Display the ANOVA table
summary(anova_model)

##                  Df Sum Sq Mean Sq F value   Pr(>F)    
## activity_level    2   3109  1554.6   23.17 9.52e-11 ***
## Residuals      5754 386089    67.1                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

YOUR TURN - Extract and interpret the results:

F-statistic: 23.17
Degrees of freedom: 2 (activity level groups) and 5754 (residual)
p-value: 9.52e-11
Decision (reject or fail to reject H₀):Since p < 0.05, we Reject Ho
Statistical conclusion in words: Based on the ANOVA results above, we can see that p-value is far less than 0.05 so, we reject the null hypothesis. Hence, there is statistically Significant evidence that the mean number of bad mental health days differs across at least one of the activity‑level groups. —

Step 6: Post-Hoc Tests

# YOUR TURN: Conduct Tukey HSD test
# Only if your ANOVA p-value < 0.05


tukey_results <- TukeyHSD(anova_model)
print(tukey_results)

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = DaysMentHlthBad ~ activity_level, data = mental_health_data)
## 
## $activity_level
##                         diff       lwr        upr     p adj
## Moderate-None     -1.2725867 -2.045657 -0.4995169 0.0003386
## Vigorous-None     -1.5464873 -2.109345 -0.9836298 0.0000000
## Vigorous-Moderate -0.2739006 -1.098213  0.5504114 0.7159887

# Visualize the confidence intervals
plot(tukey_results, las = 0)

YOUR TURN - Complete the table:

Comparison	Mean Difference	95% CI Lower	95% CI Upper	p-value	Significant?
Moderate - None	-1.27	-2.05	-0.5	0.0003	Yes
Vigorous - None	-1.55	-2.11	-0.98	0.0000	Yes
Vigorous - Moderate	-0.27	-1.10	0.55	0.71	No

Interpretation:

Which specific groups differ significantly? Both Moderate and Vigorous activity levels are significantly different than the None exercising group. Individuals with Moderate activity report about 1.27 fewer bad mental health days, while those with Vigorous activity report about 1.55 fewer bad mental health days compared to no activity. Their p-values are also small and their Cis do not include zero. However, there is no significant difference between Moderate and Vigorous activity levels due to the large p-value and CI including zero (p = 0.71, CI (-1.10- 0.55)). —

Step 7: Calculate Effect Size

# YOUR TURN: Calculate eta-squared
# Hint: Extract Sum Sq from the ANOVA summary
# Extract sum of squares from ANOVA table
anova_summary <- summary(anova_model)[[1]]
ss_treatment <- anova_summary$`Sum Sq`[1]
ss_total <- sum(anova_summary$`Sum Sq`)

# Calculate eta-squared
eta_squared <- ss_treatment / ss_total
cat("Eta-squared (η²):", round(eta_squared, 4), "\n")

## Eta-squared (η²): 0.008

cat("Percentage of variance explained:", round(eta_squared * 100, 2), "%")

## Percentage of variance explained: 0.8 %

YOUR TURN - Interpret:

η² = 0.008
Percentage of variance explained: 0.8% of the variance in bad mental health days is explained by activity level.
Effect size classification (small/medium/large): 0.008 is way below the small‑effect threshold, so it is very small.
What does this mean practically? The effect size Activity level is associated to mental health, but it explains less than 1% of why people differ in their bad mental health days.This means many other factors (stress, income, sleep, social support, health conditions, etc.) likely play a much larger role.

Step 8: Check Assumptions

# YOUR TURN: Create diagnostic plots
# Create diagnostic plots
par(mfrow = c(2, 2), mar = c(3,3,2,1))
plot(anova_model)

ANOVA Assumptions:

Independence: Observations are independent (assumed based on study design)
Normality: Residuals are approximately normally distributed
Homogeneity of variance: Equal variances across groups YOUR TURN - Evaluate each plot:

Diagnostic Plot Interpretation:

Residuals vs Fitted: Points show random scatter around zero with no clear pattern → Good!
Q-Q Plot: Points follow the diagonal line reasonably well → Normality assumption is reasonable
Scale-Location: Red line is relatively flat → Equal variance assumption is reasonable
Residuals vs Leverage: No points beyond Cook’s distance lines → No highly influential outliers

For the data, here is the observations based on above assumptions:

Residuals vs Fitted: The points range from 3.5 to 5 and we can see them scattered around 0. There is no strong curve also, we can say that linearity is true.
Q-Q Plot:The points range from about -4 to 4 and follows the line till the middle and heavy right tail deviation with points curve sharply upward at the upper end.- right-skewed data (positive skew) and departures from normality.
Scale-Location: Similar vertical banding pattern is visible like as plot 1( residuals vs Fitted).The red line is relatively flat across fitted values. Variances is fairly constant across Fitted values.
Residuals vs Leverage: Values are from 0.0000 to 0.0012- very small. No points beyond Cook’s distance lines. No individual observations are influencing the results.

The ANOVA assumptions are moderately violated.

# YOUR TURN: Conduct Levene's test

# Levene's test for homogeneity of variance
levene_test <- leveneTest(DaysMentHlthBad ~ activity_level, data = mental_health_data)
print(levene_test)

## Levene's Test for Homogeneity of Variance (center = median)
##         Df F value    Pr(>F)    
## group    2  23.168 9.517e-11 ***
##       5754                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Levene’s Test Interpretation:

YOUR TURN - Overall assessment:

Are assumptions reasonably met?

Levene’s test is statistically significant with F value (2, 5754)= 23.17, p= 9.52e-11. It means variances across the three groups are not equal.

Do any violations threaten your conclusions? It not necessarily threatens the conclusions because the study has large sample size (n- 5757) and the test is still reliable. —

Step 9: Write Up Results

YOUR TURN - Write a complete 2-3 paragraph results section:

Include: 1. Sample description and descriptive statistics 2. F-test results 3. Post-hoc comparisons (if applicable) 4. Effect size interpretation 5. Public health significance

Your Results Section:

The analytic sample included 5,757 adults aged 18 years and older from the NHANES dataset. Participants were categorized into three physical activity groups: None (n = 3,139), Moderate (n = 768), and Vigorous (n = 1,850). Individuals reporting no physical activity had the highest mean number of bad mental health days, while those in the vigorous activity group reported the lowest mean number of poor mental health days. Overall, it shows fewer days of poor mental health as physical activity level increased.

A one-way ANOVA was conducted to compare the mean number of bad mental health days across physical activity levels. The analysis showed a statistically significant difference between groups (F(2, 5754) = 23.17, p < 0.001). There is statistically Significant evidence that the mean number of bad mental health days differs across at least one of the activity‑level groups.

Post-hoc Tukey HSD tests further revealed that both the moderate and vigorous activity groups reported significantly fewer bad mental health days compared to the no activity group. Physical activity level explained less than 1% of the variability in bad mental health days. While statistically significant, this suggests that other social, behavioral, and environmental factors play a much larger role in determining mental health outcomes. From a public health perspective, increasing physical activity may still offer meaningful mental health benefits at the population level, especially given its low cost and additional physical health benefits.

Reflection Questions

1. How does the effect size help you understand the practical vs. statistical significance?

The effect size helps us to understand the practical vs. statistically significant results as in analysis, the ANOVA showed a very small p-value, largely due to the large sample size. However, the effect size (η² = 0.008) indicates that physical activity explains less than 1% of the variation in bad mental health days. This means that while physical activity is associated with mental health, it is only a small part of the overall picture, and many other factors probably have a stronger influence.

2. Why is it important to check ANOVA assumptions? What might happen if they’re violated?

Checking ANOVA assumptions is important because violations can affect the validity of the results. If assumptions like normality or equal variances are seriously violated, the F-test may produce misleading p-values, increasing the risk of incorrect conclusions. However, because the sample size was large, ANOVA is considered relatively robust, and the conclusions are still considered reliable. If we don’t check assumptions, these issues might go unnoticed and unexplained.

3. In public health practice, when might you choose to use ANOVA?

ANOVA is useful in public health when comparing means of a continous outcomes across three or more groups, such as mental health outcomes across activity levels, none, moderate and vigorous. It is commonly used in population health studies, program evaluations for interventions, analysing demographic differences and surveillance data to identify group differences that may inform further interventions or policy decisions.

4. What was the most challenging part of this lab activity?

The most challenging part of this lab was looking at the charts and plots and interpreting results. Sometimes, understanding the small effect size into a larger public health context was also tough. Statistical findings has to be balanced with real-world relevance and recognizing that to design meaningful public health interventions is important and which will often involve multiple contributing factors rather than a single exposure.

Submission Checklist

Before submitting, verify you have:

Completed all code chunks in Part B
Filled in all interpretation questions
Completed the Tukey HSD comparison table
Written a complete results section
Answered all reflection questions
Rendered your .Rmd file to HTML without errors
Checked that all outputs display correctly

To submit: Upload both your .Rmd file and the HTML output to Brightspace.

Lab completed on: February 05, 2026

GRADING RUBRIC (For TA Use)

Total Points: 15

Category	Criteria	Points	Notes
Code Execution	All code chunks run without errors	4	- Deduct 1 pt per major error - Deduct 0.5 pt per minor warning
Completion	All “YOUR TURN” sections attempted	4	- Part B Steps 1-9 completed - All fill-in-the-blank answered - Tukey table filled in
Interpretation	Correct statistical interpretation	4	- Hypotheses correctly stated (1 pt) - ANOVA results interpreted (1 pt) - Post-hoc results interpreted (1 pt) - Assumptions evaluated (1 pt)
Results Section	Professional, complete write-up	3	- Includes descriptive stats (1 pt) - Reports F-test & post-hoc (1 pt) - Effect size & significance (1 pt)

Detailed Grading Guidelines

Code Execution (4 points):

4 pts: All code runs perfectly, produces correct output
3 pts: Minor issues (1-2 small errors or warnings)
2 pts: Several errors but demonstrates understanding
1 pt: Major errors, incomplete code
0 pts: Code does not run at all

Completion (4 points):

4 pts: All sections attempted thoughtfully
3 pts: 1-2 sections incomplete or minimal effort
2 pts: Several sections missing
1 pt: Only partial completion
0 pts: Little to no work completed

Interpretation (4 points):

4 pts: All interpretations correct and well-explained
3 pts: Minor errors in interpretation
2 pts: Several interpretation errors
1 pt: Significant misunderstanding of concepts
0 pts: No interpretation provided

Results Section (3 points):

3 pts: Publication-quality, complete results section
2 pts: Good but missing some elements
1 pt: Incomplete or poorly written
0 pts: No results section written

Common Deductions

-0.5 pts: Missing sample sizes in write-up
-0.5 pts: Not reporting confidence intervals
-1 pt: Incorrect hypothesis statements
-1 pt: Misinterpreting p-values
-1 pt: Not checking assumptions
-0.5 pts: Poor formatting (no tables, unclear output)

In-Class Lab Activity: Analysis of Variance (ANOVA)

EPI 553: Principles of Statistical Inference II

Muntasir Masum

2026-02-05

Lab Overview

PART A: GUIDED EXAMPLE

Example: Blood Pressure and BMI Categories

Research Question: Is there a difference in mean systolic blood pressure (SBP) across three BMI categories (Normal weight, Overweight, Obese)?

Step 1: Setup and Data Preparation

Step 2: Descriptive Statistics

But is this difference statistically significant?

Step 3: Visualize the Data

Step 4: Set Up Hypotheses

Step 5: Fit the ANOVA Model

Step 6: Post-Hoc Tests (Tukey HSD)

Step 7: Calculate Effect Size

Step 8: Check Assumptions

Step 9: Report Results

PART B: YOUR TURN - INDEPENDENT PRACTICE

Practice Problem: Physical Activity and Depression

Research Question: Is there a difference in the number of days with poor mental health across three physical activity levels (None, Moderate, Vigorous)?

Step 1: Data Preparation

Vigorous: 1850 people are in Vigorous physical activity group.

Step 2: Descriptive Statistics

Step 3: Visualization

Step 4: Set Up Hypotheses

Step 5: Fit the ANOVA Model

Step 6: Post-Hoc Tests

Step 7: Calculate Effect Size

Step 8: Check Assumptions

Step 9: Write Up Results

Reflection Questions

Submission Checklist

GRADING RUBRIC (For TA Use)

Detailed Grading Guidelines

Common Deductions