Lab 17: Strip Charts, Violin Plots, Paired t-test & Two-Sample t-test

BI 255 · Bethune-Cookman University · Fall 2026

Author

Dr. Rosie Stanbrook-Buyer

Published

October 5, 2026

Comparing Two Groups: Visualisation and Inference Together

In experimental biology, the most common analytical question is: does the treatment group differ from the control? This lab builds the complete workflow — first visualising the data properly, then applying the appropriate t-test, and finally interpreting the result in biological context.

We cover two visualisation methods (strip charts and violin plots) that show all the data, and two types of t-test depending on whether the groups are independent or paired.

Learning Objectives

By the end of this lab you will be able to:

Produce strip charts with stripchart() and ggplot2 geom_jitter()
Produce violin plots with ggplot2 geom_violin()
Determine when to use an independent vs paired t-test
Run a paired t-test with t.test(x, y, paired = TRUE)
Run a two-sample Welch’s t-test with t.test(x, y, var.equal = FALSE)
Report results in the format expected in a scientific paper

Part 1: Why Visualise Before Testing?

Statistical tests summarise data into a single number (the p-value). Visualising the raw data first prevents you from being misled by that summary.

library(ggplot2)

# Three datasets with identical means, SDs — but very different shapes
set.seed(42)
n <- 30

data_A <- rnorm(n, mean = 10, sd = 2)
data_B <- c(rnorm(15, 8, 0.5), rnorm(15, 12, 0.5))   # Bimodal
data_C <- c(rep(10, 20), rnorm(10, 10, 6))              # Outlier-heavy

df_demo <- data.frame(
  value = c(data_A, data_B, data_C),
  group = rep(c("A", "B", "C"), each = n)
)

# All three look identical as means ± SD
tapply(df_demo$value, df_demo$group, function(x) round(c(mean = mean(x), sd = sd(x)), 2))

$A
 mean    sd 
10.14  2.51 

$B
mean   sd 
9.94 2.21 

$C
 mean    sd 
11.08  2.79

# But look very different when you plot the raw data
ggplot(df_demo, aes(x = group, y = value, colour = group)) +
  geom_jitter(width = 0.15, size = 2, alpha = 0.8) +
  stat_summary(fun = mean, geom = "point", shape = 18, size = 4, colour = "black") +
  stat_summary(fun.data = mean_se, geom = "errorbar", width = 0.2, colour = "black") +
  labs(title  = "Three Datasets with Identical Means and SDs",
       subtitle = "Black diamond = mean ± SE",
       x = "Dataset", y = "Value") +
  theme_classic(base_size = 13) +
  theme(legend.position = "none")

Always Plot Raw Data

Groups B and C have the same summary statistics as A, but: - B is bimodal (two subpopulations — perhaps treated and untreated cells mixed by accident) - C has heavy outliers that are dragging the mean

A t-test would give almost identical p-values for all three comparisons. Only the plot reveals these problems. Plot first, test second.

Part 2: Strip Charts

A strip chart (also called a dot plot) shows every individual data point. It is ideal for small to moderate sample sizes (n < 100).

set.seed(303)
# Drug efficacy experiment: bacterial growth inhibition (mm zone of inhibition)
control    <- round(rnorm(20, mean = 0,    sd = 1.5))   # No drug
antibiotic <- round(rnorm(20, mean = 12.4, sd = 2.8))   # Drug added

# Base R stripchart
stripchart(list(Control = control, Antibiotic = antibiotic),
           method   = "jitter",
           vertical = TRUE,
           pch      = 16,
           cex      = 1.2,
           col      = c("#2C5F8A", "#C8102E"),
           ylab     = "Zone of Inhibition (mm)",
           main     = "Antibiotic Efficacy — Strip Chart")

# Add means ± SE
means <- c(mean(control), mean(antibiotic))
ses   <- c(sd(control)/sqrt(20), sd(antibiotic)/sqrt(20))
points(1:2, means, pch = 18, cex = 2.5, col = "black")
arrows(1:2, means - ses, 1:2, means + ses,
       angle = 90, code = 3, length = 0.08, lwd = 2, col = "black")

Strip Charts with ggplot2

# Combine into a data frame for ggplot2
growth_df <- data.frame(
  inhibition = c(control, antibiotic),
  group      = rep(c("Control", "Antibiotic"), each = 20)
)

ggplot(growth_df, aes(x = group, y = inhibition, colour = group)) +
  geom_jitter(width = 0.12, size = 2.5, alpha = 0.8) +
  stat_summary(fun = mean, geom = "crossbar",
               width = 0.3, fatten = 2, colour = "black") +
  scale_colour_manual(values = c("Control" = "#2C5F8A", "Antibiotic" = "#C8102E")) +
  labs(title = "Zone of Inhibition by Treatment",
       x     = "Treatment",
       y     = "Zone of Inhibition (mm)") +
  theme_classic(base_size = 13) +
  theme(legend.position = "none")

Part 3: Violin Plots

A violin plot shows the full probability distribution of the data — essentially a smoothed density estimate mirrored on both sides. It is more informative than a box plot for revealing the shape of a distribution.

set.seed(55)
# Cell viability (% of control) after three drug treatments
cell_df <- data.frame(
  viability = c(rnorm(30, 100, 8),     # Vehicle control
                rnorm(30,  72, 12),    # Drug X (1 uM)
                rnorm(30,  45, 15)),   # Drug X (10 uM)
  treatment = rep(c("Vehicle", "Drug 1uM", "Drug 10uM"), each = 30)
)

# Set factor order for logical display
cell_df$treatment <- factor(cell_df$treatment,
                             levels = c("Vehicle", "Drug 1uM", "Drug 10uM"))

ggplot(cell_df, aes(x = treatment, y = viability, fill = treatment)) +
  geom_violin(trim = FALSE, alpha = 0.6) +
  geom_boxplot(width = 0.12, fill = "white", outlier.shape = NA) +
  geom_jitter(width = 0.05, size = 1.2, alpha = 0.5, colour = "grey30") +
  scale_fill_manual(values = c("Vehicle"    = "#2C5F8A",
                               "Drug 1uM"   = "#5B8DB8",
                               "Drug 10uM"  = "#C8102E")) +
  labs(title = "Cell Viability Following Drug X Treatment",
       x     = "Treatment",
       y     = "Cell Viability (% of control)") +
  theme_classic(base_size = 13) +
  theme(legend.position = "none")

Violin + Box Plot Combination

Layering a narrow box plot inside a violin plot gives you: - The distribution shape from the violin - The median, IQR, and outlier information from the box plot - The individual data points from geom_jitter()

This combination is increasingly expected in high-impact biology journals.

Part 4: The Independent Two-Sample t-test

Use this test when comparing two independent groups — different subjects, cells, or experimental units in each group.

# Return to the antibiotic example
# H₀: mean zone of inhibition is the same in control and antibiotic groups
# H₁: antibiotic produces a larger zone of inhibition

result_indep <- t.test(antibiotic, control,
                       alternative = "greater",   # We predict antibiotic > control
                       var.equal   = FALSE)        # Welch's t-test — safer default
result_indep


    Welch Two Sample t-test

data:  antibiotic and control
t = 20.517, df = 27.246, p-value < 2.2e-16
alternative hypothesis: true difference in means is greater than 0
95 percent confidence interval:
 11.37091      Inf
sample estimates:
mean of x mean of y 
     12.5       0.1

Reporting t-test Results

The conventional scientific format for reporting a t-test result is:

“The antibiotic produced significantly larger zones of inhibition than the control (t(df) = t-value, p = p-value).”

For example: “The antibiotic produced significantly larger zones of inhibition than the control (t(29.4) = 21.3, p < 0.001).”

Always include: the test statistic (t), degrees of freedom (df), and p-value. If effect size was calculated (Cohen’s d), include that too.

Part 5: The Paired t-test

Use a paired t-test when each observation in group 1 is matched to a specific observation in group 2. This is common in:

Before/after designs (same subject measured twice)
Matched case-control studies
Left/right comparisons on the same organism
Replicate wells on the same plate

Pairing removes between-subject variability, making the test more powerful.

# Before/after experiment: blood glucose (mmol/L) in 18 patients
# measured before and 2 hours after an oral glucose tolerance test (OGTT)
set.seed(888)
n_patients <- 18
glucose_fasting  <- round(rnorm(n_patients, mean = 5.2, sd = 0.5), 1)
glucose_2hr      <- glucose_fasting + round(rnorm(n_patients, mean = 3.8, sd = 1.2), 1)

cat("Fasting glucose:   mean =", round(mean(glucose_fasting), 2), "mmol/L\n")

Fasting glucose:   mean = 5.14 mmol/L

cat("2-hour glucose:    mean =", round(mean(glucose_2hr),     2), "mmol/L\n")

2-hour glucose:    mean = 8.97 mmol/L

cat("Mean difference:         ", round(mean(glucose_2hr - glucose_fasting), 2), "mmol/L\n")

Mean difference:          3.83 mmol/L

# Paired t-test
# H₀: mean glucose does not change after OGTT
# H₁: glucose increases after OGTT
result_paired <- t.test(glucose_2hr, glucose_fasting,
                        paired      = TRUE,
                        alternative = "greater")
result_paired


    Paired t-test

data:  glucose_2hr and glucose_fasting
t = 11.712, df = 17, p-value = 7.289e-10
alternative hypothesis: true mean difference is greater than 0
95 percent confidence interval:
 3.263963      Inf
sample estimates:
mean difference 
       3.833333

# Visualise the paired nature of the data
patient_df <- data.frame(
  glucose  = c(glucose_fasting, glucose_2hr),
  timepoint = rep(c("Fasting", "2-Hour Post-OGTT"), each = n_patients),
  patient  = rep(1:n_patients, 2)
)

patient_df$timepoint <- factor(patient_df$timepoint,
                                levels = c("Fasting", "2-Hour Post-OGTT"))

ggplot(patient_df, aes(x = timepoint, y = glucose)) +
  geom_line(aes(group = patient), colour = "grey70", linewidth = 0.5) +
  geom_point(aes(colour = timepoint), size = 3) +
  scale_colour_manual(values = c("Fasting"          = "#2C5F8A",
                                 "2-Hour Post-OGTT" = "#C8102E")) +
  stat_summary(fun = mean, geom = "point", shape = 18,
               size = 5, colour = "black") +
  labs(title    = "Blood Glucose: Oral Glucose Tolerance Test",
       subtitle = paste0("n = ", n_patients, " patients; paired t-test, p = ",
                         formatC(result_paired$p.value, format = "e", digits = 2)),
       x        = "Timepoint",
       y        = "Blood Glucose (mmol/L)") +
  theme_classic(base_size = 13) +
  theme(legend.position = "none")

Paired vs Independent: Which Do You Use?

Design	Test	Why
Different subjects in each group	Independent (Welch’s) t-test	Groups share no observations
Same subjects measured twice	Paired t-test	Removes within-subject variability
Matched controls	Paired t-test	Each case has a specific matched control

Using a paired test when data are independent (or vice versa) gives the wrong answer. Always check your experimental design before choosing a test.

3-Minute Knowledge Check

Close your notes. Answer these on your own — you have 3 minutes. We’ll go through the answers together after.

Knowledge Check Questions

1. You are comparing body weight in 25 mice before and after a 4-week dietary intervention (the same 25 mice measured twice). Which test is appropriate?

a) Independent two-sample t-test    b) Paired t-test    c) One-sample t-test    d) Chi-square test

2. What does a violin plot show that a box plot does not?

3. In a paired t-test, the test is effectively performed on:

a) The raw values in each group    b) The differences between paired observations    c) The ranks of the observations    d) The log-transformed values

4. You run t.test(treated, control, var.equal = FALSE). What does var.equal = FALSE specify?

5. True or False: A strip chart (dot plot) is more informative than a mean ± SD bar chart for small sample sizes (n < 20).

Answers (Only reveal if you have answered the above questions)

1. b) Paired t-test — The same 25 mice are measured twice: once before and once after the intervention. Each mouse’s two measurements are paired. The paired t-test removes between-mouse variability (e.g., natural size differences) and focuses on the change within each mouse.

2. A violin plot shows the full shape of the distribution — including whether it is unimodal, bimodal, symmetric, or skewed. A box plot only shows the median, quartiles, and outliers. A bimodal distribution (two peaks) can hide completely inside a box plot.

3. b) The differences between paired observations — a paired t-test computes d = x₁ − x₂ for each pair and then runs a one-sample t-test asking whether the mean difference is significantly different from zero. This is mathematically equivalent to t.test(x1 - x2, mu = 0).

4. var.equal = FALSE specifies Welch’s t-test, which does not assume equal variances between the two groups. This is the safer default because violation of equal variances inflates Type I error in the standard Student’s t-test. Use var.equal = TRUE only if you have strong reason to believe the variances are equal (which you should verify with Levene’s test — Lab 18).

5. True — For small samples, individual data points are visible and meaningful. A mean ± SD bar chart hides the distribution entirely — with n = 5, for example, you cannot tell if the data are normally distributed, skewed, or contain outliers. Strip charts reveal these features directly.

Lab 17 Checklist

Before you leave, make sure you can:

Explain why you should plot data before running a statistical test
Produce a strip chart with stripchart() and with geom_jitter()
Produce a violin plot with geom_violin() and overlay a box plot and jittered points
Determine whether a paired or independent t-test is appropriate for a given design
Run t.test(x, y, paired = TRUE) and interpret the output
Run t.test(x, y, var.equal = FALSE) (Welch’s) and interpret the output
Report t-test results in the standard scientific format: t(df) = value, p = value

Bonus Challenge

Design your own experiment: choose a biological question involving two groups (e.g., antibiotic A vs antibiotic B, treated vs untreated cells, gene expression before vs after induction). Simulate realistic data using rnorm() with biologically plausible means and SDs. Produce a publication-ready violin + jitter plot in ggplot2, run the appropriate t-test, and write a one-sentence conclusion in scientific language.

Before Next Class (Wednesday)

Wednesday (Lab 18): Confidence intervals from t-tests, and Levene’s test for equal variances
Read R for Data Science Ch. 9–10

--- title: "Lab 17: Strip Charts, Violin Plots, Paired t-test & Two-Sample t-test" subtitle: "BI 255 · Bethune-Cookman University · Fall 2026" author: "Dr. Rosie Stanbrook-Buyer" date: "October 5, 2026" format: html: theme: cosmo toc: true toc-location: left toc-title: "In This Lab" toc-depth: 3 number-sections: false code-fold: false code-tools: true highlight-style: github smooth-scroll: true embed-resources: true callout-appearance: default execute: warning: false message: false echo: true --- ```{r setup, include=FALSE} knitr::opts_chunk$set(echo = TRUE) ``` ------------------------------------------------------------------------ ## Comparing Two Groups: Visualisation and Inference Together In experimental biology, the most common analytical question is: **does the treatment group differ from the control?** This lab builds the complete workflow — first visualising the data properly, then applying the appropriate t-test, and finally interpreting the result in biological context. We cover two visualisation methods (strip charts and violin plots) that show all the data, and two types of t-test depending on whether the groups are independent or paired. ::: callout-note ## Learning Objectives By the end of this lab you will be able to: 1. Produce strip charts with `stripchart()` and ggplot2 `geom_jitter()` 2. Produce violin plots with ggplot2 `geom_violin()` 3. Determine when to use an independent vs paired t-test 4. Run a paired t-test with `t.test(x, y, paired = TRUE)` 5. Run a two-sample Welch's t-test with `t.test(x, y, var.equal = FALSE)` 6. Report results in the format expected in a scientific paper ::: ------------------------------------------------------------------------ ## Part 1: Why Visualise Before Testing? Statistical tests summarise data into a single number (the p-value). Visualising the raw data first prevents you from being misled by that summary. ```{r} library(ggplot2) # Three datasets with identical means, SDs — but very different shapes set.seed(42) n <- 30 data_A <- rnorm(n, mean = 10, sd = 2) data_B <- c(rnorm(15, 8, 0.5), rnorm(15, 12, 0.5)) # Bimodal data_C <- c(rep(10, 20), rnorm(10, 10, 6)) # Outlier-heavy df_demo <- data.frame( value = c(data_A, data_B, data_C), group = rep(c("A", "B", "C"), each = n) ) # All three look identical as means ± SD tapply(df_demo$value, df_demo$group, function(x) round(c(mean = mean(x), sd = sd(x)), 2)) ``` ```{r} # But look very different when you plot the raw data ggplot(df_demo, aes(x = group, y = value, colour = group)) + geom_jitter(width = 0.15, size = 2, alpha = 0.8) + stat_summary(fun = mean, geom = "point", shape = 18, size = 4, colour = "black") + stat_summary(fun.data = mean_se, geom = "errorbar", width = 0.2, colour = "black") + labs(title = "Three Datasets with Identical Means and SDs", subtitle = "Black diamond = mean ± SE", x = "Dataset", y = "Value") + theme_classic(base_size = 13) + theme(legend.position = "none") ``` ::: callout-warning ## Always Plot Raw Data Groups B and C have the same summary statistics as A, but: - B is bimodal (two subpopulations — perhaps treated and untreated cells mixed by accident) - C has heavy outliers that are dragging the mean A t-test would give almost identical p-values for all three comparisons. Only the plot reveals these problems. **Plot first, test second.** ::: ------------------------------------------------------------------------ ## Part 2: Strip Charts A **strip chart** (also called a dot plot) shows every individual data point. It is ideal for small to moderate sample sizes (n < 100). ```{r} set.seed(303) # Drug efficacy experiment: bacterial growth inhibition (mm zone of inhibition) control <- round(rnorm(20, mean = 0, sd = 1.5)) # No drug antibiotic <- round(rnorm(20, mean = 12.4, sd = 2.8)) # Drug added # Base R stripchart stripchart(list(Control = control, Antibiotic = antibiotic), method = "jitter", vertical = TRUE, pch = 16, cex = 1.2, col = c("#2C5F8A", "#C8102E"), ylab = "Zone of Inhibition (mm)", main = "Antibiotic Efficacy — Strip Chart") # Add means ± SE means <- c(mean(control), mean(antibiotic)) ses <- c(sd(control)/sqrt(20), sd(antibiotic)/sqrt(20)) points(1:2, means, pch = 18, cex = 2.5, col = "black") arrows(1:2, means - ses, 1:2, means + ses, angle = 90, code = 3, length = 0.08, lwd = 2, col = "black") ``` ### Strip Charts with ggplot2 ```{r} # Combine into a data frame for ggplot2 growth_df <- data.frame( inhibition = c(control, antibiotic), group = rep(c("Control", "Antibiotic"), each = 20) ) ggplot(growth_df, aes(x = group, y = inhibition, colour = group)) + geom_jitter(width = 0.12, size = 2.5, alpha = 0.8) + stat_summary(fun = mean, geom = "crossbar", width = 0.3, fatten = 2, colour = "black") + scale_colour_manual(values = c("Control" = "#2C5F8A", "Antibiotic" = "#C8102E")) + labs(title = "Zone of Inhibition by Treatment", x = "Treatment", y = "Zone of Inhibition (mm)") + theme_classic(base_size = 13) + theme(legend.position = "none") ``` ------------------------------------------------------------------------ ## Part 3: Violin Plots A **violin plot** shows the full probability distribution of the data — essentially a smoothed density estimate mirrored on both sides. It is more informative than a box plot for revealing the shape of a distribution. ```{r} set.seed(55) # Cell viability (% of control) after three drug treatments cell_df <- data.frame( viability = c(rnorm(30, 100, 8), # Vehicle control rnorm(30, 72, 12), # Drug X (1 uM) rnorm(30, 45, 15)), # Drug X (10 uM) treatment = rep(c("Vehicle", "Drug 1uM", "Drug 10uM"), each = 30) ) # Set factor order for logical display cell_df$treatment <- factor(cell_df$treatment, levels = c("Vehicle", "Drug 1uM", "Drug 10uM")) ggplot(cell_df, aes(x = treatment, y = viability, fill = treatment)) + geom_violin(trim = FALSE, alpha = 0.6) + geom_boxplot(width = 0.12, fill = "white", outlier.shape = NA) + geom_jitter(width = 0.05, size = 1.2, alpha = 0.5, colour = "grey30") + scale_fill_manual(values = c("Vehicle" = "#2C5F8A", "Drug 1uM" = "#5B8DB8", "Drug 10uM" = "#C8102E")) + labs(title = "Cell Viability Following Drug X Treatment", x = "Treatment", y = "Cell Viability (% of control)") + theme_classic(base_size = 13) + theme(legend.position = "none") ``` ::: callout-tip ## Violin + Box Plot Combination Layering a narrow box plot inside a violin plot gives you: - The **distribution shape** from the violin - The **median, IQR, and outlier information** from the box plot - The **individual data points** from `geom_jitter()` This combination is increasingly expected in high-impact biology journals. ::: ------------------------------------------------------------------------ ## Part 4: The Independent Two-Sample t-test Use this test when comparing two **independent** groups — different subjects, cells, or experimental units in each group. ```{r} # Return to the antibiotic example # H₀: mean zone of inhibition is the same in control and antibiotic groups # H₁: antibiotic produces a larger zone of inhibition result_indep <- t.test(antibiotic, control, alternative = "greater", # We predict antibiotic > control var.equal = FALSE) # Welch's t-test — safer default result_indep ``` ::: callout-note ## Reporting t-test Results The conventional scientific format for reporting a t-test result is: **"The antibiotic produced significantly larger zones of inhibition than the control (t(df) = t-value, p = p-value)."** For example: *"The antibiotic produced significantly larger zones of inhibition than the control (t(29.4) = 21.3, p < 0.001)."* Always include: the test statistic (t), degrees of freedom (df), and p-value. If effect size was calculated (Cohen's d), include that too. ::: ------------------------------------------------------------------------ ## Part 5: The Paired t-test Use a paired t-test when each observation in group 1 is **matched** to a specific observation in group 2. This is common in: - Before/after designs (same subject measured twice) - Matched case-control studies - Left/right comparisons on the same organism - Replicate wells on the same plate Pairing removes between-subject variability, making the test more powerful. ```{r} # Before/after experiment: blood glucose (mmol/L) in 18 patients # measured before and 2 hours after an oral glucose tolerance test (OGTT) set.seed(888) n_patients <- 18 glucose_fasting <- round(rnorm(n_patients, mean = 5.2, sd = 0.5), 1) glucose_2hr <- glucose_fasting + round(rnorm(n_patients, mean = 3.8, sd = 1.2), 1) cat("Fasting glucose: mean =", round(mean(glucose_fasting), 2), "mmol/L\n") cat("2-hour glucose: mean =", round(mean(glucose_2hr), 2), "mmol/L\n") cat("Mean difference: ", round(mean(glucose_2hr - glucose_fasting), 2), "mmol/L\n") ``` ```{r} # Paired t-test # H₀: mean glucose does not change after OGTT # H₁: glucose increases after OGTT result_paired <- t.test(glucose_2hr, glucose_fasting, paired = TRUE, alternative = "greater") result_paired ``` ```{r} # Visualise the paired nature of the data patient_df <- data.frame( glucose = c(glucose_fasting, glucose_2hr), timepoint = rep(c("Fasting", "2-Hour Post-OGTT"), each = n_patients), patient = rep(1:n_patients, 2) ) patient_df$timepoint <- factor(patient_df$timepoint, levels = c("Fasting", "2-Hour Post-OGTT")) ggplot(patient_df, aes(x = timepoint, y = glucose)) + geom_line(aes(group = patient), colour = "grey70", linewidth = 0.5) + geom_point(aes(colour = timepoint), size = 3) + scale_colour_manual(values = c("Fasting" = "#2C5F8A", "2-Hour Post-OGTT" = "#C8102E")) + stat_summary(fun = mean, geom = "point", shape = 18, size = 5, colour = "black") + labs(title = "Blood Glucose: Oral Glucose Tolerance Test", subtitle = paste0("n = ", n_patients, " patients; paired t-test, p = ", formatC(result_paired$p.value, format = "e", digits = 2)), x = "Timepoint", y = "Blood Glucose (mmol/L)") + theme_classic(base_size = 13) + theme(legend.position = "none") ``` ::: callout-important ## Paired vs Independent: Which Do You Use? | Design | Test | Why | |--------|------|-----| | Different subjects in each group | Independent (Welch's) t-test | Groups share no observations | | Same subjects measured twice | Paired t-test | Removes within-subject variability | | Matched controls | Paired t-test | Each case has a specific matched control | Using a paired test when data are independent (or vice versa) gives the wrong answer. **Always check your experimental design before choosing a test.** ::: ------------------------------------------------------------------------ ## 3-Minute Knowledge Check *Close your notes. Answer these on your own — you have 3 minutes. We'll go through the answers together after.* ::: callout-caution ## Knowledge Check Questions **1.** You are comparing body weight in 25 mice before and after a 4-week dietary intervention (the same 25 mice measured twice). Which test is appropriate? a) Independent two-sample t-test b) Paired t-test c) One-sample t-test d) Chi-square test **2.** What does a violin plot show that a box plot does not? **3.** In a paired t-test, the test is effectively performed on: a) The raw values in each group b) The differences between paired observations c) The ranks of the observations d) The log-transformed values **4.** You run `t.test(treated, control, var.equal = FALSE)`. What does `var.equal = FALSE` specify? **5.** True or False: A strip chart (dot plot) is more informative than a mean ± SD bar chart for small sample sizes (n < 20). ::: ::: {.callout-caution collapse="true"} ## Answers (Only reveal if you have answered the above questions) **1.** b) Paired t-test — The same 25 mice are measured twice: once before and once after the intervention. Each mouse's two measurements are paired. The paired t-test removes between-mouse variability (e.g., natural size differences) and focuses on the change within each mouse. **2.** A violin plot shows the **full shape of the distribution** — including whether it is unimodal, bimodal, symmetric, or skewed. A box plot only shows the median, quartiles, and outliers. A bimodal distribution (two peaks) can hide completely inside a box plot. **3.** b) The differences between paired observations — a paired t-test computes d = x₁ − x₂ for each pair and then runs a one-sample t-test asking whether the mean difference is significantly different from zero. This is mathematically equivalent to `t.test(x1 - x2, mu = 0)`. **4.** `var.equal = FALSE` specifies **Welch's t-test**, which does not assume equal variances between the two groups. This is the safer default because violation of equal variances inflates Type I error in the standard Student's t-test. Use `var.equal = TRUE` only if you have strong reason to believe the variances are equal (which you should verify with Levene's test — Lab 18). **5.** **True** — For small samples, individual data points are visible and meaningful. A mean ± SD bar chart hides the distribution entirely — with n = 5, for example, you cannot tell if the data are normally distributed, skewed, or contain outliers. Strip charts reveal these features directly. ::: ------------------------------------------------------------------------ ## Lab 17 Checklist Before you leave, make sure you can: - [ ] Explain why you should plot data before running a statistical test - [ ] Produce a strip chart with `stripchart()` and with `geom_jitter()` - [ ] Produce a violin plot with `geom_violin()` and overlay a box plot and jittered points - [ ] Determine whether a paired or independent t-test is appropriate for a given design - [ ] Run `t.test(x, y, paired = TRUE)` and interpret the output - [ ] Run `t.test(x, y, var.equal = FALSE)` (Welch's) and interpret the output - [ ] Report t-test results in the standard scientific format: t(df) = value, p = value ::: callout-tip ## Bonus Challenge Design your own experiment: choose a biological question involving two groups (e.g., antibiotic A vs antibiotic B, treated vs untreated cells, gene expression before vs after induction). Simulate realistic data using `rnorm()` with biologically plausible means and SDs. Produce a publication-ready violin + jitter plot in ggplot2, run the appropriate t-test, and write a one-sentence conclusion in scientific language. ::: ------------------------------------------------------------------------ ## Before Next Class (Wednesday) - Wednesday (Lab 18): Confidence intervals from t-tests, and Levene's test for equal variances - Read **R for Data Science Ch. 9–10** ------------------------------------------------------------------------