How to use this document. Run the code along with me. Comments start with #. Each section mirrors the live lab; code chunks show the command and its output together.

Today’s plan

Clean environment + setup
Import & understand Life Expectancy data
Working with categorical variables
One-sample t-test (Life Expectancy)
Two-sample t-test (Developed vs. Developing)
Quick practice
Wrap-up

1 Clean Environment + Setup

rm(list = ls())   # clean environment

# Load the packages
library(dplyr)
library(ggplot2)
library(stats)

In the live session we set the working directory with setwd(...). In this document the data file Life Expectancy Data.csv sits next to the .Rmd, so no setwd() is needed.

2 Import & Understand Data

The dataset is the WHO Life Expectancy data.

data <- read.csv("Life Expectancy Data.csv")

# In RStudio you would run View(data); here we preview the first rows.
knitr::kable(head(data), caption = "First rows of the Life Expectancy data")

First rows of the Life Expectancy data
Country	Year	Status	Life.expectancy	Adult.Mortality	infant.deaths	Alcohol	percentage.expenditure	Hepatitis.B	Measles	BMI	under.five.deaths	Polio	Total.expenditure	Diphtheria	HIV.AIDS	GDP	Population	thinness..1.19.years	thinness.5.9.years	Income.composition.of.resources	Schooling
Afghanistan	2015	Developing	65.0	263	62	0.01	71.279624	65	1154	19.1	83	6	8.16	65	0.1	584.25921	33736494	17.2	17.3	0.479	10.1
Afghanistan	2014	Developing	59.9	271	64	0.01	73.523582	62	492	18.6	86	58	8.18	62	0.1	612.69651	327582	17.5	17.5	0.476	10.0
Afghanistan	2013	Developing	59.9	268	66	0.01	73.219243	64	430	18.1	89	62	8.13	64	0.1	631.74498	31731688	17.7	17.7	0.470	9.9
Afghanistan	2012	Developing	59.5	272	69	0.01	78.184215	67	2787	17.6	93	67	8.52	67	0.1	669.95900	3696958	17.9	18.0	0.463	9.8
Afghanistan	2011	Developing	59.2	275	71	0.01	7.097109	68	3013	17.2	97	68	7.87	68	0.1	63.53723	2978599	18.2	18.2	0.454	9.5
Afghanistan	2010	Developing	58.8	279	74	0.01	79.679367	66	1989	16.7	102	66	9.20	66	0.1	553.32894	2883167	18.4	18.4	0.448	9.2

summary(data)

#>    Country               Year         Status          Life.expectancy
#>  Length:2938        Min.   :2000   Length:2938        Min.   :36.30  
#>  Class :character   1st Qu.:2004   Class :character   1st Qu.:63.10  
#>  Mode  :character   Median :2008   Mode  :character   Median :72.10  
#>                     Mean   :2008                      Mean   :69.22  
#>                     3rd Qu.:2012                      3rd Qu.:75.70  
#>                     Max.   :2015                      Max.   :89.00  
#>                                                       NA's   :10     
#>  Adult.Mortality infant.deaths       Alcohol        percentage.expenditure
#>  Min.   :  1.0   Min.   :   0.0   Min.   : 0.0100   Min.   :    0.000     
#>  1st Qu.: 74.0   1st Qu.:   0.0   1st Qu.: 0.8775   1st Qu.:    4.685     
#>  Median :144.0   Median :   3.0   Median : 3.7550   Median :   64.913     
#>  Mean   :164.8   Mean   :  30.3   Mean   : 4.6029   Mean   :  738.251     
#>  3rd Qu.:228.0   3rd Qu.:  22.0   3rd Qu.: 7.7025   3rd Qu.:  441.534     
#>  Max.   :723.0   Max.   :1800.0   Max.   :17.8700   Max.   :19479.912     
#>  NA's   :10                       NA's   :194                             
#>   Hepatitis.B       Measles              BMI        under.five.deaths
#>  Min.   : 1.00   Min.   :     0.0   Min.   : 1.00   Min.   :   0.00  
#>  1st Qu.:77.00   1st Qu.:     0.0   1st Qu.:19.30   1st Qu.:   0.00  
#>  Median :92.00   Median :    17.0   Median :43.50   Median :   4.00  
#>  Mean   :80.94   Mean   :  2419.6   Mean   :38.32   Mean   :  42.04  
#>  3rd Qu.:97.00   3rd Qu.:   360.2   3rd Qu.:56.20   3rd Qu.:  28.00  
#>  Max.   :99.00   Max.   :212183.0   Max.   :87.30   Max.   :2500.00  
#>  NA's   :553                        NA's   :34                       
#>      Polio       Total.expenditure   Diphtheria       HIV.AIDS     
#>  Min.   : 3.00   Min.   : 0.370    Min.   : 2.00   Min.   : 0.100  
#>  1st Qu.:78.00   1st Qu.: 4.260    1st Qu.:78.00   1st Qu.: 0.100  
#>  Median :93.00   Median : 5.755    Median :93.00   Median : 0.100  
#>  Mean   :82.55   Mean   : 5.938    Mean   :82.32   Mean   : 1.742  
#>  3rd Qu.:97.00   3rd Qu.: 7.492    3rd Qu.:97.00   3rd Qu.: 0.800  
#>  Max.   :99.00   Max.   :17.600    Max.   :99.00   Max.   :50.600  
#>  NA's   :19      NA's   :226       NA's   :19                      
#>       GDP              Population        thinness..1.19.years
#>  Min.   :     1.68   Min.   :3.400e+01   Min.   : 0.10       
#>  1st Qu.:   463.94   1st Qu.:1.958e+05   1st Qu.: 1.60       
#>  Median :  1766.95   Median :1.387e+06   Median : 3.30       
#>  Mean   :  7483.16   Mean   :1.275e+07   Mean   : 4.84       
#>  3rd Qu.:  5910.81   3rd Qu.:7.420e+06   3rd Qu.: 7.20       
#>  Max.   :119172.74   Max.   :1.294e+09   Max.   :27.70       
#>  NA's   :448         NA's   :652         NA's   :34          
#>  thinness.5.9.years Income.composition.of.resources   Schooling    
#>  Min.   : 0.10      Min.   :0.0000                  Min.   : 0.00  
#>  1st Qu.: 1.50      1st Qu.:0.4930                  1st Qu.:10.10  
#>  Median : 3.30      Median :0.6770                  Median :12.30  
#>  Mean   : 4.87      Mean   :0.6276                  Mean   :11.99  
#>  3rd Qu.: 7.20      3rd Qu.:0.7790                  3rd Qu.:14.30  
#>  Max.   :28.60      Max.   :0.9480                  Max.   :20.70  
#>  NA's   :34         NA's   :167                     NA's   :163

3 Categorical Variables

What is recoding / encoding? Converting categorical variables (text) into numeric values — for example, "Developed" → 1 and "Developing" → 0.

Why do we recode?

Regression models need numeric predictors.
It makes categorical data usable in statistical tests.

Create a dummy variable. Use ifelse() for binary variables.

data$is_developed <- ifelse(data$Status == "Developed", 1, 0)
head(data$is_developed)

#> [1] 0 0 0 0 0 0

Simple regression with a binary predictor. Predict life expectancy from developed/developing status.

model1 <- lm(Life.expectancy ~ is_developed, data = data)
summary(model1)

#> 
#> Call:
#> lm(formula = Life.expectancy ~ is_developed, data = data)
#> 
#> Residuals:
#>     Min      1Q  Median      3Q     Max 
#> -30.811  -4.912   1.288   6.489  21.889 
#> 
#> Coefficients:
#>              Estimate Std. Error t value Pr(>|t|)    
#> (Intercept)   67.1115     0.1698  395.28   <2e-16 ***
#> is_developed  12.0864     0.4060   29.77   <2e-16 ***
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> Residual standard error: 8.345 on 2926 degrees of freedom
#>   (10 observations deleted due to missingness)
#> Multiple R-squared:  0.2325, Adjusted R-squared:  0.2322 
#> F-statistic: 886.2 on 1 and 2926 DF,  p-value: < 2.2e-16

Intercept = mean life expectancy for Developing countries (the reference group).

is_developed = difference in mean life expectancy (Developed − Developing).

4 One-Sample t-test (Life Expectancy)

We test $H_0: \mu = 70$ against $H_1: \mu \neq 70$.

Step 1 — Sample mean.

mean(data$Life.expectancy, na.rm = TRUE)

#> [1] 69.22493

Step 2 — One-sample t-test.

t.test(data$Life.expectancy, mu = 70)

#> 
#>  One Sample t-test
#> 
#> data:  data$Life.expectancy
#> t = -4.4036, df = 2927, p-value = 1.103e-05
#> alternative hypothesis: true mean is not equal to 70
#> 95 percent confidence interval:
#>  68.87982 69.57004
#> sample estimates:
#> mean of x 
#>  69.22493

Step 3 — Extract the 95% CI bounds (for plotting).

ci_life <- t.test(data$Life.expectancy, conf.level = 0.95)$conf.int
ci_life

#> [1] 68.87982 69.57004
#> attr(,"conf.level")
#> [1] 0.95

Step 4 — Visualize the distribution with CI lines.

ggplot(data, aes(x = Life.expectancy)) +
  geom_histogram(binwidth = 2, fill = "steelblue", color = "black") +
  geom_vline(xintercept = ci_life, linetype = "dashed", color = "red") +
  labs(
    title = "Life Expectancy Distribution (95% CI)",
    x = "Life Expectancy (years)",
    y = "Count"
  )

5 Two-Sample t-test (Developed vs. Developing)

We test $H_0: \mu_{\text{developed}} = \mu_{\text{developing}}$ against $H_1: \mu_{\text{developed}} \neq \mu_{\text{developing}}$.

t.test(Life.expectancy ~ Status, data = data)

#> 
#>  Welch Two Sample t-test
#> 
#> data:  Life.expectancy by Status
#> t = 47.868, df = 1807, p-value < 2.2e-16
#> alternative hypothesis: true difference in means between group Developed and group Developing is not equal to 0
#> 95 percent confidence interval:
#>  11.59118 12.58159
#> sample estimates:
#>  mean in group Developed mean in group Developing 
#>                 79.19785                 67.11147

In t.test(y ~ x, data = ...):

y = numeric variable (the thing you’re measuring)

x = categorical variable (the grouping factor, must have 2 levels)

Visualize.

ggplot(data, aes(x = Status, y = Life.expectancy)) +
  geom_boxplot(fill = "lightblue", color = "black") +
  labs(
    title = "Life Expectancy by Country Status",
    x = "Country Status",
    y = "Life Expectancy (years)"
  )

6 Quick Practice

P1) One-sample t-test: is average GDP different from 5000?

t.test(data$GDP, mu = 5000)

#> 
#>  One Sample t-test
#> 
#> data:  data$GDP
#> t = 8.6831, df = 2489, p-value < 2.2e-16
#> alternative hypothesis: true mean is not equal to 5000
#> 95 percent confidence interval:
#>  6922.383 8043.934
#> sample estimates:
#> mean of x 
#>  7483.158

P2) One-sample t-test: is average Schooling different from 10? Create a histogram with the 95% CI.

t.test(data$Schooling, mu = 10)

#> 
#>  One Sample t-test
#> 
#> data:  data$Schooling
#> t = 31.253, df = 2774, p-value < 2.2e-16
#> alternative hypothesis: true mean is not equal to 10
#> 95 percent confidence interval:
#>  11.86777 12.11782
#> sample estimates:
#> mean of x 
#>  11.99279

ci_schooling <- t.test(data$Schooling, conf.level = 0.95)$conf.int

ggplot(data, aes(x = Schooling)) +
  geom_histogram(binwidth = 1, fill = "skyblue", color = "black") +
  geom_vline(xintercept = ci_schooling, linetype = "dashed", color = "red") +
  labs(
    title = "Schooling Distribution (95% CI)",
    x = "Years of Schooling",
    y = "Count"
  )

P3) Two-sample t-test: compare Adult.Mortality between Developed and Developing. Create boxplots by group.

t.test(Adult.Mortality ~ Status, data = data)

#> 
#>  Welch Two Sample t-test
#> 
#> data:  Adult.Mortality by Status
#> t = -30.745, df = 2174.9, p-value < 2.2e-16
#> alternative hypothesis: true difference in means between group Developed and group Developing is not equal to 0
#> 95 percent confidence interval:
#>  -109.72693  -96.56836
#> sample estimates:
#>  mean in group Developed mean in group Developing 
#>                 79.68555                182.83320

ggplot(data, aes(x = Status, y = Adult.Mortality)) +
  geom_boxplot(fill = "lightgreen", color = "black") +
  labs(
    title = "Adult Mortality by Country Status",
    x = "Country Status",
    y = "Adult Mortality Rate"
  )

7 Wrap-up

Key takeaways

Use ifelse() to create binary (dummy) variables.
Use t.test(x, mu = value) for a one-sample test.
Use t.test(y ~ x, data) for two independent samples.
Extract the CI with $conf.int, then draw vertical lines on histograms.
Visualize distributions and group comparisons with ggplot2.

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

Lab 8 — t-tests & Categorical Variables

Quantitative Reasoning · LAB 413

Instructor: Subin Na

October 29, 2025