---
title: "Session 13 — Select on extremes"
author: "Prof. Dae-Jin Lee (daelee@faculty.ie.edu)"
date: "Fall 2026"
output:
  html_document:
    toc: true
    theme: flatly
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE, message = FALSE, warning = FALSE)
library(tidyverse)
```

```{r}
set.seed(321)
n <- 500
stable_support <- rnorm(n, 50, 10)
sim <- tibble(
  wave1 = stable_support + rnorm(n, 0, 8),
  wave2 = stable_support + rnorm(n, 0, 8)
)

extreme_high <- sim |> filter(wave1 >= quantile(wave1, 0.90))
extreme_low  <- sim |> filter(wave1 <= quantile(wave1, 0.10))

extreme_high |> summarise(mean_wave1 = mean(wave1), mean_wave2 = mean(wave2))
extreme_low  |> summarise(mean_wave1 = mean(wave1), mean_wave2 = mean(wave2))
```

**Interpret:** top group’s wave-2 mean is usually lower; bottom group’s wave-2 mean is usually higher — with **zero** causal program.