---
title: "AE 03"
format: html
---

```{r}
#| warning: false
#| message: false
library(tidyverse)
```

## ANOVA Activity: Do holistic remedies lower systolic blood pressure?

A researcher tests whether three different interventions produce different **reductions in systolic blood pressure (mmHg)** after 8 weeks:

-   **Placebo** (control tea)\
-   **Herbal Tea** (a marketed calming herbal blend)\
-   **Mindfulness** (guided mindfulness practice)

You will simulate data, visualize group differences, run an ANOVA, and interpret the results.

## Exercise 1: Simulate the data

We simulate 30 participants per group. The numbers are set so the placebo group has a small mean reduction, Herbal Tea a moderate reduction, and Mindfulness a larger reduction.

Run the following code to simulate the data.

```{r}
set.seed(2025)

n <- 30

bp_data <- data.frame(
  group = rep(c("Placebo", "HerbalTea", "Mindfulness"), each = n),
  reduction = c(
    rnorm(n, mean = 2, sd = 5),   # Placebo: mean reduction ~2 mmHg
    rnorm(n, mean = 5, sd = 5),   # Herbal Tea: mean reduction ~5 mmHg
    rnorm(n, mean = 7, sd = 5)    # Mindfulness: mean reduction ~7 mmHg
  )
)

head(bp_data)
```

## Exercise 2: Visualize the data

Use the following code to create a boxplot of reduction by group. What pattern(s) do you notice?

```{r}
ggplot(bp_data, 
       aes(x = group, y = reduction, fill = group)) +
  geom_boxplot(alpha = 0.7) +
  labs(title = "Systolic BP Reduction by Intervention",
       x = "Intervention",
       y = "Reduction in systolic BP (mmHg)") +
  theme_minimal() +
  theme(legend.position = "none")
```

\[type response here\]

## Exercise 3: Run the ANOVA

We test:

$H_0$: mean reduction is the same in all groups

$H_A$: at least one group is different

Assume a significance level of $\alpha = 0.05$. Run an ANOVA using the syntax in the slides, printing out your output.

```{r}
# type code here
```

## Exercise 4: Conclusion

Based on your ANOVA result, what is your p-value? Do we reject or fail to reject $H_0$? What is your conclusion statement?