---
title: "Understanding and Interpreting Compact Letter Displays"
output: rmarkdown::html_document
vignette: >
  %\VignetteIndexEntry{Understanding and Interpreting Compact Letter Displays}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)
```

```{r setup}
library(cld)
```

## What is a Compact Letter Display?

A Compact Letter Display (CLD) visualizes multiple pairwise comparison results in a compact format by assigning letters to groups:

- **Groups sharing at least one letter** are **NOT significantly different**
- **Groups with no shared letters** are **significantly different**

This convention is widely used in agricultural research, biology, and statistics to present post-hoc test results.

## Basic Example

```{r example-shared}
# Example with shared letters
result <- pairwise.wilcox.test(chickwts$weight, chickwts$feed, exact = FALSE)
cld_result <- make_cld(result)
cld_result
```

**Interpretation:**

- Groups with shared letters  → **not significantly different**, e.g.:
    - `casein` (a) and `sunflower` (a) share letter "a"
    - `linseed` (bc) and `meatmeal` (ac) share letter "c"
    - `horsebean` (b) and `linseed` (bc) share letter "b"
- Groups with no shared letters  → **significantly different**, e.g.:
    - `horsebean` (b) and `soybean` (c) share no letters
    - `horsebean` (b) and `sunflower` (a) share no letters
    - `casein` (a) and `horsebean` (b) share no letters

## Common Patterns

**Pattern 1:** All different (a, b, c) → all groups significantly different

```{r pattern-examples-1}
set.seed(123)
data1 <- data.frame(
  value = c(rnorm(10, 10, 1), rnorm(10, 20, 1), rnorm(10, 30, 1)),
  group = rep(c("Low", "Medium", "High"), each = 10)
)
make_cld(pairwise.t.test(data1$value, data1$group))
```

**Pattern 2:** One different (a, a, b) → first two groups not different from each other

```{r pattern-examples-2}
set.seed(455)
data2 <- data.frame(
  value = c(rnorm(10, 10, 1.5), rnorm(10, 10.1, 1.5), rnorm(10, 20, 1.5)),
  group = rep(c("A", "B", "C"), each = 10)
)
make_cld(pairwise.t.test(data2$value, data2$group))
```

**Pattern 3:** Overlapping (a, ab, bc, c) → creates chain of non-significant differences

```{r pattern-examples-3}
set.seed(889)
data3 <- data.frame(
  value = c(rnorm(10, 10, 3), rnorm(10, 13, 3), rnorm(10, 16, 3), rnorm(10, 19, 3)),
  group = rep(c("G1", "G2", "G3", "G4"), each = 10)
)
make_cld(pairwise.t.test(data3$value, data3$group))
```

## Spaced CLD Format

The `spaced_cld` column aligns letters vertically using underscores (`_`) for spaces, making patterns easier to visualize in monospaced fonts.

## Statistical Considerations

### Significance Level (Alpha)

Lower alpha values are more conservative, resulting in fewer significant differences:

```{r alpha-comparison}
result <- pairwise.wilcox.test(chickwts$weight, chickwts$feed, exact = FALSE)
```

```{r alpha-comparison-1}
make_cld(result, alpha = 0.05)   # Standard
```

```{r alpha-comparison-2}
make_cld(result, alpha = 0.01)   # Stringent
```

```{r alpha-comparison-3}
make_cld(result, alpha = 0.001)  # Very stringent
```

### Multiple Comparison Adjustment

P-value adjustment methods (Bonferroni, Holm, FDR, etc.) control Type I error inflation and can significantly impact results. Use the `p.adjust.method` argument in your pairwise test function.

## Common Misinterpretations

❌ **Wrong:** "Group 'a' has higher values than group 'b'"  
✅ **Correct:** Letters indicate grouping, not magnitude or rank. They only show which groups differ statistically.  

💡 **Tip:** Sort groups by their original means/medians to understand which groups have higher or lower values.



## Accessing Metadata

```{r metadata}
result <- pairwise.wilcox.test(chickwts$weight, chickwts$feed, exact = FALSE)
cld_result <- make_cld(result)

# Access stored information
attr(cld_result, "alpha")           # Significance level
attr(cld_result, "method")          # Statistical method
attr(cld_result, "n_comparisons")   # Total comparisons
attr(cld_result, "n_significant")   # Significant comparisons
```

## Quick Reference

| Comparison | Shared Letters? | Interpretation |
|------------|----------------|----------------|
| "a" vs "a" | Yes | Not significantly different |
| "a" vs "b" | No | Significantly different |
| "ab" vs "bc" | Yes (letter "b") | Not significantly different |
| "ab" vs "cd" | No | Significantly different |


## Further Reading

- `vignette("cld")` -- Basic usage guide
- `vignette("cld-input-formats")` -- Supported input types
- `vignette("cld-advanced-features")` -- Advanced features and customization
- `?cld::make_cld` -- Function documentation
