---
title: "Mixed ANOVA Analysis for Domain Means"
author: "Irina"
date: "`r Sys.Date()`"
output: 
  html_document:
    toc: true
    toc_float: true
    code_folding: hide
    theme: flatly
    highlight: tango
    fig_width: 10
    fig_height: 6
---

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

# Introduction

This analysis examines domain-level differences in mean scores across time periods using a mixed ANOVA design. The analysis focuses on four domains (Preferences, Personality, Values, Life) across two time periods (Past, Future) with a between-subjects factor (TEMPORAL_DO).

# Data Preparation and Setup

```{r libraries}
library(tidyverse)
library(ez)
library(car)
library(nortest)      # For normality tests
library(emmeans)      # For post-hoc comparisons
library(purrr)        # For map functions
library(effsize)      # For Cohen's d calculations
library(ggplot2)      # For plotting

options(scipen = 999)
options(contrasts = c("contr.sum", "contr.poly"))

setwd("C:/Users/irina/Documents/DND/EOHI/eohi1")
```

```{r data-loading}
# Read the data
data <- read.csv("exp1.csv")

required_vars <- c("NPast_mean_pref", "NPast_mean_pers", "NPast_mean_val", "NPast_mean_life",
                   "NFut_mean_pref", "NFut_mean_pers", "NFut_mean_val", "NFut_mean_life")

# Define domain mapping
domain_mapping <- data.frame(
  variable = c("NPast_mean_pref", "NPast_mean_pers", "NPast_mean_val", "NPast_mean_life",
               "NFut_mean_pref", "NFut_mean_pers", "NFut_mean_val", "NFut_mean_life"),
  time = c(rep("Past", 4), rep("Future", 4)),
  domain = rep(c("Preferences", "Personality", "Values", "Life"), 2),
  stringsAsFactors = FALSE
)
```

```{r data-reshaping}
long_data <- data %>%
  select(pID, ResponseId, TEMPORAL_DO, all_of(required_vars)) %>%
  pivot_longer(
    cols = all_of(required_vars),
    names_to = "variable",
    values_to = "MEAN_DIFFERENCE"
  ) %>%
  left_join(domain_mapping, by = "variable") %>%
  # Convert to factors with proper levels (note: columns are 'time' and 'domain' from mapping)
  mutate(
    TIME = factor(time, levels = c("Past", "Future")),
    DOMAIN = factor(domain, levels = c("Preferences", "Personality", "Values", "Life")),
    pID = as.factor(pID),
    TEMPORAL_DO = as.factor(TEMPORAL_DO)
  ) %>%
  # Select final columns and remove any rows with missing values
  select(pID, ResponseId, TEMPORAL_DO, TIME, DOMAIN, MEAN_DIFFERENCE) %>%
  filter(!is.na(MEAN_DIFFERENCE))

# Create clean dataset for analysis (fixing the reference issue)
long_data_clean <- long_data
```

# Descriptive Statistics

## Overall Descriptive Statistics by TIME and DOMAIN

```{r descriptive-stats}
desc_stats <- long_data %>%
  group_by(TIME, DOMAIN) %>%
  summarise(
    n = n(),
    mean = round(mean(MEAN_DIFFERENCE, na.rm = TRUE), 5),
    variance = round(var(MEAN_DIFFERENCE, na.rm = TRUE), 5),
    sd = round(sd(MEAN_DIFFERENCE, na.rm = TRUE), 5),
    median = round(median(MEAN_DIFFERENCE, na.rm = TRUE), 5),
    q1 = round(quantile(MEAN_DIFFERENCE, 0.25, na.rm = TRUE), 5),
    q3 = round(quantile(MEAN_DIFFERENCE, 0.75, na.rm = TRUE), 5),
    min = round(min(MEAN_DIFFERENCE, na.rm = TRUE), 5),
    max = round(max(MEAN_DIFFERENCE, na.rm = TRUE), 5),
    .groups = 'drop'
  )

print(desc_stats)
```

## Descriptive Statistics by Between-Subjects Factors

```{r descriptive-stats-temporal}
desc_stats_by_temporal <- long_data %>%
  group_by(TEMPORAL_DO, TIME, DOMAIN) %>%
  summarise(
    n = n(),
    mean = round(mean(MEAN_DIFFERENCE, na.rm = TRUE), 5),
    variance = round(var(MEAN_DIFFERENCE, na.rm = TRUE), 5),
    sd = round(sd(MEAN_DIFFERENCE, na.rm = TRUE), 5),
    .groups = 'drop'
  )

print(desc_stats_by_temporal)
```

# Assumption Testing

## Missing Values Check

```{r missing-values}
missing_summary <- long_data %>%
  group_by(TIME, DOMAIN) %>%
  summarise(
    n_total = n(),
    n_missing = sum(is.na(MEAN_DIFFERENCE)),
    pct_missing = round(100 * n_missing / n_total, 2),
    .groups = 'drop'
  )

print(missing_summary)
```

## Outlier Detection

```{r outlier-detection}
outlier_summary <- long_data_clean %>%
  group_by(TIME, DOMAIN) %>%
  summarise(
    n = n(),
    mean = mean(MEAN_DIFFERENCE),
    sd = sd(MEAN_DIFFERENCE),
    q1 = quantile(MEAN_DIFFERENCE, 0.25),
    median = median(MEAN_DIFFERENCE),
    q3 = quantile(MEAN_DIFFERENCE, 0.75),
    iqr = q3 - q1,
    lower_bound = q1 - 1.5 * iqr,
    upper_bound = q3 + 1.5 * iqr,
    n_outliers = sum(MEAN_DIFFERENCE < lower_bound | MEAN_DIFFERENCE > upper_bound),
    .groups = 'drop'
  )

print(outlier_summary)
```

## Anderson-Darling Normality Test

```{r normality-test}
normality_results <- long_data_clean %>%
  group_by(TIME, DOMAIN) %>%
  summarise(
    n = n(),
    ad_statistic = ad.test(.data$MEAN_DIFFERENCE)$statistic,
    ad_p_value = ad.test(.data$MEAN_DIFFERENCE)$p.value,
    .groups = 'drop'
  )

print(normality_results)
```

## Homogeneity of Variance (Levene's Test)

### Test homogeneity across TIME within each DOMAIN

```{r homogeneity-time}
homogeneity_time <- long_data_clean %>%
  group_by(DOMAIN) %>%
  summarise(
    levene_F = leveneTest(MEAN_DIFFERENCE ~ TIME)$`F value`[1],
    levene_p = leveneTest(MEAN_DIFFERENCE ~ TIME)$`Pr(>F)`[1],
    .groups = 'drop'
  )

print(homogeneity_time)
```

### Test homogeneity across DOMAIN within each TIME

```{r homogeneity-domain}
homogeneity_domain <- long_data_clean %>%
  group_by(TIME) %>%
  summarise(
    levene_F = leveneTest(MEAN_DIFFERENCE ~ DOMAIN)$`F value`[1],
    levene_p = leveneTest(MEAN_DIFFERENCE ~ DOMAIN)$`Pr(>F)`[1],
    .groups = 'drop'
  )

print(homogeneity_domain)
```

