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analysis/analysis.Rmd

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+---
+title: "Analysis"
+output: rmarkdown::html_vignette
+vignette: >
+  %\VignetteIndexEntry{Analysis}
+  %\VignetteEncoding{UTF-8}
+  %\VignetteEngine{knitr::rmarkdown}
+editor_options: 
+  chunk_output_type: console
+---
+
+```{r, include = FALSE}
+knitr::opts_chunk$set(
+  collapse = TRUE,
+  comment = "#>"
+)
+```
+
+In this document, we do the analysis presented in the paper.
+
+Currently, the analysis uses fake data.
+
+## Setup
+
+```{r}
+library(testthat)
+```
+
+## Reading the data
+
+```{r}
+ratings <- readr::read_csv("ratings.csv", show_col_types = FALSE)
+n_ratings <- nrow(ratings)
+```
+
+There are `r n_ratings` ratings.
+
+## Analysis
+
+Connecting the ratings to the formations:
+
+```{r}
+songs <- dplyr::select(heyahmama::get_songs(), cd_title, song_title)
+n_songs <- nrow(songs)
+```
+
+There are `r n_songs` songs.
+
+```{r}
+cds <- dplyr::select(heyahmama::get_cds(), cd_title, formation)
+n_cds <- nrow(cds)
+n_formations <- length(unique(cds$formation))
+```
+
+There are `r n_cds` CDs.
+
+```{r}
+songs_per_formation <- dplyr::select(merge(songs, cds), song_title, formation)
+testthat::expect_equal(n_songs, nrow(songs_per_formation))
+knitr::kable(head(songs_per_formation))
+```
+
+Add the formations to the ratings:
+
+```{r}
+ratings_per_formation <- dplyr::select(merge(ratings, songs_per_formation), formation, rating)
+testthat::expect_equal(n_ratings, nrow(ratings_per_formation))
+ratings_per_formation$formation <- as.factor(ratings_per_formation$formation)
+knitr::kable(head(ratings_per_formation))
+```
+
+Plot:
+
+```{r}
+ggplot2::ggplot(
+  ratings_per_formation,
+  ggplot2::aes(x = formation, y = rating)
+) + ggplot2::geom_violin()
+```
+
+Order formations by ratings:
+
+```{r}
+average_rating_per_formation <-
+  ratings_per_formation |> 
+  dplyr::group_by(formation) |> 
+  dplyr::summarise(average_rating = mean(rating))
+testthat::expect_equal(n_formations, nrow(average_rating_per_formation))
+
+ordered_average_rating_per_formation <- 
+  average_rating_per_formation |> 
+  dplyr::arrange(dplyr::desc(average_rating))
+testthat::expect_equal(n_formations, nrow(ordered_average_rating_per_formation))
+
+knitr::kable(ordered_average_rating_per_formation)
+```
+
+## Statistics
+
+Do the formations have different ratings?
+
+```{r}
+n_combinations <- factorial(n_formations - 1)
+```
+
+There will be `r n_combinations` comparisons.
+
+```{r}
+alpha <- 0.05 / n_combinations
+```
+
+Due to `r n_combinations` comparisons,
+the alpha value is (`0.05` divided by
+`r n_combinations` equals) `r alpha`.
+
+```{r}
+p_values_table <- tibble::tibble(
+  a = rep(NA, n_combinations), 
+  b = NA, 
+  p_value = NA
+)
+
+i <- 1
+for (lhs in seq(1, n_formations - 1)) {
+  ratings_lhs <- ratings_per_formation[ratings_per_formation$formation == lhs, ]$rating
+  for (rhs in seq(lhs + 1, n_formations)) {
+    ratings_rhs <- ratings_per_formation[ratings_per_formation$formation == rhs, ]$rating
+    p_value <- wilcox.test(ratings_lhs, ratings_rhs, alternative = "two.sided")$p.value
+    testthat::expect_true(i >= 1)
+    testthat::expect_true(i <= nrow(p_values_table))
+    p_values_table$a[i] <- lhs
+    p_values_table$b[i] <- rhs
+    p_values_table$p_value[i] <- p_value
+    i <- i + 1
+  }
+}
+p_values_table$is_the_same <- p_values_table$p_value > alpha
+knitr::kable(p_values_table)
+```
+