第8章 データ指標化・可視化のプロセス

図の右上のshowボタンを押すとRのコードが表示されます。

8.1 効果的な可視化のテクニック

8.1.1 見づらい図と見やすい図

library(conflicted)
library(tidyverse)
library(patchwork)

base_plot <- tibble(
  x = seq(0, 10, length.out = 100),
  y1 = sin(x),
  y2 = cos(x),
  y3 = y1 + y2
  ) |>
  pivot_longer(!x, names_to = "y") |>
  ggplot(aes(x = x, y = value, color = y, linetype = y)) +
  coord_cartesian(xlim = c(0 ,10), ylim = c(-3, 3)) +
  scale_color_hue(name = "", labels = c(y1 = "y = sin(x)", y2 ="y = cos(x)", y3 ="y = sin(x) + cos(x)")) +
  scale_linetype_discrete(name = "", labels = c(y1 = "y = sin(x)", y2 ="y = cos(x)", y3 ="y = sin(x) + cos(x)")) +
  theme(
    legend.title = element_blank(),
    legend.position = c(0.75, 0.85),
    aspect.ratio = 1
    )

# 見づらい図
p1 <- base_plot + 
  geom_line(linewidth = 0.2) +
  scale_x_continuous(breaks = seq(0, 10, by = 0.5)) +
  scale_y_continuous(breaks = seq(-3, 3, by = 0.2)) +
  labs(x = "x-axis label, x", y = "y-axis label, y", title = "見づらいグラフ") +
  theme(
    axis.title = element_text(size = 6, family = "Times New Roman"),
    axis.text = element_text(size = 6, family = "Times New Roman"),
    legend.text = element_text(size = 8, family = "Times New Roman")
    )

# 見やすい図
p2 <- base_plot + 
  geom_line(linewidth = 1) +
  scale_x_continuous(breaks = seq(0, 10, by = 2)) +
  scale_y_continuous(breaks = seq(-3, 3, by = 1)) +
  labs(x = "x-axis label, x", y = "y-axis label, y", title = "見やすいグラフ") +
  theme(
    axis.title = element_text(size = 14, family = "Arial"),
    axis.text = element_text(size = 14, family = "Arial"),
    legend.text = element_text(size = 12, family = "Arial")
  )
  
p1 + p2

8.1.2 グラフの縦横比と軸の範囲

library(conflicted)
library(tidyverse)

# データの定義
df <- data.frame(
  x = c(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10),
  y1 = c(11, 11.2, 11.5, 12, 12.2, 13, 14.2, 14.5, 15, 15.6, 16),
  y2 = c(11.1, 11.3, 11.4, 11.9, 12.1, 12.8, 14.0, 14.2, 14.7, 15.0, 15.5)
  ) |>
  pivot_longer(!x, names_to = "y")

# グラフ
p1 <- df |>
  ggplot(aes(x = x, y = value, color = y, shape = y)) +
  geom_line() +
  geom_point() +
  labs(x = "x", y = "y", title = "基準とする描画例") +
  theme(legend.title = element_blank(), legend.position = c(0.1, 0.8))

p2 <- df |>
  ggplot(aes(x = x, y = value, color = y, shape = y)) +
  geom_line() +
  geom_point() +
  labs(x = "x", y = "y", title = "縦軸範囲広げすぎ？") +
  coord_cartesian(ylim = c(0, 30)) +
  theme(legend.title = element_blank(), legend.position = c(0.1, 0.8))

p3 <- df |>
  ggplot(aes(x = x, y = value, color = y, shape = y)) +
  geom_line() +
  geom_point() +
  labs(x = "x", y = "y", title = "縦軸方向を強調") +
  theme(legend.title = element_blank(), legend.position = c(0.2, 0.9))

p4 <- df |>
  ggplot(aes(x = x, y = value, color = y, shape = y)) +
  geom_line() +
  geom_point() +
  labs(x = "x", y = "y", title = "横軸方向を強調") +
  theme(legend.title = element_blank(), legend.position = c(0.1, 0.8))

design <- "
  113
  223
  444
"

p1 + p2 + p3 + p4 + plot_layout(design = design)

8.1.3 片対数グラフを利用する

library(conflicted)
library(tidyverse)
library(zoo)
library(scales)

# 加工前のデータはこちらにあります。
# https://covid19.who.int/WHO-COVID-19-global-data.csv

# ファイルを読み込む
# 日本、アメリカ、中国のデータを抜き出す
# Date_reportedは日付型に
# 14日間の移動平均を計算
df <- read_csv("https://raw.githubusercontent.com/tkEzaki/data_visualization/main/8%E7%AB%A0/data/covid_data_dummy.csv") |>
  dplyr::filter(Country %in% c("Japan", "United States of America", "China")) |>
  mutate(
    Date_reported = as.Date(Date_reported),
    `14_day_avg` = rollmean(New_cases, 14, fill = NA),
    .by = Country
    ) |>
  mutate(Country = factor(Country, levels = c("Japan", "United States of America", "China")))


# 通常の縦軸
p1 <- df |>
  ggplot(aes(x = Date_reported)) +
  geom_line(aes(y = New_cases, color = Country)) +
  scale_y_continuous(labels = label_comma()) +
  theme(axis.text.x = element_text(angle = 30, hjust = 1)) +
  labs(x = "", y = "新規感染者数", title = "縦軸をそのままプロットしたもの") +
  theme(legend.title = element_blank(), legend.position = c(0.2, 0.8), aspect.ratio = 1/2)

# 対数縦軸
p2 <- df |>
  ggplot(aes(x = Date_reported)) +
  geom_line(aes(y = New_cases, color = Country)) +
  scale_y_continuous(trans = "log10", labels = label_comma()) +
  theme(axis.text.x = element_text(angle = 30, hjust = 1)) +
  labs(x = "", y = "新規感染者数", title = "縦軸を対数でプロットしたもの") +
  theme(legend.title = element_blank(), legend.position = "bottom", aspect.ratio = 1/2)

p1 / p2

8.1.4 凡例を近くに置く

コメントは「普段の平日より1.5倍の来客」となっているがコードは1.4倍？

原点がゼロになっていないが、ゼロにした

library(conflicted)
library(tidyverse)
library(ggrepel)
library(geomtextpath)
library(patchwork)

# データフレームを作成
# 月曜日から日曜日までの7日間, 各時刻
df_base <- expand_grid(
  days_of_week = c("月", "火", "水", "木", "金", "土", "日"),
  hours_of_day = 10:20
  ) 

n <- nrow(df_base)

# 水曜日は12時と17時以外の時間に、普段の平日より1.5倍の来客
# 休日は11:00 - 17:00 までまんべんなく多い
# 平日は12時と17時が多い
set.seed(0)
df_visitor_count <- tibble(
  days_of_week = factor(df_base$days_of_week, levels = c("月", "火", "水", "木", "金", "土", "日")),
  hours_of_day = df_base$hours_of_day,
  visitor_count = case_when(
    days_of_week == "水" & !(hours_of_day %in% c(12, 17)) ~ sample(50:80, 77, replace = TRUE), 
    days_of_week == "水" & hours_of_day %in% c(12, 17) ~ sample(20:50, 77, replace = TRUE) * 1.5,
    days_of_week %in% c("土", "日") & hours_of_day %in% 11:17 ~ sample(70:100, 77, replace = TRUE),
    days_of_week %in% c("土", "日") & !(hours_of_day %in% 11:17) ~ sample(30:60, 77, replace = TRUE),
    !(days_of_week %in% c("水", "土", "日")) & hours_of_day %in% c(12, 17) ~ sample(50:80, 77, replace = TRUE),
    !(days_of_week %in% c("水", "土", "日")) & !(hours_of_day %in% c(12, 17)) ~ sample(20:50, 77, replace = TRUE)
  )
)

# 折れ線グラフを描画
p1 <- df_visitor_count |>
  ggplot(aes(x=hours_of_day, y=visitor_count, group=days_of_week, color=days_of_week)) +
  scale_x_continuous(breaks = seq(10, 20, 1)) +
  coord_cartesian(ylim = c(0, 100)) +
  geom_line() +
  geom_point() +
  labs(x="時刻", y="来客数", color = "曜日", title = "凡例をまとめて表示した例") +
  theme(aspect.ratio = 1/2)

# 凡例を近くに表示した例(1) ggrepelの例（個別に位置設定）
p2 <- df_visitor_count |>
  ggplot(aes(x=hours_of_day, y=visitor_count, group=days_of_week, color=days_of_week)) +
  scale_x_continuous(breaks = seq(10, 20, 1)) +
  coord_cartesian(ylim = c(0, 100)) +
  geom_line() +
  geom_point() +
  geom_text_repel(
    data = data.frame(
      days_of_week =  c("月", "火", "水", "木", "金", "土", "日"),
      hours_of_day =  c(  14,   14,   20,   10.5,   14.1,   13,   16),
      visitor_count = c(  37.5,   48,   79,   50,   21,  91,   96)
    ),
    aes(label = days_of_week), size = 5
  ) +
  theme(legend.position = "none", aspect.ratio = 1/2) +
  labs(x="時刻", y="来客数", color = "曜日", title = "凡例を近くに表示した例(1)", subtitle = "ggrepel1")


# 凡例を近くに表示した例(2) ggrepelの例（終点に配置）
p3 <- df_visitor_count |>
  ggplot(aes(x=hours_of_day, y=visitor_count, group=days_of_week, color=days_of_week)) +
  scale_x_continuous(breaks = seq(10, 20, 1)) +
  coord_cartesian(ylim = c(0, 100)) +
  geom_line() +
  geom_point() +
  geom_text_repel(
    data = df_visitor_count |> slice_max(hours_of_day, n = 1),
    aes(label = days_of_week),
    nudge_x = 1,
    segment.alpha = 0.3,
    size = 5
  ) +
  theme(legend.position = "none", aspect.ratio = 1/2) +
  labs(x="時刻", y="来客数", color = "曜日", title = "凡例を近くに表示した例(2)", subtitle = "ggrepel2")


# 凡例を近くに表示した例(2) geomtextpathの例 おしゃれだが日本語が通らない
p4 <- df_visitor_count |>
  mutate(
    days_of_week_en = case_when(
      days_of_week == "月" ~ "Mon.",
      days_of_week == "火" ~ "Tue.",
      days_of_week == "水" ~ "Wed.",
      days_of_week == "木" ~ "Thu.",
      days_of_week == "金" ~ "Fri.",
      days_of_week == "土" ~ "Sat.",
      days_of_week == "日" ~ "Sun."
      )
    ) |>
  ggplot(aes(x=hours_of_day, y=visitor_count, group=days_of_week, color=days_of_week, label = days_of_week_en)) +
  geom_textline(size = 4, vjust = -0.5) +
  scale_x_continuous(breaks = seq(10, 20, 1)) +
  coord_cartesian(ylim = c(0, 100)) +
  geom_point() +
  theme(legend.position = "none", aspect.ratio = 1/2) +
  labs(x="時刻", y="来客数", color = "曜日", title = "凡例を近くに表示した例(3)", subtitle = "geomtextpath")

p1/p2/p3/p4

8.1.5 色を抑えて強調

library(conflicted)
library(tidyverse)

# データフレームを作成
# 月曜日から日曜日までの7日間, 各時刻
df_base <- expand_grid(
  days_of_week = c("月", "火", "水", "木", "金", "土", "日"),
  hours_of_day = 10:20
) 

n <- nrow(df_base)

# 水曜日は12時と17時以外の時間に、普段の平日より1.5倍の来客
# 休日は11:00 - 17:00 までまんべんなく多い
# 平日は12時と17時が多い
set.seed(0)
df_visitor_count <- tibble(
  days_of_week = factor(df_base$days_of_week, levels = c("月", "火", "水", "木", "金", "土", "日")),
  hours_of_day = df_base$hours_of_day,
  visitor_count = case_when(
    days_of_week == "水" & !(hours_of_day %in% c(12, 17)) ~ sample(50:80, 77, replace = TRUE),
    days_of_week == "水" & hours_of_day %in% c(12, 17) ~ sample(20:50, 77, replace = TRUE) * 1.5,
    days_of_week %in% c("土", "日") & hours_of_day %in% 11:17 ~ sample(70:100, 77, replace = TRUE),
    days_of_week %in% c("土", "日") & !(hours_of_day %in% 11:17) ~ sample(30:60, 77, replace = TRUE),
    !(days_of_week %in% c("水", "土", "日")) & hours_of_day %in% c(12, 17) ~ sample(50:80, 77, replace = TRUE),
    !(days_of_week %in% c("水", "土", "日")) & !(hours_of_day %in% c(12, 17)) ~ sample(20:50, 77, replace = TRUE)
  )
)

# 折れ線グラフを描画
days_of_week <- c("月", "火", "水", "木", "金", "土", "日")
df_visitor_count |>
  ggplot(aes(x = hours_of_day, y = visitor_count, group = days_of_week, color = days_of_week, linetype = days_of_week)) +
  geom_line() +
  geom_point() +
  scale_x_continuous(breaks = seq(10, 20, 1)) +
  coord_cartesian(ylim = c(0, 100)) +
  scale_color_manual(
    values = c(rep("black", 2), "#F8766D", rep("black", 4)),
    breaks = days_of_week
    ) +
  scale_linetype_manual(
    values = c(rep("solid", 5), rep("dashed", 2)),
    breaks = days_of_week
  ) +
  annotate("text", x = 13, y = 95, label="土日", size = 5, color = "black") +
  annotate("text", x = 20, y = 85, label="水", size = 5, color = "#F8766D") +
  annotate("text", x = 15, y = 15, label="その他の平日", size = 5, color = "black") +
  labs(x = "時刻", y = "来客数", title = "注目しているデータだけハイライト") +
  theme(legend.position = "none", aspect.ratio = 1/2)

8.1.6 図内に値を直接記入する

library(conflicted)
library(tidyverse)
library(patchwork)

set.seed(5)

# 10変数、各時系列の長さはL=20でランダムデータを生成（正の値のみ）
# 乱数は0から1の範囲で生成されるため、それに50を（掛けて）足して負にならないようにする
df <- as.data.frame(
  matrix(runif(20 * 6) * 50, ncol = 6),
  make.names = FALSE
  )
names(df) <- LETTERS[1:6]

# 相関係数を計算
correlation_matrix <- df |>
  cor() |>
  as.data.frame() |>
  rownames_to_column()|>
  pivot_longer(!rowname)

# データフレームを準備
df_plot <- df |>
  pivot_longer(everything()) |>
  mutate(name = factor(name, levels =LETTERS[6:1]))

# 棒グラフを描画
p1 <- df_plot |>
  dplyr::filter(name == "A") |>
  ggplot(aes(y = value, x=1:20, label = round(value, 2))) +
  geom_col() +
  coord_cartesian(xlim = c(1, 10)) +
  theme(
    axis.title.x = element_blank(),
    axis.title.y = element_blank(),
    aspect.ratio = 1
    )

# ヒートマップを描画
p2 <- correlation_matrix |>
  ggplot(aes(x = rowname, y = name, fill = value, label = round(value, 2))) +
  scale_fill_viridis_c(option = "turbo") + 
  geom_tile() +
  theme_minimal() +
  theme(
    axis.title.x = element_blank(),
    axis.title.y = element_blank(),
    legend.title = element_blank(),
    aspect.ratio = 1
  )

# 数値入れる
p3 <- p1 +
  geom_text(nudge_y = 1, size = 2.5)

p4 <- p2 +
  geom_text(size = 3, aes(color = (value > 0.75 | value < -0.5))) +
  scale_color_manual(values = c("black", "white")) +
  guides(color = "none")

{p1 | p2} / {p3 | p4}

8.1.7 軸ラベルを説明的にする

library(conflicted)
library(tidyverse)
library(patchwork)

data(iris)

base_p <- iris |>
  ggplot(aes(x = Petal.Length, y = Petal.Width, color = Species)) +
  geom_point() +
  theme(aspect.ratio = 1)

p1 <- base_p + labs(
    x = expression(paste(italic("L")[italic("p")])),
    y = expression(paste(italic("W")[italic("p")]))
    ) +
  theme(legend.position = "none") +
  labs(title = "軸ラベルがわかりにくい図")

p2 <- base_p +
  labs(
    x = expression(paste("花弁の長さ [cm], ", italic("L")[italic("p")])),
    y = expression(paste("花弁の幅 [cm], ", italic("W")[italic("p")]))
    ) +
  scale_color_hue(labels = c("setosa" = "セトサ", "versicolor" ="バージカラー", "virginica" ="バージニカ")) +
  theme(
    legend.position = c(0.2, 0.8),
    legend.title = element_blank()
    ) +
  labs(title = "軸ラベルをわかりやすくした図")

p1 + p2

8.1.8 パネルのレイアウトを考える

8.1.8.1 わかりにくいレイアウト

library(conflicted)
library(tidyverse)
library(patchwork)

data(iris)

p1 <- iris |>
  dplyr::filter(Species == "setosa") |>
  ggplot(aes(x = Petal.Length, y = Petal.Width)) +
  geom_point() +
  labs(x = "花弁の長さ [cm]", y = "花弁の幅 [cm]", title = "セトサ (花弁長 vs 花弁幅)") +
  theme(aspect.ratio = 1)

p2 <- iris |>
  dplyr::filter(Species == "setosa") |>
  ggplot(aes(x = Sepal.Length, y = Petal.Length)) +
  geom_point() +
  labs(x = "がく片の長さ [cm]", y = "花弁の長さ [cm]", title = "セトサ (がく片長さ vs 花弁長)") +
  theme(aspect.ratio = 1)

p3 <- iris |>
  dplyr::filter(Species == "versicolor") |>
  ggplot(aes(x = Petal.Length, y = Petal.Width)) +
  geom_point() +
  labs(x = "花弁の長さ [cm]", y = "花弁の幅 [cm]", title = "バージカラー (花弁長 vs 花弁幅)") +
  theme(aspect.ratio = 1)

p4 <-  iris |>
  dplyr::filter(Species == "versicolor") |>
  ggplot(aes(x = Sepal.Length, y = Petal.Length)) +
  geom_point() +
  labs(x = "がく片の長さ [cm]", y = "花弁の長さ [cm]", title = "バージカラー (がく片長さ vs 花弁長)") +
  theme(aspect.ratio = 1)

p5 <- iris |>
  dplyr::filter(Species == "virginica") |>
  ggplot(aes(x = Petal.Length, y = Petal.Width)) +
  geom_point() +
  labs(x = "花弁の長さ [cm]", y = "花弁の幅 [cm]", title = "バージニカ (花弁長 vs 花弁幅)") +
  theme(aspect.ratio = 1)

p6 <-  iris |>
  dplyr::filter(Species == "virginica") |>
  ggplot(aes(x = Sepal.Length, y = Petal.Length)) +
  geom_point() +
  labs(x = "がく片の長さ [cm]", y = "花弁の長さ [cm]", title = "バージニカ (がく片長さ vs 花弁長)") +
  theme(aspect.ratio = 1)

{p1 | p2 | p3} / {p4 | p5 | p6}

8.1.8.2 わかりやすいレイアウト

library(conflicted)
library(tidyverse)
library(patchwork)

data(iris)

plot_iris <- iris |>
  mutate(
    Species = case_when(
      Species == "setosa" ~ "セトサ",
      Species == "versicolor" ~ "バージカラー",
      Species == "virginica" ~ "バージニカ"
      )
    )

p1 <- plot_iris |>
  ggplot(aes(x = Petal.Length, y = Petal.Width, color = Species)) +
  geom_point() +
  labs(x = "花弁の長さ [cm]", y = "花弁の幅 [cm]") +
  theme(legend.position = "none", aspect.ratio = 1) +
  facet_wrap(vars(Species), scales = "free")
p2 <- plot_iris |>
  ggplot(aes(x = Petal.Length, y = Sepal.Length, color = Species)) +
  geom_point() +
  labs(x = "花弁の長さ [cm]", y = "がく片の長さ [cm]") +
  theme(legend.position = "none", aspect.ratio = 1) +
  facet_wrap(vars(Species), scales = "free")


p1 / p2

これについては、スケールを揃えたほうが誤解が無いと思う。

こんな風に。

library(conflicted)
library(tidyverse)
library(patchwork)

data(iris)

plot_iris <- iris |>
  mutate(
    Species = case_when(
      Species == "setosa" ~ "セトサ",
      Species == "versicolor" ~ "バージカラー",
      Species == "virginica" ~ "バージニカ"
    )
  )

p1 <- plot_iris |>
  ggplot(aes(x = Petal.Length, y = Petal.Width, color = Species)) +
  geom_point() +
  labs(x = "花弁の長さ [cm]", y = "花弁の幅 [cm]") +
  theme(legend.position = "none", aspect.ratio = 1) +
  facet_wrap(vars(Species))
p2 <- plot_iris |>
  ggplot(aes(x = Petal.Length, y = Sepal.Length, color = Species)) +
  geom_point() +
  labs(x = "花弁の長さ [cm]", y = "がく片の長さ [cm]") +
  theme(legend.position = "none", aspect.ratio = 1) +
  facet_wrap(vars(Species))


p1 / p2

8.2 指標化から可視化の戦略を考える

8.2.4 外れ値・異常値を指標化してしまうと……

library(conflicted)
library(tidyverse)
library(ggbeeswarm)

n <- 20
set.seed(0)
samples <- purrr::map2(
  c(10, 15, 12, 20), #mean
  c(5, 5, 5, 5),     #sd
  \(x, y) rnorm(n, x, y)
  )

# サンプルAに外れ値を追加
samples[[1]][1] <- 100

names(samples) <- LETTERS[1:4]

# データフレームを作成
df <- samples |>
  as.data.frame() |>
  pivot_longer(everything())

# スウォームプロット
p1 <- df |>
  ggplot(aes(x = name, y = value, color = name)) +
  geom_quasirandom() +
  theme(
    legend.position = "none",
    axis.title = element_blank(),
    aspect.ratio = 1
  ) + 
  labs(title = "元となるデータ")

# 棒グラフ（平均値）
p2 <- df |>
  summarise(mean = mean(value), .by = name) |>
  ggplot(aes(x = name, y = mean, fill = name)) +
  geom_col() +
  theme(
    legend.position = "none",
    axis.title = element_blank(),
    aspect.ratio = 1
  ) + 
  labs(title = "指標化したもの（平均）")


p1 + p2

8.3.2 ばらつき度合いと特徴の強さ

タイトルの斜体や下付き文字とオブジェクトが同居できない

教えていただいてできました！

library(conflicted)
library(tidyverse)
library(ggbeeswarm)
library(broom)
library(scales) #muted()
library(patchwork)

# データの生成
set.seed(2)
samples <- purrr::pmap(
  list(
    n = c(20, 20, 400, 400),
    mean = c(6, 6, 6, 5.75),
    sd = c(2, 2, 2, 2)
  ),
  \(n, mean, sd) rnorm(n, mean, sd)
)

names(samples) <- c("v11", "v12", "v21", "v22")

# t検定
t_test1 <- tidy(t.test(samples$v11, samples$v12))
t_test2 <- tidy(t.test(samples$v21, samples$v22))

# データの整形
data1 <- data.frame(
  Group = rep(c("Group 1", "Group 2"), each = 20),
  Value = c(samples$v11, samples$v12)
  )
data1_mean <- data1 |>
  summarise(mean = mean(Value), .by = Group)

data2 <- data.frame(
  Group = rep(c("Group 1", "Group 2"), each = 400),
  Value = c(samples$v21, samples$v22)
  )

data2_mean <- data2 |>
  summarise(mean = mean(Value), .by = Group)

p1 <- ggplot() +
  geom_col(data = data1_mean, aes(x = Group, y = mean, fill = Group )) +
  geom_quasirandom(data = data1, aes(x = Group, y = Value, color = Group)) +
  scale_fill_manual(values = c("#CAB2D6", "#B2DF8A")) +
  scale_color_manual(values = c("#6A3D9A", "#33A02C")) + 
  coord_cartesian(ylim = c(0, 12)) +
  labs(
    title = "標本平均の差は大きいが……？", 
    subtitle = bquote(italic(t)[20] == .(round(t_test1$statistic, 2)) ~ ", p-value = " ~ .(round(t_test1$p.value, 4)))
 #   subtitle = expression(paste({italic(t)[20]}, " = ", round(t_test1$statistic, 2), ", p-value = ", round(t_test1$p.value, 4)))
#    subtitle = paste("t20 = ", round(t_test1$statistic, 2), ", p-value = ", round(t_test1$p.value, 4))

    ) +
  theme(legend.position = "none", axis.title = element_blank()) 

test <- expression({italic(t)[400]})
p2 <- ggplot() +
  geom_col(data = data2_mean, aes(x = Group, y = mean, fill = Group )) +
  geom_quasirandom(data = data2, aes(x = Group, y = Value, color = Group)) +
  scale_fill_manual(values = c("#CAB2D6", "#B2DF8A")) +
  scale_color_manual(values = c("#6A3D9A", "#33A02C")) +
  coord_cartesian(ylim = c(0, 12)) +
  labs(
    title = "標本平均の差は小さいが……？",
    subtitle = bquote(italic(t)[400] == .(round(t_test1$statistic, 2)) ~ ", p-value = " ~ .(round(t_test2$p.value, 4)))
  #  subtitle = paste("t400 = ", round(t_test2$statistic, 2), ", p-value = ", round(t_test2$p.value, 4))
    ) +
  theme(legend.position = "none", axis.title = element_blank()) 

p1 + p2

第8章ここまで