Kapitel 16 Lesbarkeitsindices

(Reading ease indices)

16.1 Zur theoretischen Begründung

“Lesbarkeitsformeln sind in der Forschung weitgehend etabliert. Viele, die sich mit Lesbarkeitsformeln befassen, stellen sich dennoch die Frage, wieso man bei Berücksichtigung nur sehr weniger Kriterien Aufschluss über die Lesbarkeit von Texten erhalten kann. Man hat ja doch leicht den Eindruck, dass Wort- und Satzlänge keine besonders triftigen Kriterien sein sollten. Schaut man sich aber an, mit welchen anderen Kriterien diese beiden genannten – und andere – verknüpft sind, kann man erkennen, dass zwar nur zwei Texteigenschaften direkt gemessen werden, damit aber indirekt eine ganze Reihe andere ebenfalls berücksichtigt werden.” — https://de.wikipedia.org/wiki/Lesbarkeitsindex

16.2 Programme

library(tidyverse)
library(tidytext)
library(quanteda)
library(readtext)
library(nsyllable)

16.3 Texte lesen

stringsAsFactor = F
prozess = read_lines("novels/book05.txt")
enfants = read_lines("novels/book12.txt")

romane = readtext("novels/*.txt")
coronavirus2020 <- readtext("news/*.json", 
                            text_field = "text", encoding = "LATIN1")

16.4 Flesch Reading Ease - deutsche Version

knitr::include_graphics(
  "pictures/Lesbarkeitsindex Flesch Ease deutsch.png")

flres_de = readxl::read_xlsx("data/Flesch-Reading-Ease-Score-deutsch.xlsx")
flres_de %>% 
  mutate(`Verständlich für` = replace_na(`Verständlich für`," ")) %>%
  rmarkdown::paged_table()

16.5 Romane (deutsche oder ins Deutsche übersetzte)

lesbarkeitsindex_romane = as_tibble(romane) %>%
  mutate(sentences = nsentence(text),
         words = ntoken(text, remove_punct = TRUE),
         syllables = nsyllable(text),
         flesch_ease_de = 180 - (words/sentences) - 58.5*(syllables/words))

lesbarkeitsindex_romane %>% 
  select(doc_id, syllables, sentences, words, flesch_ease_de) %>% 
  arrange(flesch_ease_de) %>% 
  rmarkdown::paged_table()

# write_excel_csv2(lesbarkeitsindex_romane, "data/lesbarkeitsindex_romane.csv")

lesbarkeitsindex_romane = lesbarkeitsindex_romane %>% 
  mutate(book_name = str_sub(text, 1, 12)) # extract string in position 1-12

# reading score chart
ggplot(lesbarkeitsindex_romane, aes(x = syllables/words, y = flesch_ease_de, 
                                    color = book_name, name = book_name,
                                    size = sentences)) +
  geom_count(alpha = 0.5) +
  # scale_x_log10() +
  geom_smooth(se = FALSE, color = "red", method = "lm", size = 0.5, 
              linetype = "dashed") +
  scale_y_continuous(breaks = c(60,65,70,75,80,85)) +
  scale_x_continuous(breaks = c(1.3,1.4,1.5,1.6)) +
  scale_size_area(max_size = 12, guide = FALSE) +
  theme_minimal(base_size = 14) +
  labs(color = "Roman", x = "# Silben pro Wort", y = "Lesbarkeitsindex")

book <- book[str_sub(book, 1, 12) == “review/text:”] # extract string in position 1-12 book <- str_sub(book, start = 14) # extract substring starting in position 14

library(plotly)
p <- lesbarkeitsindex_romane %>%
  ggplot(aes(syllables/words, flesch_ease_de, 
             color = book_name, name = book_name, size = sentences)) +
  geom_count() +
  geom_smooth(se = FALSE, color = "red", method = "lm", size = 0.5, 
              linetype = "dashed") +
  scale_y_continuous(breaks = c(60,65,70,75,80,85)) +
  scale_x_continuous(breaks = c(1.3,1.4,1.5,1.6)) +
  scale_size_area(max_size = 12, guide = FALSE) +
  theme_minimal(base_size = 14) +
  labs(color = "Roman", x = "# Silben pro Wort", y = "Lesbarkeitsindex")

ggplotly(p, height = 500)

16.6 Zeitungen

lesbarkeitsindex_news = as_tibble(coronavirus2020) %>%
  mutate(syllables = nsyllable(text),
         sentences = nsentence(text),
         words = ntoken(text, remove_punct = TRUE),
         flesch_ease_de = 180 - (words/sentences) - 58.5*(syllables/words))

lesbarkeitsindex_news %>% 
  select(doc_id, syllables, sentences, words, flesch_ease_de) %>%
  arrange(flesch_ease_de) %>% 
  rmarkdown::paged_table()

# write_excel_csv2(lesbarkeitsindex_news,
#                  "data/lesbarkeitsindex_news_coronavirus_2020.csv")

# reading score chart
ggplot(lesbarkeitsindex_news, aes(x = syllables/words, y = flesch_ease_de, 
                                  color = lubridate::month(date),
                                  size = sentences)) +
  geom_count(alpha = 0.5) +
  geom_jitter() +
  # scale_x_log10() +
  geom_smooth(se = FALSE, color = "red", method = "lm", size = 0.5, 
              linetype = "dashed") +
  scale_y_continuous(breaks = c(20,30,40,50,60,70,80,90,100)) +
  scale_x_continuous(limits = c(1,2.5), breaks = c(1.0,1.25,1.5,1.75,2.0,2.25,2.5)) +
  scale_size_area(max_size = 12, guide = "none") +
  theme_minimal(base_size = 14) +
  labs(color = "month 2020", x = "# Syllables per word", y = "Reading level")

lesbarkeitsindex_news = lesbarkeitsindex_news %>% mutate(news_name = str_sub(doc_id, 1, 7))

# reading score chart
ggplot(lesbarkeitsindex_news, aes(x = syllables/words, y = flesch_ease_de, 
                                  color = news_name,
                                  name = news_name,
                                  size = sentences)) +
  geom_count(alpha = 0.5) +
  geom_jitter() +
  scale_y_continuous(breaks = c(20,30,40,50,60,70,80,90,100)) +
  scale_x_continuous(limits = c(1,2.5), breaks = c(1,1.5,2.0,2.5)) +
  facet_wrap(~ news_name) +
  geom_smooth(se = FALSE, color = 1, method = "lm", size = 0.5,
              linetype = "dashed") +
  scale_size_area(max_size = 12, guide = "none") +
  theme_light(base_size = 14) +
  labs(color = "Zeitung", x = "# Silben pro Wort", y = "Lesbarkeitsindex")

library(plotly)
q = lesbarkeitsindex_news %>%
  ggplot(aes(syllables/words, flesch_ease_de, 
             color = lubridate::month(date), name = news_name, size = sentences)) +
  geom_point() +
  facet_wrap(~ news_name) +
  geom_jitter() +
  geom_smooth(se = FALSE, color = "black", method = "lm", size = 0.5, 
              linetype = "dashed") +
  scale_y_continuous(breaks = c(20,30,40,50,60,70,80,90,100)) +
  scale_x_continuous(limits = c(1,2.5), breaks = c(1,1.5,2.0,2.5)) +
  scale_size_area(max_size = 12, guide = "none") +
  theme_light(base_size = 14) +
  labs(color = "month 2020", x = "# Silben pro Wort", y = "Lesbarkeitsindex")

ggplotly(q, height = 500)

16.7 Statistische Tests: News

Können wir statistisch signifikante Unterschiede zwischen den Lesbarkeitsindices nachweisen?

Mit dem t-Test können wir immer nur zwei Stichproben miteinander vergleichn.

lesbarkeitsindex_news %>% 
  filter(news_name != "welt_co" & news_name != "stern_g" & news_name != "focus_c") %>% 
  t.test(flesch_ease_de ~ news_name, data = ., paired = F, var.equal = T)

## 
##  Two Sample t-test
## 
## data:  flesch_ease_de by news_name
## t = -10.532, df = 4924, p-value < 2.2e-16
## alternative hypothesis: true difference in means between group faz_cor and group spiegel is not equal to 0
## 95 percent confidence interval:
##  -3.313378 -2.273477
## sample estimates:
## mean in group faz_cor mean in group spiegel 
##              50.62753              53.42096

lesbarkeitsindex_news %>% 
  filter(news_name != "spiegel" & news_name != "stern_g" & news_name != "focus_c") %>% 
  t.test(flesch_ease_de ~ news_name, data = ., paired = F, var.equal = T)

## 
##  Two Sample t-test
## 
## data:  flesch_ease_de by news_name
## t = -13.358, df = 4215, p-value < 2.2e-16
## alternative hypothesis: true difference in means between group faz_cor and group welt_co is not equal to 0
## 95 percent confidence interval:
##  -4.819682 -3.586028
## sample estimates:
## mean in group faz_cor mean in group welt_co 
##              50.62753              54.83038

lesbarkeitsindex_news %>% 
  filter(news_name != "faz_cor" & news_name != "stern_g" & news_name != "focus_c") %>% 
  t.test(flesch_ease_de ~ news_name, data = ., paired = F, var.equal = T)

## 
##  Two Sample t-test
## 
## data:  flesch_ease_de by news_name
## t = -6.1477, df = 5941, p-value = 8.374e-10
## alternative hypothesis: true difference in means between group spiegel and group welt_co is not equal to 0
## 95 percent confidence interval:
##  -1.8588644 -0.9599905
## sample estimates:
## mean in group spiegel mean in group welt_co 
##              53.42096              54.83038

Eine lineare Regression ermöglicht den Vergleich von mehreren Stichproben und mehreren Variablen (Faktoren, Prädiktoren).

lesbarkeitsindex_news %>% 
  lm(flesch_ease_de ~ news_name, data = .) %>% 
  summary()

## 
## Call:
## lm(formula = flesch_ease_de ~ news_name, data = .)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -68.487  -5.290  -0.583   5.397  53.357 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)       50.6275     0.2255 224.481   <2e-16 ***
## news_namefocus_c  -0.6147     2.3402  -0.263    0.793    
## news_namespiegel   2.7934     0.2745  10.178   <2e-16 ***
## news_namestern_g  11.2601     0.4856  23.187   <2e-16 ***
## news_namewelt_co   4.2029     0.2863  14.680   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 9.021 on 7993 degrees of freedom
## Multiple R-squared:  0.06919,    Adjusted R-squared:  0.06872 
## F-statistic: 148.5 on 4 and 7993 DF,  p-value: < 2.2e-16

16.8 Datensätze vereinen

lesbarkeitsindex = lesbarkeitsindex_romane %>% 
  mutate(book_name = "romane") %>% 
  rename(news_name = book_name) %>% 
  bind_rows(lesbarkeitsindex_news[,c(1:2,7:11)])

(les_mean = mean(lesbarkeitsindex$flesch_ease_de))

## [1] 53.81142

(les_sd = sd(lesbarkeitsindex$flesch_ease_de))

## [1] 9.375399

(syl_mean = mean(lesbarkeitsindex$syllables/lesbarkeitsindex$words))

## [1] 1.875349

library(plotly)
p <- lesbarkeitsindex %>%
  ggplot(aes(syllables/words, flesch_ease_de, 
             color = news_name, name = news_name, size = sentences)) +
  geom_count() +
  geom_smooth(se = FALSE, color = "red", method = "lm", size = 0.5, 
              linetype = "dashed") +
  geom_vline(xintercept = syl_mean, lty = 2) +
  geom_hline(yintercept = les_mean, lty = 2) +
  geom_hline(yintercept = les_mean + 2*les_sd, lty = 3) +
  geom_hline(yintercept = les_mean - 2*les_sd, lty = 3) +
  scale_y_continuous(
    breaks = c(0,10,20,30,40,50,60,70,80,90,100,110)) +
  scale_x_continuous(
    breaks = c(1.0,1.2,1.4,1.6,1.8,2.0,2.2,2.4,2.6)) +
  scale_size_area(max_size = 12, guide = "none") +
  theme_minimal(base_size = 14) +
  labs(color = "Medium", x = "# Silben pro Wort", y = "Lesbarkeitsindex")

ggplotly(p, height = 400)

16.9 Zeitungen im Vergleich

# global options
# options(contrasts=c('contr.sum','contr.poly'))

lesbarkeitsindex$news_name = as.factor(lesbarkeitsindex$news_name)
# set contrast to "contr.sum"
contrasts(lesbarkeitsindex$news_name) <- "contr.sum"
contrasts(lesbarkeitsindex$news_name) # take a look

##         [,1] [,2] [,3] [,4] [,5]
## faz_cor    1    0    0    0    0
## focus_c    0    1    0    0    0
## romane     0    0    1    0    0
## spiegel    0    0    0    1    0
## stern_g    0    0    0    0    1
## welt_co   -1   -1   -1   -1   -1

lesbarkeitsindex %>% 
  lm(flesch_ease_de ~ news_name, data = .) %>% 
  summary()

## 
## Call:
## lm(formula = flesch_ease_de ~ news_name, data = .)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -68.487  -5.290  -0.581   5.397  53.357 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  57.2894     0.5892  97.241  < 2e-16 ***
## news_name1   -6.6618     0.6173 -10.793  < 2e-16 ***
## news_name2   -7.2765     1.9908  -3.655 0.000259 ***
## news_name3   15.6675     2.2062   7.102 1.34e-12 ***
## news_name4   -3.8684     0.6028  -6.417 1.47e-10 ***
## news_name5    4.5982     0.6858   6.705 2.16e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 9.02 on 8004 degrees of freedom
## Multiple R-squared:  0.07494,    Adjusted R-squared:  0.07436 
## F-statistic: 129.7 on 5 and 8004 DF,  p-value: < 2.2e-16

lesbarkeitsindex %>% 
  lm(flesch_ease_de ~ news_name, data = .) %>% 
  tidy() %>% 
  # filter(term != "(Intercept)") %>% 
  mutate(term = str_replace(term, "news_name", "")) %>% 
  arrange(estimate)

## # A tibble: 6 x 5
##   term        estimate std.error statistic  p.value
##   <chr>          <dbl>     <dbl>     <dbl>    <dbl>
## 1 2              -7.28     1.99      -3.66 2.59e- 4
## 2 1              -6.66     0.617    -10.8  5.71e-27
## 3 4              -3.87     0.603     -6.42 1.47e-10
## 4 5               4.60     0.686      6.70 2.16e-11
## 5 3              15.7      2.21       7.10 1.34e-12
## 6 (Intercept)    57.3      0.589     97.2  0

# global default option
# options(contrasts=c('contr.treatment','contr.poly'))

# set contrast back to default ("contr.treatment")
contrasts(lesbarkeitsindex$news_name) <- NULL
contrasts(lesbarkeitsindex$news_name) # take a look

##         focus_c romane spiegel stern_g welt_co
## faz_cor       0      0       0       0       0
## focus_c       1      0       0       0       0
## romane        0      1       0       0       0
## spiegel       0      0       1       0       0
## stern_g       0      0       0       1       0
## welt_co       0      0       0       0       1

lesbarkeitsindex %>% 
  lm(flesch_ease_de ~ news_name, data = .) %>% 
  summary()

## 
## Call:
## lm(formula = flesch_ease_de ~ news_name, data = .)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -68.487  -5.290  -0.581   5.397  53.357 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)       50.6275     0.2255 224.511   <2e-16 ***
## news_namefocus_c  -0.6147     2.3399  -0.263    0.793    
## news_nameromane   22.3293     2.6136   8.543   <2e-16 ***
## news_namespiegel   2.7934     0.2744  10.179   <2e-16 ***
## news_namestern_g  11.2601     0.4856  23.190   <2e-16 ***
## news_namewelt_co   4.2029     0.2863  14.682   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 9.02 on 8004 degrees of freedom
## Multiple R-squared:  0.07494,    Adjusted R-squared:  0.07436 
## F-statistic: 129.7 on 5 and 8004 DF,  p-value: < 2.2e-16

lesbarkeitsindex %>% 
  lm(flesch_ease_de ~ news_name, data = .) %>% 
  tidy() %>% 
  # filter(term != "(Intercept)") %>% 
  mutate(term = str_replace(term, "news_name", ""),
         term = str_replace(term, "(Intercept)", "faz_cor")) %>% 
  arrange(estimate)

## # A tibble: 6 x 5
##   term      estimate std.error statistic   p.value
##   <chr>        <dbl>     <dbl>     <dbl>     <dbl>
## 1 focus_c     -0.615     2.34     -0.263 7.93e-  1
## 2 spiegel      2.79      0.274    10.2   3.46e- 24
## 3 welt_co      4.20      0.286    14.7   3.53e- 48
## 4 stern_g     11.3       0.486    23.2   3.37e-115
## 5 romane      22.3       2.61      8.54  1.54e- 17
## 6 (faz_cor)   50.6       0.226   225.    0

library(effects)
lesbarkeitsindex %>% 
  lm(flesch_ease_de ~ news_name, data = .) -> mymodel  
plot(allEffects(mymodel))

16.10 Alle Texte im Vergleich

Die ausgewählten zwölf Romane haben einen deutlich höheren Lesbarkeitsindex als die Zeitungstexte. Woran liegt das: an der Wortlänge, der Silbenanzahl oder an der Satzlänge?

lesbarkeitsindex %>% 
  mutate(wordnum_utterance = (words/sentences),
         sylnum_utterance = (syllables/sentences)) %>% 
  lm(flesch_ease_de ~ news_name*wordnum_utterance + news_name*sylnum_utterance, data = .) %>% 
  tidy() %>% 
  mutate(term = str_replace(term, "news_name", "")) %>% 
  arrange(-estimate)

## # A tibble: 18 x 5
##    term                      estimate std.error statistic  p.value
##    <chr>                        <dbl>     <dbl>     <dbl>    <dbl>
##  1 (Intercept)                68.7       0.210    327.    0       
##  2 romane                     23.7       2.45       9.67  5.18e-22
##  3 stern_g                    10.2       0.539     18.9   4.70e-78
##  4 wordnum_utterance           5.49      0.0420   131.    0       
##  5 welt_co                     4.29      0.250     17.1   1.46e-64
##  6 spiegel                     1.99      0.284      7.02  2.48e-12
##  7 romane:sylnum_utterance     0.558     0.409      1.37  1.72e- 1
##  8 focus_c:wordnum_utterance   0.389     0.918      0.424 6.72e- 1
##  9 spiegel:wordnum_utterance   0.211     0.0561     3.76  1.71e- 4
## 10 welt_co:sylnum_utterance   -0.0184    0.0253    -0.728 4.67e- 1
## 11 focus_c:sylnum_utterance   -0.131     0.395     -0.333 7.39e- 1
## 12 spiegel:sylnum_utterance   -0.182     0.0261    -6.98  3.20e-12
## 13 stern_g:sylnum_utterance   -0.219     0.0563    -3.90  9.88e- 5
## 14 stern_g:wordnum_utterance  -0.220     0.114     -1.92  5.44e- 2
## 15 welt_co:wordnum_utterance  -0.227     0.0531    -4.28  1.88e- 5
## 16 romane:wordnum_utterance   -2.22      0.668     -3.33  8.75e- 4
## 17 focus_c                    -2.45      4.03      -0.607 5.44e- 1
## 18 sylnum_utterance           -3.39      0.0195  -174.    0

Nur statistisch signifikante Interaktionen:

lesbarkeitsindex %>% 
  mutate(wordnum_utterance = (words/sentences),
         sylnum_utterance = (syllables/sentences)) %>% 
  lm(flesch_ease_de ~ news_name*wordnum_utterance + news_name*sylnum_utterance, data = .) %>% 
  tidy() %>% 
  mutate(term = str_replace(term, "news_name", "")) %>% 
  mutate(pval = case_when(
    p.value < 0.05 ~ "significant", 
    TRUE ~ "---")) %>% 
  mutate(pval = ifelse(term == "(Intercept)", "xxx", pval)) %>% 
  filter(pval == "significant" | pval == "xxx") %>% 
  filter(str_detect(term, ":")) %>% 
  arrange(-estimate)

## # A tibble: 5 x 6
##   term                      estimate std.error statistic  p.value pval       
##   <chr>                        <dbl>     <dbl>     <dbl>    <dbl> <chr>      
## 1 spiegel:wordnum_utterance    0.211    0.0561      3.76 1.71e- 4 significant
## 2 spiegel:sylnum_utterance    -0.182    0.0261     -6.98 3.20e-12 significant
## 3 stern_g:sylnum_utterance    -0.219    0.0563     -3.90 9.88e- 5 significant
## 4 welt_co:wordnum_utterance   -0.227    0.0531     -4.28 1.88e- 5 significant
## 5 romane:wordnum_utterance    -2.22     0.668      -3.33 8.75e- 4 significant

In den Romanen sind die Wörter im Durchschnitt kürzer als in den Zeitungstexten (Spiegel …). “Tidy”-Version:

lesbarkeitsindex %>% 
  group_by(news_name) %>% 
  summarise(syl_per_wrd = mean(syllables/words),
            sd_syl_per_wrd = sd(syllables/words))

## # A tibble: 6 x 3
##   news_name syl_per_wrd sd_syl_per_wrd
##   <fct>           <dbl>          <dbl>
## 1 faz_cor          1.91         0.143 
## 2 focus_c          1.93         0.0888
## 3 romane           1.47         0.0719
## 4 spiegel          1.89         0.116 
## 5 stern_g          1.75         0.109 
## 6 welt_co          1.86         0.135

Die Anzahl der Silben pro Äußerung in den Romanen ist vergleichbar mit der in Zeitungstexten (z.B. Spiegel).

lesbarkeitsindex %>% 
  group_by(news_name) %>% 
  summarise(syl_per_utt = mean(syllables/sentences),
            sd_syl_per_utt = sd(syllables/sentences))

## # A tibble: 6 x 3
##   news_name syl_per_utt sd_syl_per_utt
##   <fct>           <dbl>          <dbl>
## 1 faz_cor          33.8           8.61
## 2 focus_c          33.3           5.88
## 3 romane           31.0           8.88
## 4 spiegel          30.6           5.91
## 5 stern_g          27.9           5.89
## 6 welt_co          30.4           8.74

Die Romane haben durchschnittlich mehr Wörter pro Äußerung.

lesbarkeitsindex %>% 
  group_by(news_name) %>% 
  summarise(wrds_per_utt = mean(words/sentences),
            sd_wrds_per_utt = sd(words/sentences))

## # A tibble: 6 x 3
##   news_name wrds_per_utt sd_wrds_per_utt
##   <fct>            <dbl>           <dbl>
## 1 faz_cor           17.6            3.99
## 2 focus_c           17.2            2.53
## 3 romane            20.9            5.43
## 4 spiegel           16.2            2.75
## 5 stern_g           15.9            2.93
## 6 welt_co           16.2            4.37

lesbarkeit = lesbarkeitsindex %>% 
  mutate(functiontype = case_when(
    news_name == "romane" ~ "literatur",
    news_name != "romane" ~ "zeitung",
    TRUE ~ "other"
  )) %>% 
  mutate(syl_per_wrd = (syllables/words),
         wordnum_utterance = (words/sentences),
         sylnum_utterance = (syllables/sentences))

lesbarkeit %>% 
  slice_sample(n = 30) %>% 
  select(-text) %>% 
  rmarkdown::paged_table()

Die Romane haben kürzere Wörter als die Zeitungstexte (d.h. weniger Silben).

# set contrast back to default ("contr.treatment")
contrasts(lesbarkeitsindex$news_name) <- NULL
levels(lesbarkeitsindex$news_name)

## [1] "faz_cor" "focus_c" "romane"  "spiegel" "stern_g" "welt_co"

contrasts(lesbarkeitsindex$news_name) <- contr.treatment(6, base = 3) # base = romane !
contrasts(lesbarkeitsindex$news_name) # take a look

##         1 2 4 5 6
## faz_cor 1 0 0 0 0
## focus_c 0 1 0 0 0
## romane  0 0 0 0 0
## spiegel 0 0 1 0 0
## stern_g 0 0 0 1 0
## welt_co 0 0 0 0 1

lesbarkeit %>% 
  lm(syl_per_wrd ~ news_name, data = .) %>% 
  summary()

## 
## Call:
## lm(formula = syl_per_wrd ~ news_name, data = .)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.73696 -0.07736  0.00306  0.07656  0.56661 
## 
## Coefficients:
##                   Estimate Std. Error t value Pr(>|t|)    
## (Intercept)       1.910836   0.003187 599.592  < 2e-16 ***
## news_namefocus_c  0.016906   0.033068   0.511    0.609    
## news_nameromane  -0.438972   0.036937 -11.884  < 2e-16 ***
## news_namespiegel -0.023832   0.003878  -6.145 8.39e-10 ***
## news_namestern_g -0.163793   0.006862 -23.869  < 2e-16 ***
## news_namewelt_co -0.048874   0.004045 -12.081  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1275 on 8004 degrees of freedom
## Multiple R-squared:  0.08559,    Adjusted R-squared:  0.08502 
## F-statistic: 149.8 on 5 and 8004 DF,  p-value: < 2.2e-16

Die Romane haben durchschnittlich mehr Wörter pro Äußerung.

contrasts(lesbarkeitsindex$news_name) <- NULL
levels(lesbarkeitsindex$news_name)

## [1] "faz_cor" "focus_c" "romane"  "spiegel" "stern_g" "welt_co"

contrasts(lesbarkeitsindex$news_name) <- contr.treatment(6, base = 3) # base = romane !
contrasts(lesbarkeitsindex$news_name) # take a look

##         1 2 4 5 6
## faz_cor 1 0 0 0 0
## focus_c 0 1 0 0 0
## romane  0 0 0 0 0
## spiegel 0 0 1 0 0
## stern_g 0 0 0 1 0
## welt_co 0 0 0 0 1

lesbarkeit %>% 
  lm(wordnum_utterance ~ news_name, data = .) %>% 
  summary()

## 
## Call:
## lm(formula = wordnum_utterance ~ news_name, data = .)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -10.245  -2.098  -0.345   1.811  66.755 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      17.58859    0.09039 194.575  < 2e-16 ***
## news_namefocus_c -0.37430    0.93796  -0.399  0.68986    
## news_nameromane   3.35050    1.04770   3.198  0.00139 ** 
## news_namespiegel -1.39927    0.11001 -12.720  < 2e-16 ***
## news_namestern_g -1.67816    0.19464  -8.622  < 2e-16 ***
## news_namewelt_co -1.34374    0.11475 -11.710  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.616 on 8004 degrees of freedom
## Multiple R-squared:  0.02589,    Adjusted R-squared:  0.02528 
## F-statistic: 42.55 on 5 and 8004 DF,  p-value: < 2.2e-16

Noch deutlicher sichtbar in der Gegenüberstellung (Literatur vs. Zeitung):

lesbarkeit %>% 
  lm(wordnum_utterance ~ functiontype, data = .) %>% 
  summary()

## 
## Call:
## lm(formula = wordnum_utterance ~ functiontype, data = .)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -10.474  -2.239  -0.258   1.602  66.526 
## 
## Coefficients:
##                     Estimate Std. Error t value Pr(>|t|)    
## (Intercept)           20.939      1.056  19.826  < 2e-16 ***
## functiontypezeitung   -4.465      1.057  -4.225 2.42e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.659 on 8008 degrees of freedom
## Multiple R-squared:  0.002224,   Adjusted R-squared:  0.002099 
## F-statistic: 17.85 on 1 and 8008 DF,  p-value: 2.42e-05

Längere Wörter (mehr Silben pro Wort) in Zeitungen als in Romanen.

lesbarkeit %>% 
  lm(syl_per_wrd ~ functiontype, data = .) %>% 
  summary()

## 
## Call:
## lm(formula = syl_per_wrd ~ functiontype, data = .)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.75095 -0.08350  0.00680  0.08442  0.55262 
## 
## Coefficients:
##                     Estimate Std. Error t value Pr(>|t|)    
## (Intercept)          1.47186    0.03821   38.52   <2e-16 ***
## functiontypezeitung  0.40409    0.03824   10.57   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1324 on 8008 degrees of freedom
## Multiple R-squared:  0.01376,    Adjusted R-squared:  0.01363 
## F-statistic: 111.7 on 1 and 8008 DF,  p-value: < 2.2e-16

Aber die Anzahl der Silben pro Äußerung in den Romanen und Zeitungstexten unterscheidet sich nicht wesentlich (p = 0,979).

lesbarkeit %>% 
  lm(sylnum_utterance ~ functiontype, data = .) %>% 
  summary()

## 
## Call:
## lm(formula = sylnum_utterance ~ functiontype, data = .)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -24.274  -4.649  -0.522   3.946 125.976 
## 
## Coefficients:
##                     Estimate Std. Error t value Pr(>|t|)    
## (Intercept)         30.96610    2.20905  14.018   <2e-16 ***
## functiontypezeitung  0.05815    2.21071   0.026    0.979    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 7.652 on 8008 degrees of freedom
## Multiple R-squared:  8.64e-08,   Adjusted R-squared:  -0.0001248 
## F-statistic: 0.0006919 on 1 and 8008 DF,  p-value: 0.979

16.11 Flesch-Kincade Grade Level (USA, GB)

https://paldhous.github.io/NICAR/2019/r-text-analysis.html

The code below uses the quanteda functions ntoken, nsentence and nsyllable to count the words, sentences, and syllables in each addresss. Then it uses those values to calculate the Flesch-Kincaid reading grade level, a widely used measure of linguistic complexity.

sou = read_csv("data/sou.csv")

# word, sentence, and syllable counts, plus reading scores
sou = sou %>%
  mutate(syllables = nsyllable(text),
         sentences = nsentence(text),
         words = ntoken(text, remove_punct = TRUE),
         fk_grade = 0.39*(words/sentences) + 11.8*(syllables/words) - 15.59) %>%
  arrange(date)

The following chart shows how the reading grade level of State of the Union addresses has declined over the years. The points on the chart are colored by party, and scaled by the length of the address in words.

# color palette for parties
party_pal <- c("#1482EE","#228B22","#E9967A","#686868","#FF3300","#EEC900")

# reading score chart
ggplot(sou, aes(x = date, y = fk_grade, color = party, size = words)) +
  geom_point(alpha = 0.5) +
  geom_smooth(se = FALSE, color = "black", method = "lm", size = 0.5, linetype = "dotted") +
  scale_size_area(max_size = 10, guide = "none") +
  scale_color_manual(values = party_pal, name = "", breaks = c("Democratic","Republican","Whig","Democratic-Republican","Federalist","None")) +
  scale_y_continuous(limits = c(4,27), breaks = c(5,10,15,20,25)) +
  theme_minimal(base_size = 18) +
  xlab("") +
  ylab("Reading level") +
  guides(col = guide_legend(ncol = 2, override.aes = list(size = 4))) +
  theme(legend.position = c(0.4,0.22),
        legend.text = element_text(color="#909090", size = 16),
        panel.grid.minor = element_blank())

library(plotly)

# color palette for parties
party_pal <- c("#1482EE","#228B22","#E9967A","#686868","#FF3300","#EEC900")

# reading score chart
u <- ggplot(sou, aes(x = date, y = fk_grade, color = party, size = words)) +
  geom_point(alpha = 0.5) +
  geom_smooth(se = FALSE, color = "black", method = "lm", size = 0.5, linetype = "dotted") +
  scale_size_area(max_size = 10, guide = "none") +
  scale_color_manual(values = party_pal, name = "", breaks = c("Democratic","Republican","Whig","Democratic-Republican","Federalist","None")) +
  scale_y_continuous(limits = c(4,27), breaks = c(5,10,15,20,25)) +
  theme_minimal(base_size = 18) +
  xlab("") +
  ylab("Reading level") +
  guides(col = guide_legend(ncol = 2, override.aes = list(size = 4))) +
  theme(legend.position = c(0.4,0.22),
        legend.text = element_text(color="#909090", size = 16),
        panel.grid.minor = element_blank())

ggplotly(u, height = 500, width = 1000)

16.12 Wiener Sachtextformel

https://de.wikipedia.org/wiki/Lesbarkeitsindex

Die Wiener Sachtextformel dient zur Berechnung der Lesbarkeit deutschsprachiger Texte. Sie gibt an, für welche Schulstufe ein Sachtext geeignet ist. Die Skala beginnt bei Schulstufe 4 und endet bei 15, wobei ab der Stufe 12 eher von Schwierigkeitsstufen als von Schulstufen gesprochen werden sollte. Ein Wert von 4 steht demnach für sehr leichten Text, dagegen bezeichnet 15 einen sehr schwierigen Text.

Die Formel wurde aufgestellt von Richard Bamberger und Erich Vanecek.

MS ist der Prozentanteil der Wörter mit drei oder mehr Silben, SL ist die mittlere Satzlänge (Anzahl Wörter), IW ist der Prozentanteil der Wörter mit mehr als sechs Buchstaben, ES ist der Prozentanteil der einsilbigen Wörter.

Die erste Wiener Sachtextformel WSTF1 = 0.1935 * MS + 0.1672 * SL + 0.1297 * IW - 0.0327 * ES - 0.875 Die zweite Wiener Sachtextformel WSTF2 = 0.2007 * MS + 0.1682 * SL + 0.1373 * IW - 2.7 Die dritte Wiener Sachtextformel WSTF3 = 0.2963 * MS + 0.1905 * SL - 1.114 Die vierte Wiener Sachtextformel („im Hinblick auf die Jahrgangsstufe“) WSTF4 = 0.2744 * MS + 0.2656 * SL - 1.69

# Das Beispiel mit den Entchen liefert mit der ersten WSTF einen Index von 3.8:
satz="Alle meine Entchen schwimmen auf dem See, Köpfchen unters Wasser, Schwänzchen in die Höh."
WSTF1 = 0.1935 * 0 + 0.1672 * 14 + 0.1297 * 29 - 0.0327 * 43 - 0.875

In unserem Korpus:

lesbarkeitsindex %>% 
  filter(news_name == "faz_cor") %>% 
  add_count(news_name) %>% 
  unnest_tokens(word, text) %>% 
  mutate(ms = ifelse(nsyllable(word) > 2, 1, 0), # Wort mit mehr als 2 Silben
         iw = ifelse(nchar(word) > 5, 1, 0), # Wort mit mehr als 5 Buchstaben
         es = ifelse(nsyllable(word) < 2, 1, 0)) %>% # Wort mit einer Silbe
  drop_na() %>% 
  group_by(news_name) %>% 
  summarise(MS = sum(100*ms/(words*n)), # MS: Prozentanteil der Wörter mit 3 oder mehr Silben
            SL = mean(words/sentences), # SL: mittlere Satzlänge (Anzahl Wörter)
            IW = sum(100*iw/(words*n)), # IW: Prozentanteil der Wörter mit mehr als 6 Buchstaben
            ES = sum(100*es/(words*n))) %>% # ES: Prozentanteil der einsilbigen Wörter
  mutate(WSTF1 = 0.1935 * MS + 0.1672 * SL + 0.1297 * IW - 0.0327 * ES - 0.875,
         WSTF2 = 0.2007 * MS + 0.1682 * SL + 0.1373 * IW - 2.7, 
         WSTF3 = 0.2963 * MS + 0.1905 * SL - 1.114, 
         WSTF4 = 0.2744 * MS + 0.2656 * SL - 1.69)

## # A tibble: 1 x 9
##   news_name    MS    SL    IW    ES WSTF1 WSTF2 WSTF3 WSTF4
##   <fct>     <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 faz_cor    25.4  17.8  43.8  47.1  11.1  11.4  9.80  10.0

lesbarkeitsindex %>% 
  filter(news_name == "spiegel") %>% 
  add_count(news_name) %>% 
  unnest_tokens(word, text) %>% 
  mutate(ms = ifelse(nsyllable(word) > 2, 1, 0), # Wort mit mehr als 2 Silben
         iw = ifelse(nchar(word) > 5, 1, 0), # Wort mit mehr als 5 Buchstaben
         es = ifelse(nsyllable(word) < 2, 1, 0)) %>% # Wort mit einer Silbe
  drop_na() %>% 
  group_by(news_name) %>% 
  summarise(MS = sum(100*ms/(words*n)), # MS: Prozentanteil der Wörter mit 3 oder mehr Silben
            SL = mean(words/sentences), # SL: mittlere Satzlänge (Anzahl Wörter)
            IW = sum(100*iw/(words*n)), # IW: Prozentanteil der Wörter mit mehr als 6 Buchstaben
            ES = sum(100*es/(words*n))) %>% # ES: Prozentanteil der einsilbigen Wörter
  mutate(WSTF1 = 0.1935 * MS + 0.1672 * SL + 0.1297 * IW - 0.0327 * ES - 0.875,
         WSTF2 = 0.2007 * MS + 0.1682 * SL + 0.1373 * IW - 2.7, 
         WSTF3 = 0.2963 * MS + 0.1905 * SL - 1.114, 
         WSTF4 = 0.2744 * MS + 0.2656 * SL - 1.69)

## # A tibble: 1 x 9
##   news_name    MS    SL    IW    ES WSTF1 WSTF2 WSTF3 WSTF4
##   <fct>     <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 spiegel    24.8  16.3  44.2  47.3  10.8  11.1  9.33  9.43

lesbarkeitsindex %>% 
  filter(news_name == "welt_co") %>% 
  add_count(news_name) %>% 
  unnest_tokens(word, text) %>% 
  mutate(ms = ifelse(nsyllable(word) > 2, 1, 0), # Wort mit mehr als 2 Silben
         iw = ifelse(nchar(word) > 5, 1, 0), # Wort mit mehr als 5 Buchstaben
         es = ifelse(nsyllable(word) < 2, 1, 0)) %>% # Wort mit einer Silbe
  drop_na() %>% 
  group_by(news_name) %>% 
  summarise(MS = sum(100*ms/(words*n)), # MS: Prozentanteil der Wörter mit 3 oder mehr Silben
            SL = mean(words/sentences), # SL: mittlere Satzlänge (Anzahl Wörter)
            IW = sum(100*iw/(words*n)), # IW: Prozentanteil der Wörter mit mehr als 6 Buchstaben
            ES = sum(100*es/(words*n))) %>% # ES: Prozentanteil der einsilbigen Wörter
  mutate(WSTF1 = 0.1935 * MS + 0.1672 * SL + 0.1297 * IW - 0.0327 * ES - 0.875,
         WSTF2 = 0.2007 * MS + 0.1682 * SL + 0.1373 * IW - 2.7, 
         WSTF3 = 0.2963 * MS + 0.1905 * SL - 1.114, 
         WSTF4 = 0.2744 * MS + 0.2656 * SL - 1.69)

## # A tibble: 1 x 9
##   news_name    MS    SL    IW    ES WSTF1 WSTF2 WSTF3 WSTF4
##   <fct>     <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 welt_co    24.0  16.4  43.1  48.6  10.5  10.8  9.11  9.24

lesbarkeitsindex %>% 
  filter(news_name == "stern_g") %>% 
  add_count(news_name) %>% 
  unnest_tokens(word, text) %>% 
  mutate(ms = ifelse(nsyllable(word) > 2, 1, 0), # Wort mit mehr als 2 Silben
         iw = ifelse(nchar(word) > 5, 1, 0), # Wort mit mehr als 5 Buchstaben
         es = ifelse(nsyllable(word) < 2, 1, 0)) %>% # Wort mit einer Silbe
  drop_na() %>% 
  group_by(news_name) %>% 
  summarise(MS = sum(100*ms/(words*n)), # MS: Prozentanteil der Wörter mit 3 oder mehr Silben
            SL = mean(words/sentences), # SL: mittlere Satzlänge (Anzahl Wörter)
            IW = sum(100*iw/(words*n)), # IW: Prozentanteil der Wörter mit mehr als 6 Buchstaben
            ES = sum(100*es/(words*n))) %>% # ES: Prozentanteil der einsilbigen Wörter
  mutate(WSTF1 = 0.1935 * MS + 0.1672 * SL + 0.1297 * IW - 0.0327 * ES - 0.875,
         WSTF2 = 0.2007 * MS + 0.1682 * SL + 0.1373 * IW - 2.7, 
         WSTF3 = 0.2963 * MS + 0.1905 * SL - 1.114, 
         WSTF4 = 0.2744 * MS + 0.2656 * SL - 1.69)

## # A tibble: 1 x 9
##   news_name    MS    SL    IW    ES WSTF1 WSTF2 WSTF3 WSTF4
##   <fct>     <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 stern_g    20.3  16.0  39.8  49.1  9.28  9.53  7.95  8.13

lesbarkeitsindex %>% 
  filter(news_name == "focus_c") %>% 
  add_count(news_name) %>% 
  unnest_tokens(word, text) %>% 
  mutate(ms = ifelse(nsyllable(word) > 2, 1, 0), # Wort mit mehr als 2 Silben
         iw = ifelse(nchar(word) > 5, 1, 0), # Wort mit mehr als 5 Buchstaben
         es = ifelse(nsyllable(word) < 2, 1, 0)) %>% # Wort mit einer Silbe
  drop_na() %>% 
  group_by(news_name) %>% 
  summarise(MS = sum(100*ms/(words*n)), # MS: Prozentanteil der Wörter mit 3 oder mehr Silben
            SL = mean(words/sentences), # SL: mittlere Satzlänge (Anzahl Wörter)
            IW = sum(100*iw/(words*n)), # IW: Prozentanteil der Wörter mit mehr als 6 Buchstaben
            ES = sum(100*es/(words*n))) %>% # ES: Prozentanteil der einsilbigen Wörter
  mutate(WSTF1 = 0.1935 * MS + 0.1672 * SL + 0.1297 * IW - 0.0327 * ES - 0.875,
         WSTF2 = 0.2007 * MS + 0.1682 * SL + 0.1373 * IW - 2.7, 
         WSTF3 = 0.2963 * MS + 0.1905 * SL - 1.114, 
         WSTF4 = 0.2744 * MS + 0.2656 * SL - 1.69)

## # A tibble: 1 x 9
##   news_name    MS    SL    IW    ES WSTF1 WSTF2 WSTF3 WSTF4
##   <fct>     <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 focus_c    26.2  16.9  45.2  46.0  11.4  11.6  9.86  9.98

lesbarkeitsindex %>% 
  filter(news_name == "romane") %>% 
  add_count(news_name) %>% 
  unnest_tokens(word, text) %>% 
  mutate(ms = ifelse(nsyllable(word) > 2, 1, 0), # Wort mit mehr als 2 Silben
         iw = ifelse(nchar(word) > 5, 1, 0), # Wort mit mehr als 5 Buchstaben
         es = ifelse(nsyllable(word) < 2, 1, 0)) %>% # Wort mit einer Silbe
  drop_na() %>% 
  group_by(news_name) %>% 
  summarise(MS = sum(100*ms/(words*n)), # MS: Prozentanteil der Wörter mit 3 oder mehr Silben
            SL = mean(words/sentences), # SL: mittlere Satzlänge (Anzahl Wörter)
            IW = sum(100*iw/(words*n)), # IW: Prozentanteil der Wörter mit mehr als 6 Buchstaben
            ES = sum(100*es/(words*n))) %>% # ES: Prozentanteil der einsilbigen Wörter
  mutate(WSTF1 = 0.1935 * MS + 0.1672 * SL + 0.1297 * IW - 0.0327 * ES - 0.875,
         WSTF2 = 0.2007 * MS + 0.1682 * SL + 0.1373 * IW - 2.7, 
         WSTF3 = 0.2963 * MS + 0.1905 * SL - 1.114, 
         WSTF4 = 0.2744 * MS + 0.2656 * SL - 1.69)

## # A tibble: 1 x 9
##   news_name    MS    SL    IW    ES WSTF1 WSTF2 WSTF3 WSTF4
##   <fct>     <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 romane     13.3  19.0  31.1  51.9  7.21  7.44  6.45  7.01

wstf1_idx = lesbarkeitsindex_romane %>% 
  unnest_tokens(word, text) %>% 
  mutate(ms = ifelse(nsyllable(word) > 2, 1, 0),
         iw = ifelse(nchar(word) > 5, 1, 0),
         es = ifelse(nsyllable(word) < 2, 1, 0)) %>% 
  drop_na() %>% 
  group_by(book_name) %>% 
  summarise(MS = sum(100*ms/words),
            SL = mean(words/sentences),
            IW = sum(100*iw/words),
            ES = sum(100*es/words))

wstf1_idx %>% rmarkdown::paged_table()

lesbarkeitsindex_romane %>% 
  # filter(str_detect(book_name, "Der Prozess")) %>%
  unnest_tokens(word, text) %>% 
  mutate(ms = ifelse(nsyllable(word) > 2, 1, 0),
         iw = ifelse(nchar(word) > 5, 1, 0),
         es = ifelse(nsyllable(word) < 2, 1, 0)) %>% 
  drop_na() %>% 
  group_by(book_name) %>% 
  summarise(MS = sum(100*ms/words),
            SL = mean(words/sentences),
            IW = sum(100*iw/words),
            ES = sum(100*es/words)) %>% 
  mutate(WSTF1 = 0.1935 * MS + 0.1672 * SL + 0.1297 * IW - 0.0327 * ES - 0.875,
         WSTF2 = 0.2007 * MS + 0.1682 * SL + 0.1373 * IW - 2.7, 
         WSTF3 = 0.2963 * MS + 0.1905 * SL - 1.114, 
         WSTF4 = 0.2744 * MS + 0.2656 * SL - 1.69) %>% 
  rmarkdown::paged_table()