070-Fallstudie-Normierung.Rmd

# Fallstudie Normierung


```{r message=FALSE}
library(tidyverse)
library(DataExplorer)
library(easystats)
```



```{r include=FALSE}
library(knitr)   # für "kable", erstellt HTML-Tabellen
```


## Explorative Datenanalyse

```{r load-extra-web, message = FALSE}
data_url <- "https://raw.githubusercontent.com/sebastiansauer/modar/master/datasets/extra.csv"
extra <- read_csv(data_url)
```



```{r plot-distribs}
extra %>% 
  select(ends_with("_mean")) %>% 
  plot_histogram()
```


```{r}
extra %>% 
  select(extra_mean, n_facebook_friends, n_hangover, age, sex, time_conversation, sleep_week, sleep_wend) %>% 
  describe_distribution()
```


## Normwerte berechnen


### Hilfsfunktionen

Zwei Hilfskräfte (in Form von R-Funktionen) brauchen wir: Die erste Funktion berechnet Normwerte, s.[Infos here](https://de.wikipedia.org/wiki/Normwertskala):

```{r}
convert_to_norm_value <- 
  function(score, data_vec, mu = 0, sigma = 1) {
  numerator <- (score - mean(data_vec, na.rm = TRUE))
  out <-  (numerator / sd(data_vec)) * sigma + mu
  return(out)
}
```



Probieren wir es aus. Aber zuerst müssen wir die `NA` entfernen,
da das `convert_to_norm_value` nicht kann.

```{r}
extra_drop_na <- 
extra %>% 
  select(extra_mean) %>% 
  drop_na()
  
convert_to_norm_value(score = 3, data_vec = extra_drop_na$extra_mean)
```


Diese Funktion wenden wir für mehrere Normierungsarten an, im Rahmen einer zweiten Funktion:

```{r}
compute_all_norms <- function(x, min_score = 0, max_score = max(x), by = .5){
  
  x_ecdf <- ecdf(x)  # empircal cumulative distribution function - gives back function
  
  out <-
    tibble(
      score = seq(from = min_score, to = max_score, by = by),
      perc_rank = x_ecdf(score),
      z = map_dbl(score, ~ convert_to_norm_value(.x, data_vec = x)),
      stanine = map_dbl(score, ~ convert_to_norm_value(.x, data_vec = x, mu = 5, sigma = 2)),
      T = map_dbl(score, ~ convert_to_norm_value(.x, data_vec = x, mu = 50, sigma = 10)),
      perc_normal = map_dbl(z, pnorm)
    ) %>% 
    mutate(stanine = case_when(
      stanine > 9 ~ 9,
      stanine < 1 ~ 1,
      TRUE ~ stanine
    ))
  return(out)
}
```





### Normwerte berechnen


```{r norms-overall, results = "asis"}
extra %>% 
  select(ends_with("_mean")) %>% 
  drop_na() %>% 
  map(~ kable(compute_all_norms(., min_score = 1, max_score = 4, by = .1), 
                     digits = 2)) %>% 
  print()
```