---
title: "Numerical Summaries"
---

## Summarizing data in R 1/2

-   Have seen `summary` (5-number summary of each column). But what if
    we want:
    -   a summary or two of just one column
    -   a count of observations in each category of a categorical
        variable
    -   summaries by group
    -   a different summary of all columns (eg. SD)
-   To do this, meet pipe operator `%>%`. This takes input data frame,
    does something to it, and outputs result. (Learn: `Ctrl-Shift-M`.)

## Summarizing data in R 2/2

-   Output from a pipe can be used as input to something else, so can
    have a sequence of pipes.
-   Summaries include: `mean`, `median`, `min`, `max`, `sd`, `IQR`,
    `quantile` (for obtaining quartiles or any percentile), `n` (for
    counting observations).
-   Use our Australian athletes data again.

## Packages for this section

```{r numsum-R-1}
library(tidyverse)
```

```{r numsum-R-2, echo=F, message=F}
my_url <- url("http://ritsokiguess.site/datafiles/ais.txt")
athletes <- read_tsv(my_url)
```

```{r}
summary(athletes)
```

## Summarizing one column

-   Mean height:

```{r numsum-R-3}
athletes %>% summarize(m=mean(Ht))
```

or to get mean and SD of BMI:

```{r numsum-R-4}
athletes %>% summarize(m = mean(BMI), s = sd(BMI)) -> d
d
```

This doesn't work:

```{r}
#| error: true
mean(BMI)
```

## Quartiles

-   `quantile` calculates percentiles ("fractiles"), so we want the 25th
    and 75th percentiles:

```{r numsum-R-5}
athletes %>% summarize( Q1=quantile(Wt, 0.25),
                        Q3=quantile(Wt, 0.75))
```

## Creating new columns

-   These weights are in kilograms. Maybe we want to summarize the
    weights in pounds.
-   Convert kg to lb by multiplying by 2.2.
-   Create new column and summarize that:

```{r numsum-R-6}
athletes %>% mutate(wt_lb=Wt*2.2) %>%
  summarize(Q1_lb=quantile(wt_lb, 0.25),
            Q3_lb=quantile(wt_lb, 0.75)) 

```

## Counting how many

for example, number of athletes in each sport:

```{r numsum-R-7}
athletes %>% count(Sport)
```

## Counting how many, variation 2:

Another way (which will make sense in a moment):

```{r numsum-R-8}
athletes %>% group_by(Sport) %>%
  summarize(count=n())
```

## Summaries by group

-   Might want separate summaries for each "group", eg. mean and SD of
    height for males and females. Strategy is `group_by` (to define the
    groups) and then `summarize`:

```{r numsum-R-9}
athletes %>% group_by(Sex) %>% 
  summarize(mean_Ht = mean(Ht), sd_Ht = sd(Ht))
```

## Count plus stats

-   If you want number of observations per group plus some stats, you
    need to go the `n()` way:

```{r}
athletes %>% group_by(Sex) %>%
summarize(n = n(), mean_Ht = mean(Ht), sd_Ht = sd(Ht))
```

-   This explains second variation on counting within group: "within
    each sport/Sex, how many athletes were there?"

## Summarizing several columns

-   Standard deviation of each (numeric) column:

```{r numsum-R-10}
athletes %>% summarize(across(where(is.numeric), \(x) sd(x))) 
```

-   Median and IQR of all columns whose name starts with H:

```{r numsum-R-11}
athletes %>% summarize(across(starts_with("H"),
                       list(med = \(x) median(x), 
                            iqr = \(x) IQR(x))))
```

## Same thing by group

```{r numsum-R-post-15}
athletes %>% 
  group_by(Sex) %>% 
  summarize(across(starts_with("H"), 
                   list(med = \(h) median(h), 
                        iqr = \(h) IQR(h))))
```

```{r}
athletes %>% 
  group_by(Sex) %>% 
  summarize(across(ends_with("C"), 
                   list(med = \(h) median(h), 
                        iqr = \(h) IQR(h))))
```