Review for PSQF 6243

This serves as a non-exhaustive review for the course. These are elements that I assume you have knowledge of prior to starting the course.

• Variable vs constant attributes
• Types of variables (ie., nominal, ordinal, integer, ratio)
• Descriptive Statistics (eg., mean, median, standard deviation, variance, percentiles)
• Higher order moments (eg., skewness and kurtosis)
• Exploring/summarizing univariate distributions (eg., histogram or density figure)
• What is a statistical model? Why do we use them?
• Population vs Sample

Examples

Mario Kart 64 world record data:

# load some libraries
library(tidyverse)

## ── Attaching packages ─────────────────────────────────────── tidyverse 1.3.2 ──
## ✔ ggplot2 3.3.6      ✔ purrr   0.3.4 
## ✔ tibble  3.1.8      ✔ dplyr   1.0.10
## ✔ tidyr   1.2.1      ✔ stringr 1.4.1 
## ✔ readr   2.1.2      ✔ forcats 0.5.2 
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag()    masks stats::lag()

library(ggformula)

## Loading required package: ggstance
## 
## Attaching package: 'ggstance'
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## The following objects are masked from 'package:ggplot2':
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##     geom_errorbarh, GeomErrorbarh
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## Loading required package: scales
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## Attaching package: 'scales'
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## The following object is masked from 'package:purrr':
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##     discard
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## The following object is masked from 'package:readr':
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##     col_factor
## 
## Loading required package: ggridges
## 
## New to ggformula?  Try the tutorials: 
## 	learnr::run_tutorial("introduction", package = "ggformula")
## 	learnr::run_tutorial("refining", package = "ggformula")

library(lubridate)

## 
## Attaching package: 'lubridate'
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## The following objects are masked from 'package:base':
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##     date, intersect, setdiff, union

library(mosaic)

## Registered S3 method overwritten by 'mosaic':
##   method                           from   
##   fortify.SpatialPolygonsDataFrame ggplot2
## 
## The 'mosaic' package masks several functions from core packages in order to add 
## additional features.  The original behavior of these functions should not be affected by this.
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## Attaching package: 'mosaic'
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## The following object is masked from 'package:Matrix':
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##     mean
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##     rescale
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##     count, do, tally
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##     binom.test, cor, cor.test, cov, fivenum, IQR, median, prop.test,
##     quantile, sd, t.test, var
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## The following objects are masked from 'package:base':
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##     max, mean, min, prod, range, sample, sum

library(e1071)

theme_set(theme_bw(base_size = 18))

# load in some data
mariokart <- readr::read_csv('https://raw.githubusercontent.com/rfordatascience/tidytuesday/master/data/2021/2021-05-25/records.csv') %>%
    mutate(year = year(date),
           month = month(date),
           day = month(date))

## Rows: 2334 Columns: 9
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr  (6): track, type, shortcut, player, system_played, time_period
## dbl  (2): time, record_duration
## date (1): date
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

head(mariokart)

## # A tibble: 6 × 12
##   track      type  short…¹ player syste…² date       time_…³  time recor…⁴  year
##   <chr>      <chr> <chr>   <chr>  <chr>   <date>     <chr>   <dbl>   <dbl> <dbl>
## 1 Luigi Rac… Thre… No      Salam  NTSC    1997-02-15 2M 12.…  133.       1  1997
## 2 Luigi Rac… Thre… No      Booth  NTSC    1997-02-16 2M 9.9…  130.       0  1997
## 3 Luigi Rac… Thre… No      Salam  NTSC    1997-02-16 2M 8.9…  129.      12  1997
## 4 Luigi Rac… Thre… No      Salam  NTSC    1997-02-28 2M 6.9…  127.       7  1997
## 5 Luigi Rac… Thre… No      Gregg… NTSC    1997-03-07 2M 4.5…  125.      54  1997
## 6 Luigi Rac… Thre… No      Rocky… NTSC    1997-04-30 2M 2.8…  123.       0  1997
## # … with 2 more variables: month <dbl>, day <dbl>, and abbreviated variable
## #   names ¹​shortcut, ²​system_played, ³​time_period, ⁴​record_duration

# univariate distribution of time
gf_histogram(~ time, data = mariokart, bins = 30) %>% 
   gf_labs(x = "Time (in seconds)")

gf_density(~ time, data = mariokart) %>% 
   gf_labs(x = "Time (in seconds)")

df_stats(~ time, data = mariokart, mean, median, sd, skewness, kurtosis, quantile(probs = c(0.1, 0.5, 0.9)))

##   response     mean median      sd skewness kurtosis   10%   50%     90%
## 1     time 90.62383  86.19 66.6721 1.771732 3.844745 31.31 86.19 171.961

Bivariate Association

cor(time ~ record_duration, data = mariokart)

## [1] -0.06736739

gf_point(time ~ record_duration, data = mariokart) %>%
  gf_labs(x = "How long the record was held",
          y = "Time (in seconds)")

Questions

1. What is problematic about the analyses above? Why?
2. What could be done to improve the analyses above?