A Very Incomplete Survey of Basic Statistical Tests in R

class: center, middle, inverse, title-slide

.title[
# A Very Incomplete Survey of Basic Statistical Tests in R
]
.author[
### EDP 613
]

---

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# Packages needed and a Note about Icons

Please load up the following packages (or install and then load them as needed)

```r
library(tidyverse)
library(car)
```

```
## Loading required package: carData
```

```
## 
## Attaching package: 'car'
```

```
## The following object is masked from 'package:dplyr':
## 
##     recode
```

```
## The following object is masked from 'package:purrr':
## 
##     some
```

```r
library(foreign)
library(lme4)
```

```
## Loading required package: Matrix
```

```
## 
## Attaching package: 'Matrix'
```

```
## The following objects are masked from 'package:tidyr':
## 
##     expand, pack, unpack
```

```r
library(MASS)
```

```
## 
## Attaching package: 'MASS'
```

```
## The following object is masked from 'package:patchwork':
## 
##     area
```

```
## The following object is masked from 'package:dplyr':
## 
##     select
```

```r
library(CCA)
```

```
## Loading required package: fda
```

```
## Loading required package: splines
```

```
## Loading required package: fds
```

```
## Loading required package: rainbow
```

```
## Loading required package: pcaPP
```

```
## Loading required package: RCurl
```

```
## 
## Attaching package: 'RCurl'
```

```
## The following object is masked from 'package:tidyr':
## 
##     complete
```

```
## Loading required package: deSolve
```

```
## 
## Attaching package: 'fda'
```

```
## The following object is masked from 'package:graphics':
## 
##     matplot
```

```
## Loading required package: fields
```

```
## Loading required package: spam
```

```
## Spam version 2.9-1 (2022-08-07) is loaded.
## Type 'help( Spam)' or 'demo( spam)' for a short introduction 
## and overview of this package.
## Help for individual functions is also obtained by adding the
## suffix '.spam' to the function name, e.g. 'help( chol.spam)'.
```

```
## 
## Attaching package: 'spam'
```

```
## The following object is masked from 'package:Matrix':
## 
##     det
```

```
## The following objects are masked from 'package:base':
## 
##     backsolve, forwardsolve
```

```
## 
## Try help(fields) to get started.
```

```r
library(psych)
```

```
## 
## Attaching package: 'psych'
```

```
## The following object is masked from 'package:fields':
## 
##     describe
```

```
## The following object is masked from 'package:car':
## 
##     logit
```

```
## The following objects are masked from 'package:scales':
## 
##     alpha, rescale
```

```
## The following object is masked from 'package:fontawesome':
## 
##     fa
```

```
## The following objects are masked from 'package:ggplot2':
## 
##     %+%, alpha
```
<br>
You may come across the following icons. The table below lists what each means.

<table class="table" style="width: auto !important; margin-left: auto; margin-right: auto;">
 <thead>
  <tr>
   <th style="text-align:center;"> Icon </th>
   <th style="text-align:left;"> Description </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:center;width: 10em; "> <svg aria-hidden="true" role="img" viewbox="0 0 512 512" style="height:1em;width:1em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:#4682b4;overflow:visible;position:relative;"><path d="M52.51 440.6l171.5-142.9V214.3L52.51 71.41C31.88 54.28 0 68.66 0 96.03v319.9C0 443.3 31.88 457.7 52.51 440.6zM308.5 440.6l192-159.1c15.25-12.87 15.25-36.37 0-49.24l-192-159.1c-20.63-17.12-52.51-2.749-52.51 24.62v319.9C256 443.3 287.9 457.7 308.5 440.6z"></path></svg> </td>
   <td style="text-align:left;width: 40em; "> Indicates that an example continues on the following slide. </td>
  </tr>
  <tr>
   <td style="text-align:center;width: 10em; "> <svg aria-hidden="true" role="img" viewbox="0 0 384 512" style="height:1em;width:0.75em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:#ff6347;overflow:visible;position:relative;"><path d="M384 128v255.1c0 35.35-28.65 64-64 64H64c-35.35 0-64-28.65-64-64V128c0-35.35 28.65-64 64-64H320C355.3 64 384 92.65 384 128z"></path></svg> </td>
   <td style="text-align:left;width: 40em; "> Indicates that a section using common syntax has ended. </td>
  </tr>
  <tr>
   <td style="text-align:center;width: 10em; "> <svg aria-hidden="true" role="img" viewbox="0 0 640 512" style="height:1em;width:1.25em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:#5cb85c;overflow:visible;position:relative;"><path d="M172.5 131.1C228.1 75.51 320.5 75.51 376.1 131.1C426.1 181.1 433.5 260.8 392.4 318.3L391.3 319.9C381 334.2 361 337.6 346.7 327.3C332.3 317 328.9 297 339.2 282.7L340.3 281.1C363.2 249 359.6 205.1 331.7 177.2C300.3 145.8 249.2 145.8 217.7 177.2L105.5 289.5C73.99 320.1 73.99 372 105.5 403.5C133.3 431.4 177.3 435 209.3 412.1L210.9 410.1C225.3 400.7 245.3 404 255.5 418.4C265.8 432.8 262.5 452.8 248.1 463.1L246.5 464.2C188.1 505.3 110.2 498.7 60.21 448.8C3.741 392.3 3.741 300.7 60.21 244.3L172.5 131.1zM467.5 380C411 436.5 319.5 436.5 263 380C213 330 206.5 251.2 247.6 193.7L248.7 192.1C258.1 177.8 278.1 174.4 293.3 184.7C307.7 194.1 311.1 214.1 300.8 229.3L299.7 230.9C276.8 262.1 280.4 306.9 308.3 334.8C339.7 366.2 390.8 366.2 422.3 334.8L534.5 222.5C566 191 566 139.1 534.5 108.5C506.7 80.63 462.7 76.99 430.7 99.9L429.1 101C414.7 111.3 394.7 107.1 384.5 93.58C374.2 79.2 377.5 59.21 391.9 48.94L393.5 47.82C451 6.731 529.8 13.25 579.8 63.24C636.3 119.7 636.3 211.3 579.8 267.7L467.5 380z"></path></svg> </td>
   <td style="text-align:left;width: 40em; "> Indicates that there is an active hyperlink on the slide. </td>
  </tr>
  <tr>
   <td style="text-align:center;width: 10em; "> <svg aria-hidden="true" role="img" viewbox="0 0 384 512" style="height:1em;width:0.75em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:#faffbd;overflow:visible;position:relative;"><path d="M384 48V512l-192-112L0 512V48C0 21.5 21.5 0 48 0h288C362.5 0 384 21.5 384 48z"></path></svg> </td>
   <td style="text-align:left;width: 40em; "> Indicates that a section covering a concept has ended. </td>
  </tr>
</tbody>
</table>

---

# A Side Note About R

Its a big deal that you have come this far with `R` especially since it was rough at times. It may not be apparent, but developing coding skills like the ones in this course have benefits, not least of all in simply understanding the structure of a given data set. There are too many examples of students and even professionals who run an analysis on data without considering the data itself. `R` and other syntax-based software packages like it to their credit make you explore your data whether it be through checks or frustration.

While proprietary softwares such as SPSS, SAS, Minitab, etc. may be easier to learn, `R` and others like Python are free, open, and widley used. Picking on SPSS, as of this writing users pay for different tiers depending on needs (such as machine learning, methods to deal with missing data, etc.) they want to use. s

With that said, learning `R` is a lifelong process and assisting student learning and growth should never be confined to a single course so please FEEL FREE to contact me if you have questions regarding R (or Python if you go there) at any time. Again, I will always make time for students.

---

# Purpose

This walk-through will provide you with information on how to perform a number of statistical tests using R. Some of these will look familiar while others you will be exposed to in future statistics courses if that is your path. In either case, hopefully these will be helpful if for no other reason than to provide a check or confirmation of results.

---

# Decisions Decisions Decisions

When deciding which test is appropriate to use, it is important to consider the type of variables that you have. Please load in the following data sets (and look at them by using `View()` or `head()`

```r
some_ed_data <- 
  read_csv("some_ed_data.csv")
```

```r
some_exercise_data <- 
  read_csv("some_exercise_data.csv")
```

```r
some_survey_data <- 
  read_csv("some_survey_data.csv")
```

---

# Source

A majority of the information included in this survey of approached was scraped from the web using `R` via the [UCLA Institute for Digital Research & Education](https://stats.idre.ucla.edu/r/whatstat/what-statistical-analysis-should-i-usestatistical-analyses-using-r/) site using the `xml2` package. They also fully support SAS, SPSS (for those of you moving on to EDP 614), Stata, and Mplus.

---

# An Incomplete Table of Approaches (1/4)

<table class="table" style="width: auto !important; margin-left: auto; margin-right: auto;">
 <thead>
  <tr>
   <th style="text-align:center;"> Number of Dependent Variables </th>
   <th style="text-align:left;"> Number and Type of Independent Variables </th>
   <th style="text-align:left;"> Type of Dependent Variables </th>
   <th style="text-align:left;"> Test(s) </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:left;"> 0 IVs (1 population) </td>
   <td style="text-align:left;"> interval &amp; normal </td>
   <td style="text-align:left;"> one-sample t-test </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:left;"> 0 IVs (1 population) </td>
   <td style="text-align:left;"> ordinal or interval </td>
   <td style="text-align:left;"> one-sample median </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:left;"> 0 IVs (1 population) </td>
   <td style="text-align:left;"> categorical (2 categories) </td>
   <td style="text-align:left;"> binomial test </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:left;"> 0 IVs (1 population) </td>
   <td style="text-align:left;"> categorical </td>
   <td style="text-align:left;"> Chi-square goodness-of-fit </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:left;"> 1 IV with 2 levels (independent groups) </td>
   <td style="text-align:left;"> interval &amp; normal </td>
   <td style="text-align:left;"> 2 independent sample t-test </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:left;"> 1 IV with 2 levels (independent groups) </td>
   <td style="text-align:left;"> ordinal or interval </td>
   <td style="text-align:left;"> Wilcoxon-Mann Whitney test </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:left;"> 1 IV with 2 levels (independent groups) </td>
   <td style="text-align:left;"> categorical </td>
   <td style="text-align:left;"> Chi-square test </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:left;"> 1 IV with 2 levels (independent groups) </td>
   <td style="text-align:left;"> categorical </td>
   <td style="text-align:left;"> Fisher’s exact test </td>
  </tr>
</tbody>
</table>

---

# An Incomplete Table of Approaches (2/4)

<table class="table" style="width: auto !important; margin-left: auto; margin-right: auto;">
 <thead>
  <tr>
   <th style="text-align:center;"> Number of Dependent Variables </th>
   <th style="text-align:left;"> Number and Type of Independent Variables </th>
   <th style="text-align:left;"> Type of Dependent Variables </th>
   <th style="text-align:left;"> Test(s) </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:left;"> 1 IV with 2 or more levels (independent groups) </td>
   <td style="text-align:left;"> interval &amp; normal </td>
   <td style="text-align:left;"> one-way ANOVA </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:left;"> 1 IV with 2 or more levels (independent groups) </td>
   <td style="text-align:left;"> ordinal or interval </td>
   <td style="text-align:left;"> Kruskal Wallis </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:left;"> 1 IV with 2 or more levels (independent groups) </td>
   <td style="text-align:left;"> categorical </td>
   <td style="text-align:left;"> Chi-square test </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:left;"> 1 IV with 2 levels (dependent/matched groups) </td>
   <td style="text-align:left;"> interval &amp; normal </td>
   <td style="text-align:left;"> paired t-test </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:left;"> 1 IV with 2 levels (dependent/matched groups) </td>
   <td style="text-align:left;"> ordinal or interval </td>
   <td style="text-align:left;"> Wilcoxon signed ranks test </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:left;"> 1 IV with 2 levels (dependent/matched groups) </td>
   <td style="text-align:left;"> categorical </td>
   <td style="text-align:left;"> McNemar </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:left;"> 1 IV with 2 or more levels (dependent/matched groups) </td>
   <td style="text-align:left;"> interval &amp; normal </td>
   <td style="text-align:left;"> one-way repeated measures ANOVA </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:left;"> 1 IV with 2 or more levels (dependent/matched groups) </td>
   <td style="text-align:left;"> ordinal or interval </td>
   <td style="text-align:left;"> Friedman test </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:left;"> 1 IV with 2 or more levels (dependent/matched groups) </td>
   <td style="text-align:left;"> categorical (2 categories) </td>
   <td style="text-align:left;"> repeated measures logistic regression </td>
  </tr>
</tbody>
</table>

---

# An Incomplete Table of Approaches (3/4)

<table class="table" style="width: auto !important; margin-left: auto; margin-right: auto;">
 <thead>
  <tr>
   <th style="text-align:center;"> Number of Dependent Variables </th>
   <th style="text-align:left;"> Number and Type of Independent Variables </th>
   <th style="text-align:left;"> Type of Dependent Variables </th>
   <th style="text-align:left;"> Test(s) </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:left;"> 2 or more IVs (independent groups) </td>
   <td style="text-align:left;"> interval &amp; normal </td>
   <td style="text-align:left;"> factorial ANOVA </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:left;"> 2 or more IVs (independent groups) </td>
   <td style="text-align:left;"> ordinal or interval </td>
   <td style="text-align:left;"> ordered logistic regression </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:left;"> 2 or more IVs (independent groups) </td>
   <td style="text-align:left;"> categorical (2 categories) </td>
   <td style="text-align:left;"> factorial logistic regression </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:left;"> 1 interval IV </td>
   <td style="text-align:left;"> interval &amp; normal </td>
   <td style="text-align:left;"> correlation </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:left;"> 1 interval IV </td>
   <td style="text-align:left;"> interval &amp; normal </td>
   <td style="text-align:left;"> simple linear regression </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:left;"> 1 interval IV </td>
   <td style="text-align:left;"> ordinal or interval </td>
   <td style="text-align:left;"> non-parametric correlation </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:left;"> 1 interval IV </td>
   <td style="text-align:left;"> categorical </td>
   <td style="text-align:left;"> simple logistic regression </td>
  </tr>
</tbody>
</table>

---

# An Incomplete Table of Approaches (4/4)

<table class="table" style="width: auto !important; margin-left: auto; margin-right: auto;">
 <thead>
  <tr>
   <th style="text-align:center;"> Number of Dependent Variables </th>
   <th style="text-align:left;"> Number and Type of Independent Variables </th>
   <th style="text-align:left;"> Type of Dependent Variables </th>
   <th style="text-align:left;"> Test(s) </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:left;"> 1 or more interval IVs and/or 1 or more categorical IVs </td>
   <td style="text-align:left;"> interval &amp; normal </td>
   <td style="text-align:left;"> multiple regression </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:left;"> 1 or more interval IVs and/or 1 or more categorical IVs </td>
   <td style="text-align:left;"> interval &amp; normal </td>
   <td style="text-align:left;"> analysis of covariance </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:left;"> 1 or more interval IVs and/or 1 or more categorical IVs </td>
   <td style="text-align:left;"> categorical </td>
   <td style="text-align:left;"> multiple logistic regression </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:left;"> 1 or more interval IVs and/or 1 or more categorical IVs </td>
   <td style="text-align:left;"> categorical </td>
   <td style="text-align:left;"> discriminant analysis </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 2+ </td>
   <td style="text-align:left;"> 1 IV with 2 or more levels (independent groups) </td>
   <td style="text-align:left;"> interval &amp; normal </td>
   <td style="text-align:left;"> one-way MANOVA </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 2+ </td>
   <td style="text-align:left;"> 2+ </td>
   <td style="text-align:left;"> interval &amp; normal </td>
   <td style="text-align:left;"> multivariate multiple linear regression </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 2+ </td>
   <td style="text-align:left;"> 0 </td>
   <td style="text-align:left;"> interval &amp; normal </td>
   <td style="text-align:left;"> factor analysis </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 2 sets of 2+ </td>
   <td style="text-align:left;"> 0 </td>
   <td style="text-align:left;"> interval &amp; normal </td>
   <td style="text-align:left;"> canonical correlation </td>
  </tr>
</tbody>
</table>

---

# Tests

---

## ANCOVA (Analysis of Covariance)

```r
summary(aov(some_ed_data$write ~ 
              some_ed_data$prog + 
              some_ed_data$read))
```

```
##                    Df Sum Sq Mean Sq F value  Pr(>F)    
## some_ed_data$prog   1    586     586    10.2 0.00164 ** 
## some_ed_data$read   1   5965    5965   103.7 < 2e-16 ***
## Residuals         197  11327      57                    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
```

---

## Binomial Test

```r
prop.test(sum(some_ed_data$female), 
          length(some_ed_data$female), 
          p = 0.5)
```

```
## 
## 	1-sample proportions test with continuity correction
## 
## data:  sum(some_ed_data$female) out of length(some_ed_data$female), null probability 0.5
## X-squared = 1.445, df = 1, p-value = 0.2293
## alternative hypothesis: true p is not equal to 0.5
## 95 percent confidence interval:
##  0.4733037 0.6149394
## sample estimates:
##     p 
## 0.545
```

---

## Canonical Correlation

```r
cc(cbind(some_ed_data$read, 
         some_ed_data$write), 
   cbind(some_ed_data$math, 
         some_ed_data$science))
```

```
## $cor
## [1] 0.7728409 0.0234784
## 
## $names
## $names$Xnames
## NULL
## 
## $names$Ynames
## NULL
## 
## $names$ind.names
## NULL
## 
## 
## $xcoef
##             [,1]       [,2]
## [1,] -0.06326131 -0.1037908
## [2,] -0.04924918  0.1219084
## 
## $ycoef
##             [,1]       [,2]
## [1,] -0.06698268  0.1201425
## [2,] -0.04824063 -0.1208860
## 
## $scores
## $scores$xscores
##               [,1]         [,2]
##   [1,] -0.26358835 -0.589561062
##   [2,] -1.30420707 -0.877901269
##   [3,]  1.49454321 -1.556539586
##   [4,] -0.24916276 -2.187572699
##   [5,]  0.36902478  0.448346869
##   [6,]  0.55880872  0.759719249
##   [7,] -0.16550344  0.990333008
##   [8,]  1.48691695  1.066177022
##   [9,] -0.88940214 -0.602764022
##  [10,] -0.41133590 -0.223835983
##  [11,] -0.15787718 -1.632383600
##  [12,] -0.90382773  0.995247615
##  [13,] -1.66976282 -1.274946875
##  [14,] -0.61554542  1.062803275
##  [15,]  0.24930149  1.265470254
##  [16,]  0.83307890  0.601575756
##  [17,]  0.36902478  0.448346869
##  [18,] -0.50983426  0.019980737
##  [19,] -1.59970217 -0.146451110
##  [20,]  0.50317366 -1.966788153
##  [21,] -0.49540867 -1.578030900
##  [22,] -1.18489724  0.128686136
##  [23,]  0.77023105 -1.325925827
##  [24,] -0.45337228 -0.900933442
##  [25,]  1.39563138  0.510987923
##  [26,]  1.93015961 -0.030998216
##  [27,] -1.40991823  0.164921269
##  [28,]  0.12277887  1.057888668
##  [29,]  1.24829729 -0.946997788
##  [30,]  0.44671169 -1.045873974
##  [31,]  1.71956420 -1.592774720
##  [32,] -1.46555329 -2.561586132
##  [33,] -1.50841660  0.408737989
##  [34,]  1.22707237 -0.373691122
##  [35,] -0.29202606  0.782751422
##  [36,] -1.09361167  0.683875235
##  [37,] -1.05796116 -1.487443067
##  [38,] -1.26217068 -0.200803810
##  [39,]  1.40325764 -2.111728685
##  [40,]  1.90934814 -1.281402340
##  [41,]  0.61527070 -0.161194929
##  [42,] -0.48181000  0.471379042
##  [43,] -0.04578015  0.173209623
##  [44,]  1.22707237 -0.373691122
##  [45,] -1.40991823  0.164921269
##  [46,] -0.48181000  0.471379042
##  [47,]  0.77023105 -1.325925827
##  [48,] -1.11442313 -0.566528889
##  [49,]  0.02428050  1.301705388
##  [50,] -0.36208671 -0.345744343
##  [51,] -0.45378574  0.922777348
##  [52,]  1.81084977 -1.037585621
##  [53,]  0.95280219 -0.215547629
##  [54,] -0.98790051 -0.358947303
##  [55,] -1.76826119 -1.031130155
##  [56,]  1.51535467 -0.306135462
##  [57,]  1.74037567 -0.342370595
##  [58,]  1.32557073 -0.617507842
##  [59,] -0.88940214 -0.602764022
##  [60,]  0.45351102 -0.021169003
##  [61,]  0.47473595 -0.594475669
##  [62,] -0.12346705  1.667430467
##  [63,]  0.95280219 -0.215547629
##  [64,]  2.12715634 -0.518631655
##  [65,]  0.67173268 -1.082109108
##  [66,]  1.10054974 -0.581272708
##  [67,] -0.55187065 -0.657116722
##  [68,]  1.00926417 -1.136461807
##  [69,] -0.19991357 -2.309481059
##  [70,]  1.11497533 -2.179284345
##  [71,]  0.95280219 -0.215547629
##  [72,] -0.55187065 -0.657116722
##  [73,] -2.01450711 -0.421588356
##  [74,] -1.30420707 -0.877901269
##  [75,]  0.20767856 -1.235337994
##  [76,]  0.96001499 -1.014553448
##  [77,] -0.58030837  0.715195762
##  [78,] -1.30420707 -0.877901269
##  [79,]  2.16919273  0.158465804
##  [80,]  0.91076580 -0.892645088
##  [81,] -0.98790051 -0.358947303
##  [82,]  1.21264678  1.224320515
##  [83,] -1.30420707 -0.877901269
##  [84,] -1.28339561  0.372502856
##  [85,]  0.40467530 -1.722971433
##  [86,] -0.62955755  0.837104122
##  [87,]  0.59445924 -1.411599054
##  [88,]  1.33916940  1.431902101
##  [89,]  1.21347370 -2.423101065
##  [90,]  0.01068183 -0.747704555
##  [91,] -0.43977362  1.148476501
##  [92,] -0.49540867 -1.578030900
##  [93,] -1.45195462 -0.512176189
##  [94,]  1.26910876  0.303406337
##  [95,]  0.95280219 -0.215547629
##  [96,] -0.31325099  1.356058087
##  [97,] -1.78948611 -0.457823489
##  [98,] -1.28339561  0.372502856
##  [99,]  1.58541532  0.822360302
## [100,] -1.18489724  0.128686136
## [101,] -1.35345626 -0.755992909
## [102,]  0.02428050  1.301705388
## [103,]  0.66451988 -0.283103289
## [104,] -0.64315622 -1.212305821
## [105,] -0.29202606  0.782751422
## [106,] -0.23556409 -0.138162756
## [107,] -0.94586412  0.318150156
## [108,]  1.96539666 -0.378605729
## [109,]  0.27052642  0.692163589
## [110,] -1.78948611 -0.457823489
## [111,] -0.26358835 -0.589561062
## [112,]  0.65730709  0.515902529
## [113,] -1.11442313 -0.566528889
## [114,] -1.59970217 -0.146451110
## [115,] -1.71901201 -1.153038515
## [116,]  1.45889269  0.614778716
## [117,]  0.52357167  1.107326761
## [118,] -2.01450711 -0.421588356
## [119,] -0.19352770  0.538934702
## [120,]  0.99483858  0.461549830
## [121,] -0.55187065 -0.657116722
## [122,]  0.17924085  0.136974490
## [123,]  0.17924085  0.136974490
## [124,]  0.66451988 -0.283103289
## [125,] -0.12346705  1.667430467
## [126,] -0.38331164  0.227562323
## [127,]  0.72098186 -1.204017467
## [128,]  0.82586610  1.400581574
## [129,]  0.32698840 -0.228750589
## [130,]  2.02865797 -0.274814935
## [131,] -0.60833263  0.263797456
## [132,] -0.90382773  0.995247615
## [133,] -1.45195462 -0.512176189
## [134,]  0.58683298  1.211117555
## [135,] -0.86137788 -0.151365716
## [136,] -2.00729431 -1.220594175
## [137,]  0.02428050  1.301705388
## [138,]  0.43228610  0.552137663
## [139,]  1.41685631 -0.062318743
## [140,]  0.20046577 -0.436332176
## [141,]  1.86648483  1.688921781
## [142,]  0.58683298  1.211117555
## [143,]  0.86151662 -0.770736728
## [144,]  0.12277887  1.057888668
## [145,] -0.29202606  0.782751422
## [146,]  0.36902478  0.448346869
## [147,] -0.31325099  1.356058087
## [148,]  0.55880872  0.759719249
## [149,]  0.91076580 -0.892645088
## [150,]  0.34779986  1.021653535
## [151,]  1.10776254 -1.380278527
## [152,] -0.86817722 -1.176070688
## [153,]  0.37582412  1.473051841
## [154,]  0.27052642  0.692163589
## [155,] -0.75608018  0.629522535
## [156,] -1.30420707 -0.877901269
## [157,] -0.09502933  0.295117983
## [158,]  0.43908543  1.576842634
## [159,]  1.32557073 -0.617507842
## [160,] -1.57167791  0.304947196
## [161,] -0.12346705  1.667430467
## [162,] -0.16508998 -0.833377782
## [163,] -0.07421787  1.545522107
## [164,] -0.75608018  0.629522535
## [165,] -0.29202606  0.782751422
## [166,]  0.95280219 -0.215547629
## [167,] -0.16550344  0.990333008
## [168,]  0.77661692  1.522489934
## [169,] -0.75608018  0.629522535
## [170,] -0.65758181  0.385705816
## [171,]  0.43908543  1.576842634
## [172,]  0.66451988 -0.283103289
## [173,]  1.47331828 -0.983232921
## [174,] -0.79811657 -0.047574923
## [175,]  0.70655627  0.393994170
## [176,] -1.03714969 -0.237038943
## [177,] -1.50841660  0.408737989
## [178,]  0.77661692  1.522489934
## [179,]  0.17924085  0.136974490
## [180,] -0.58752117  1.514201580
## [181,] -0.94586412  0.318150156
## [182,]  0.70655627  0.393994170
## [183,] -0.68601953  1.758018300
## [184,] -0.77730510  1.202829201
## [185,] -0.55949691  1.965599886
## [186,] -1.40991823  0.164921269
## [187,] -0.04578015  0.173209623
## [188,]  0.76301825 -0.526920009
## [189,] -1.13564806  0.006777776
## [190,]  0.47473595 -0.594475669
## [191,]  0.58683298  1.211117555
## [192,]  0.81865331  2.199587393
## [193,]  0.17924085  0.136974490
## [194,]  0.40384838  1.924450147
## [195,] -0.27121460  2.033155546
## [196,] -0.48181000  0.471379042
## [197,]  0.98082645  0.235850677
## [198,]  0.27815267 -1.930553019
## [199,] -0.62955755  0.837104122
## [200,] -1.28339561  0.372502856
## 
## $scores$yscores
##                [,1]        [,2]
##   [1,]  1.013980334 -0.81276184
##   [2,] -0.561661891 -1.30522812
##   [3,] -0.387441410 -0.58065576
##   [4,]  0.322640484 -0.81722302
##   [5,] -0.347186284  0.38420150
##   [6,] -0.427696537 -1.54551302
##   [7,]  0.657553868 -1.41793527
##   [8,]  1.131974678  0.63489582
##   [9,] -0.387441410 -0.58065576
##  [10,]  0.132448995  0.14614718
##  [11,]  0.054709777 -0.33665321
##  [12,] -0.427696537 -1.54551302
##  [13,] -1.670868810  1.09910797
##  [14,] -0.443667546  0.14242953
##  [15,]  1.182986345  2.20269592
##  [16,]  0.735293086 -0.93513488
##  [17,]  0.199431671  0.02600473
##  [18,] -0.789337471  0.14019895
##  [19,] -0.778580931  0.74314179
##  [20,] -0.347186284  0.38420150
##  [21,]  0.499304397 -3.83045019
##  [22,] -2.469446463  0.24993198
##  [23,]  0.360124575 -1.29927988
##  [24,] -0.733111335 -0.58288635
##  [25,]  1.131974678  0.63489582
##  [26,]  1.064992001  0.75503827
##  [27,] -1.335955426  0.49839571
##  [28,] -0.588389441 -0.22022841
##  [29,]  0.864043971  1.11546562
##  [30,]  0.092193868 -0.81871008
##  [31,] -0.057742495  1.10951738
##  [32,] -1.346711967 -0.10454714
##  [33,] -1.376210553 -0.46646155
##  [34,] -1.263758281 -1.91263214
##  [35,] -0.264232597 -1.42388351
##  [36,] -0.800094012 -0.46274390
##  [37,] -2.180002675  0.97524787
##  [38,] -1.711123937  0.13425071
##  [39,]  1.343679249  0.87741131
##  [40,]  1.466888062  0.03418356
##  [41,]  1.255183491 -0.20833193
##  [42,] -0.923302825  0.38048385
##  [43,] -0.443667546  0.14242953
##  [44,]  0.735293086 -0.93513488
##  [45,] -0.226748507 -1.90594038
##  [46,] -1.520932447 -0.82911949
##  [47,]  1.051464425 -1.29481870
##  [48,] -1.700367396  0.73719355
##  [49,] -0.749082344  1.10505620
##  [50,] -0.191707849  1.34980229
##  [51,] -0.808079517  0.38122738
##  [52,]  1.214928364 -1.17318919
##  [53,] -0.470395097  1.22742925
##  [54,]  0.092193868 -0.81871008
##  [55,] -2.190759215  0.37230502
##  [56,]  1.826085563  2.08627112
##  [57,]  1.622366497  0.99978435
##  [58,]  0.713780005 -2.14102057
##  [59,] -0.454424087 -0.46051331
##  [60,]  0.421892783  0.87146307
##  [61,]  0.215402681 -1.66193782
##  [62,] -1.386967094 -1.06940440
##  [63,]  1.775073896  0.51847102
##  [64,]  1.544627280  0.51698396
##  [65,]  0.941783188  1.59826602
##  [66,]  0.936241116 -1.29556223
##  [67,] -0.644615577  0.50285689
##  [68,]  0.853287430  0.51252278
##  [69,] -1.060039214 -0.82614537
##  [70,]  0.622840814  0.51103572
##  [71,]  1.064992001  0.75503827
##  [72,] -0.655372118 -0.10008596
##  [73,] -1.767350073  0.85733600
##  [74,] -1.427222220 -2.03426166
##  [75,]  0.148420004 -1.54179537
##  [76,]  0.976496243 -0.33070497
##  [77,]  0.046724273  0.50731807
##  [78,] -0.762609921 -0.94480077
##  [79,]  1.064992001  0.75503827
##  [80,]  0.384408693  1.35351994
##  [81,] -0.443667546  0.14242953
##  [82,] -0.532163305 -0.94331371
##  [83,] -1.912071967  0.49467806
##  [84,] -0.226748507 -1.90594038
##  [85,]  1.225684905 -0.57024634
##  [86,] -1.298471336  0.01633884
##  [87,]  0.054709777 -0.33665321
##  [88,]  1.389148845 -0.44861683
##  [89,]  1.708091219  0.63861347
##  [90,] -1.001042042 -0.10231655
##  [91,] -0.660586586  2.19079945
##  [92,] -0.438453078 -2.14845587
##  [93,] -1.654897801 -0.58883459
##  [94,]  0.421892783  0.87146307
##  [95,]  0.679066950 -0.21204958
##  [96,] -1.097523305 -0.34408851
##  [97,] -1.979054644  0.61482051
##  [98,] -2.056793862  0.13202012
##  [99,]  1.466888062  0.03418356
## [100,] -1.536903457  0.85882306
## [101,] -1.587915124 -0.70897704
## [102,] -0.907331815 -1.30745871
## [103,]  1.153487759  1.84078151
## [104,] -0.001516359  0.38643209
## [105,] -0.465180628 -1.06345616
## [106,] -0.419383429  2.79522935
## [107,] -0.872291157  1.94828395
## [108,]  0.888000485 -1.41644821
## [109,]  0.534345056 -0.57470752
## [110,] -1.392181562  1.22148101
## [111,]  0.405594171 -2.62530802
## [112,]  1.399905385  0.15432601
## [113,] -0.009501864  1.23040337
## [114,] -0.703612749 -0.22097194
## [115,] -0.443667546  0.14242953
## [116,]  1.523114198 -0.68890174
## [117,] -0.309702193 -0.09785537
## [118,] -0.923302825  0.38048385
## [119,] -1.057268178  0.62076875
## [120,]  1.466888062  0.03418356
## [121,]  0.266414348 -0.09413772
## [122,]  0.534345056 -0.57470752
## [123,]  0.596113264  1.59603543
## [124,]  0.228930258  0.38791915
## [125,]  1.373177835  1.23932572
## [126,] -0.521406764 -0.34037086
## [127,]  0.890771521  0.03046591
## [128,] -0.001516359  0.38643209
## [129,]  0.009240182  0.98937493
## [130,]  1.882311700  1.36318582
## [131,] -0.001516359  0.38643209
## [132,] -1.400167067  2.06545229
## [133,] -0.135481713  0.62671699
## [134,]  0.612084273 -0.09190713
## [135,]  0.622840814  0.51103572
## [136,] -1.223503154 -0.94777488
## [137,] -0.387441410 -0.58065576
## [138,]  0.220944753  1.23189042
## [139,]  1.791044905 -1.16947154
## [140,]  0.622840814  0.51103572
## [141,]  1.024736875 -0.20981899
## [142,]  0.266414348 -0.09413772
## [143,]  0.663095940  1.47589298
## [144,]  0.689823490  0.39089327
## [145,] -0.414168960  0.50434395
## [146,]  0.831774349 -0.69336292
## [147,]  0.628055282 -1.77984969
## [148,]  1.024736875 -0.20981899
## [149,]  1.016751370  0.63415229
## [150,]  1.440160512  1.11918327
## [151,]  1.121218137  0.03195297
## [152,] -0.856320148  0.26034140
## [153,]  0.936241116 -1.29556223
## [154,]  0.188675131 -0.57693811
## [155,] -0.521406764 -0.34037086
## [156,] -0.711598254  0.62299934
## [157,]  0.073451823 -0.57768164
## [158,]  0.344153566  0.38866268
## [159,]  1.188200814 -0.08818948
## [160,] -1.402938103  0.61853816
## [161,] -0.079255576 -0.09636831
## [162,]  0.218173717 -0.21502370
## [163,] -0.427696537 -1.54551302
## [164,] -1.737851487  1.21925042
## [165,]  0.159176545 -0.93885253
## [166,]  1.418647431 -0.08670242
## [167,] -0.465180628 -1.06345616
## [168,]  1.147945687 -1.05304674
## [169,] -0.845563607  0.86328424
## [170,]  0.054709777 -0.33665321
## [171,]  0.601327732 -0.69484998
## [172,]  1.147945687 -1.05304674
## [173,]  1.718847760  1.24155631
## [174,] -1.068024719  0.01782590
## [175,]  1.391919881  0.99829729
## [176,] -0.931288329  1.22445513
## [177,] -0.845563607  0.86328424
## [178,] -0.146238253  0.02377414
## [179,]  0.215402681 -1.66193782
## [180,] -0.692856208  0.38197091
## [181,]  0.333397025 -0.21428017
## [182,]  0.931026648  0.99532317
## [183,] -0.829592598 -0.82465831
## [184,] -0.068499036  0.50657454
## [185,] -1.577158583 -0.10603420
## [186,] -1.057268178  0.62076875
## [187,] -0.213220930  0.14391659
## [188,]  1.188200814 -0.08818948
## [189,] -0.376684870  0.02228708
## [190,] -0.079255576 -0.09636831
## [191,]  1.255183491 -0.20833193
## [192,]  0.802275763 -1.05527733
## [193,] -0.175736839 -0.33814027
## [194,]  1.574125866  0.87889837
## [195,] -0.403412420  1.10728679
## [196,]  0.518374046  1.11323503
## [197,]  1.745575310  0.15655660
## [198,] -0.443667546  0.14242953
## [199,] -0.655372118 -0.10008596
## [200,] -0.883047698  1.34534111
## 
## $scores$corr.X.xscores
##            [,1]      [,2]
## [1,] -0.9271970 -0.374574
## [2,] -0.8538903  0.520453
## 
## $scores$corr.Y.xscores
##            [,1]         [,2]
## [1,] -0.7177974  0.008701966
## [2,] -0.6750187 -0.011433002
## 
## $scores$corr.X.yscores
##            [,1]         [,2]
## [1,] -0.7165758 -0.008794398
## [2,] -0.6599214  0.012219404
## 
## $scores$corr.Y.yscores
##            [,1]       [,2]
## [1,] -0.9287778  0.3706371
## [2,] -0.8734252 -0.4869583
```

---

## Chi-square Test

```r
chisq.test(table(some_ed_data$female, 
                 some_ed_data$schtyp))
```

```
## 
## 	Pearson's Chi-squared test with Yates' continuity correction
## 
## data:  table(some_ed_data$female, some_ed_data$schtyp)
## X-squared = 0.00054009, df = 1, p-value = 0.9815
```

---

## Chi-square Goodness of Fit

```r
chisq.test(table(some_ed_data$race), 
           p = c(10, 10, 10, 70)/100)
```

```
## 
## 	Chi-squared test for given probabilities
## 
## data:  table(some_ed_data$race)
## X-squared = 5.0286, df = 3, p-value = 0.1697
```

---

## Correlation

```r
cor(some_ed_data$read, 
    some_ed_data$write)
```

```
## [1] 0.5967765
```

```r
cor.test(some_ed_data$read, 
         some_ed_data$write)
```

```
## 
## 	Pearson's product-moment correlation
## 
## data:  some_ed_data$read and some_ed_data$write
## t = 10.465, df = 198, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.4993831 0.6792753
## sample estimates:
##       cor 
## 0.5967765
```

---

## Discriminant Analysis

```r
lda(factor(some_ed_data$prog) ~ 
      some_ed_data$read + 
      some_ed_data$write + 
      some_ed_data$math, 
    data = some_ed_data)
```

```
## Call:
## lda(factor(some_ed_data$prog) ~ some_ed_data$read + some_ed_data$write + 
##     some_ed_data$math, data = some_ed_data)
## 
## Prior probabilities of groups:
##     1     2     3 
## 0.225 0.525 0.250 
## 
## Group means:
##   some_ed_data$read some_ed_data$write some_ed_data$math
## 1          49.75556           51.33333          50.02222
## 2          56.16190           56.25714          56.73333
## 3          46.20000           46.76000          46.42000
## 
## Coefficients of linear discriminants:
##                           LD1         LD2
## some_ed_data$read  0.02919876  0.04385321
## some_ed_data$write 0.03832289 -0.13698224
## some_ed_data$math  0.07034625  0.07931008
## 
## Proportion of trace:
##    LD1    LD2 
## 0.9874 0.0126
```

---

## Factor Analysis

```r
fa(r = cor(model.matrix(~read + write + math + science + socst - 1, 
                        data = some_ed_data)), 
   rotate = "none",
   fm = "pa", 2)
```

```
## maximum iteration exceeded
```

```
## Factor Analysis using method =  pa
## Call: fa(r = cor(model.matrix(~read + write + math + science + socst - 
##     1, data = some_ed_data)), nfactors = 2, rotate = "none", 
##     fm = "pa")
## Standardized loadings (pattern matrix) based upon correlation matrix
##          PA1   PA2   h2   u2 com
## read    0.81  0.06 0.66 0.34 1.0
## write   0.76  0.00 0.58 0.42 1.0
## math    0.80  0.17 0.67 0.33 1.1
## science 0.75  0.26 0.62 0.38 1.2
## socst   0.79 -0.48 0.85 0.15 1.6
## 
##                        PA1  PA2
## SS loadings           3.06 0.33
## Proportion Var        0.61 0.07
## Cumulative Var        0.61 0.68
## Proportion Explained  0.90 0.10
## Cumulative Proportion 0.90 1.00
## 
## Mean item complexity =  1.2
## Test of the hypothesis that 2 factors are sufficient.
## 
## The degrees of freedom for the null model are  10  and the objective function was  2.51
## The degrees of freedom for the model are 1  and the objective function was  0.01 
## 
## The root mean square of the residuals (RMSR) is  0.01 
## The df corrected root mean square of the residuals is  0.03 
## 
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy             
##                                                    PA1  PA2
## Correlation of (regression) scores with factors   0.95 0.79
## Multiple R square of scores with factors          0.91 0.62
## Minimum correlation of possible factor scores     0.82 0.23
```

---

## Factorial ANOVA (Analysis of Variance)

```r
anova(lm(write ~ female * ses, 
         data = some_ed_data))
```

```
## Analysis of Variance Table
## 
## Response: write
##             Df  Sum Sq Mean Sq F value    Pr(>F)    
## female       1  1176.2 1176.21 14.7212 0.0001680 ***
## ses          1  1042.3 1042.32 13.0454 0.0003862 ***
## female:ses   1     0.0    0.04  0.0005 0.9827570    
## Residuals  196 15660.3   79.90                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
```

---

## Factorial Logistic Regression

```r
summary(glm(female ~ prog * schtyp, 
            data = some_ed_data, 
            family = binomial))
```

```
## 
## Call:
## glm(formula = female ~ prog * schtyp, family = binomial, data = some_ed_data)
## 
## Deviance Residuals: 
##    Min      1Q  Median      3Q     Max  
## -1.698  -1.247   1.069   1.109   1.572  
## 
## Coefficients:
##             Estimate Std. Error z value Pr(>|z|)
## (Intercept)  -2.2765     1.8857  -1.207    0.227
## prog          1.2303     0.9398   1.309    0.191
## schtyp        2.2405     1.7017   1.317    0.188
## prog:schtyp  -1.1313     0.8622  -1.312    0.189
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 275.64  on 199  degrees of freedom
## Residual deviance: 273.65  on 196  degrees of freedom
## AIC: 281.65
## 
## Number of Fisher Scoring iterations: 4
```

---

## Friedman Test

```r
friedman.test(cbind(some_ed_data$read, 
                    some_ed_data$write, 
                    some_ed_data$math))
```

```
## 
## 	Friedman rank sum test
## 
## data:  cbind(some_ed_data$read, some_ed_data$write, some_ed_data$math)
## Friedman chi-squared = 0.64491, df = 2, p-value = 0.7244
```

---

## Kruskal Wallis Test

```r
kruskal.test(some_ed_data$write, 
             some_ed_data$prog)
```

```
## 
## 	Kruskal-Wallis rank sum test
## 
## data:  some_ed_data$write and some_ed_data$prog
## Kruskal-Wallis chi-squared = 34.045, df = 2, p-value = 4.047e-08
```

---

## McNemar Test

```r
# Some made up data in matrix form
made_up_matrixdata <- 
  matrix(c(150, 22, 21, 12), 2, 2)

mcnemar.test(made_up_matrixdata)
```

```
## 
## 	McNemar's Chi-squared test with continuity correction
## 
## data:  made_up_matrixdata
## McNemar's chi-squared = 0, df = 1, p-value = 1
```

---

## Multiple Regression

```r
lm(some_ed_data$write ~ 
     some_ed_data$female + 
     some_ed_data$read + 
     some_ed_data$math + 
     some_ed_data$science + 
     some_ed_data$socst)
```

```
## 
## Call:
## lm(formula = some_ed_data$write ~ some_ed_data$female + some_ed_data$read + 
##     some_ed_data$math + some_ed_data$science + some_ed_data$socst)
## 
## Coefficients:
##          (Intercept)   some_ed_data$female     some_ed_data$read  
##               6.1388                5.4925                0.1254  
##    some_ed_data$math  some_ed_data$science    some_ed_data$socst  
##               0.2381                0.2419                0.2293
```

---

## Multivariate Multiple Regression

```r
mmrlm <- 
  lm(cbind(write, read) ~ 
       female + math + science + socst, 
     data = some_ed_data)

summary(Anova(mmrlm))
```

```
## 
## Type II MANOVA Tests:
## 
## Sum of squares and products for error:
##          write     read
## write 7258.783 1091.057
## read  1091.057 8699.762
## 
## ------------------------------------------
##  
## Term: female 
## 
## Sum of squares and products for the hypothesis:
##           write       read
## write 1413.5284 -133.48461
## read  -133.4846   12.60544
## 
## Multivariate Tests: female
##                  Df test stat approx F num Df den Df     Pr(>F)    
## Pillai            1 0.1698853 19.85132      2    194 1.4335e-08 ***
## Wilks             1 0.8301147 19.85132      2    194 1.4335e-08 ***
## Hotelling-Lawley  1 0.2046528 19.85132      2    194 1.4335e-08 ***
## Roy               1 0.2046528 19.85132      2    194 1.4335e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------
##  
## Term: math 
## 
## Sum of squares and products for the hypothesis:
##          write      read
## write 714.8665  856.2825
## read  856.2825 1025.6735
## 
## Multivariate Tests: math
##                  Df test stat approx F num Df den Df     Pr(>F)    
## Pillai            1 0.1599321 18.46685      2    194 4.5551e-08 ***
## Wilks             1 0.8400679 18.46685      2    194 4.5551e-08 ***
## Hotelling-Lawley  1 0.1903800 18.46685      2    194 4.5551e-08 ***
## Roy               1 0.1903800 18.46685      2    194 4.5551e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------
##  
## Term: science 
## 
## Sum of squares and products for the hypothesis:
##          write     read
## write 857.8824 901.3191
## read  901.3191 946.9551
## 
## Multivariate Tests: science
##                  Df test stat approx F num Df den Df     Pr(>F)    
## Pillai            1 0.1664254 19.36631      2    194 2.1459e-08 ***
## Wilks             1 0.8335746 19.36631      2    194 2.1459e-08 ***
## Hotelling-Lawley  1 0.1996526 19.36631      2    194 2.1459e-08 ***
## Roy               1 0.1996526 19.36631      2    194 2.1459e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## ------------------------------------------
##  
## Term: socst 
## 
## Sum of squares and products for the hypothesis:
##          write     read
## write 1105.653 1277.393
## read  1277.393 1475.810
## 
## Multivariate Tests: socst
##                  Df test stat approx F num Df den Df     Pr(>F)    
## Pillai            1 0.2206710 27.46604      2    194 3.1399e-11 ***
## Wilks             1 0.7793290 27.46604      2    194 3.1399e-11 ***
## Hotelling-Lawley  1 0.2831551 27.46604      2    194 3.1399e-11 ***
## Roy               1 0.2831551 27.46604      2    194 3.1399e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
```

---

## Non-parametric Correlation

```r
cor.test(some_ed_data$read, 
         some_ed_data$write, 
         method = "spearman")
```

```
## Warning in cor.test.default(some_ed_data$read, some_ed_data$write, method =
## "spearman"): Cannot compute exact p-value with ties
```

```
## 
## 	Spearman's rank correlation rho
## 
## data:  some_ed_data$read and some_ed_data$write
## S = 510993, p-value < 2.2e-16
## alternative hypothesis: true rho is not equal to 0
## sample estimates:
##       rho 
## 0.6167455
```

---

## One Sample *t*-test

```r
t.test(some_ed_data$read, 
       mu = 50)
```

```
## 
## 	One Sample t-test
## 
## data:  some_ed_data$read
## t = 3.0759, df = 199, p-value = 0.002394
## alternative hypothesis: true mean is not equal to 50
## 95 percent confidence interval:
##  50.80035 53.65965
## sample estimates:
## mean of x 
##     52.23
```

---

## One-way Analysis of Variance (ANOVA)

```r
summary(aov(some_ed_data$read ~ 
              some_ed_data$prog))
```

```
##                    Df Sum Sq Mean Sq F value Pr(>F)  
## some_ed_data$prog   1    381   381.1   3.674 0.0567 .
## Residuals         198  20538   103.7                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
```

---

## One-way Multivariate Analysis of Variance (MANOVA)

```r
summary(manova(cbind(some_ed_data$read, 
                     some_ed_data$write, 
                     some_ed_data$math) ~ 
                 some_ed_data$prog))
```

```
##                    Df   Pillai approx F num Df den Df  Pr(>F)  
## some_ed_data$prog   1 0.035319    2.392      3    196 0.06984 .
## Residuals         198                                          
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
```

---

## One-way Repeated Measures Analysis of Variance (ANOVA)

```r
model <- 
  lm(gender ~ item_1 + item_2, 
     data = some_survey_data)

analysis <- 
  Anova(model, 
        idata = factor_surveydata, 
        idesign = ~s)

print(analysis)
```

```
## Anova Table (Type II tests)
## 
## Response: gender
##           Sum Sq Df F value Pr(>F)
## item_1    0.0601  1  0.2396 0.6307
## item_2    0.7268  1  2.8974 0.1069
## Residuals 4.2642 17
```

---

## Ordered Logistic Regression

```r
# Create ordered variable write3 as 
# a factor with levels 1, 2, and 3
some_ed_data$write3 <- 
  cut(some_ed_data$write, 
      c(0, 48, 57, 70),  
      right = TRUE, 
      labels = c(1,2,3))

table(some_ed_data$write3)
```

```
## 
##  1  2  3 
## 61 61 78
```

```r
# fit ordered logit model and store results 'some_write_data'
some_write_data <- 
  polr(write3 ~ 
         female + read + socst, data = some_ed_data, 
       Hess=TRUE)

summary(some_write_data)
```

```
## Call:
## polr(formula = write3 ~ female + read + socst, data = some_ed_data, 
##     Hess = TRUE)
## 
## Coefficients:
##          Value Std. Error t value
## female 1.28543    0.32445   3.962
## read   0.11772    0.02136   5.512
## socst  0.08019    0.01944   4.124
## 
## Intercepts:
##     Value   Std. Error t value
## 1|2  9.7037  1.1968     8.1080
## 2|3 11.8001  1.3041     9.0486
## 
## Residual Deviance: 312.5526 
## AIC: 322.5526
```

---

## Principal Components Analysis (PCA)

```r
princomp(formula = ~read + write + math + science + socst, 
         data = some_ed_data)
```

```
## Call:
## princomp(formula = ~read + write + math + science + socst, data = some_ed_data)
## 
## Standard deviations:
##    Comp.1    Comp.2    Comp.3    Comp.4    Comp.5 
## 18.252929  7.677044  6.213371  5.774331  5.429881 
## 
##  5  variables and  200 observations.
```

---

## Repeated Measures Logistic Regression

```r
glmer(highpulse ~ diet + (1 | id), 
      data = some_exercise_data, 
      family = binomial)
```

```
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: binomial  ( logit )
## Formula: highpulse ~ diet + (1 | id)
##    Data: some_exercise_data
##      AIC      BIC   logLik deviance df.resid 
## 105.4679 112.9674 -49.7340  99.4679       87 
## Random effects:
##  Groups Name        Std.Dev.
##  id     (Intercept) 1.821   
## Number of obs: 90, groups:  id, 30
## Fixed Effects:
## (Intercept)         diet  
##      -3.148        1.145
```

---

## Simple Linear Regression

```r
lm(some_ed_data$write ~ 
     some_ed_data$read)
```

```
## 
## Call:
## lm(formula = some_ed_data$write ~ some_ed_data$read)
## 
## Coefficients:
##       (Intercept)  some_ed_data$read  
##           23.9594             0.5517
```

---

## Simple Logistic Regression

```r
glm(some_ed_data$female ~ 
      some_ed_data$read, 
    family = binomial)
```

```
## 
## Call:  glm(formula = some_ed_data$female ~ some_ed_data$read, family = binomial)
## 
## Coefficients:
##       (Intercept)  some_ed_data$read  
##           0.72609           -0.01044  
## 
## Degrees of Freedom: 199 Total (i.e. Null);  198 Residual
## Null Deviance:	    275.6 
## Residual Deviance: 275.1 	AIC: 279.1
```

---

## Two Independent Samples *t*-test

```r
t.test(some_ed_data$read ~ 
         some_ed_data$female)
```

```
## 
## 	Welch Two Sample t-test
## 
## data:  some_ed_data$read by some_ed_data$female
## t = 0.74506, df = 188.46, p-value = 0.4572
## alternative hypothesis: true difference in means between group 0 and group 1 is not equal to 0
## 95 percent confidence interval:
##  -1.796263  3.976725
## sample estimates:
## mean in group 0 mean in group 1 
##        52.82418        51.73394
```

---

## Wilcoxon-Mann-Whitney Test

```r
wilcox.test(some_ed_data$read ~ 
              some_ed_data$female)
```

```
## 
## 	Wilcoxon rank sum test with continuity correction
## 
## data:  some_ed_data$read by some_ed_data$female
## W = 5300, p-value = 0.4029
## alternative hypothesis: true location shift is not equal to 0
```

---

## Wilcoxon Signed Rank Sum Test

```r
wilcox.test(some_ed_data$write, 
            some_ed_data$read, 
            paired = TRUE)
```

```
## 
## 	Wilcoxon signed rank test with continuity correction
## 
## data:  some_ed_data$write and some_ed_data$read
## V = 9261, p-value = 0.3666
## alternative hypothesis: true location shift is not equal to 0
```

---

# Other Approaches
There are so many other approaches that are for specific cases or use statistical approaches, but aren't [themselves statistics](https://www.nature.com/articles/nmeth.4642). With that said, the ones given in this overview are overkill for most of you and should cover any statistics you come across.

---

# Additional Things

---

## Reporting 
After running a statistical test successfully, it can be difficult to know how to report the results. The `report` package automatically produces reports of models and dataframes according to best practices guidelines. Click [here](https://easystats.github.io/report/) for more information.

---

## Visualizations
Interested in making incredible visuals? Check out [#tidytuesday](https://twitter.com/hashtag/tidytuesday) on Twitter. You do not need an account for access.

---

## Something useless
If you are a fan of the show Rick & Morty, consider downloading the most pointless package `mortyr` to do pointless statistics on pointless data. More about the package [here](https://github.com/mikejohnpage/mortyr).

---

## Thats it!