11-pairedMeans.Rmd

# t TEST FOR THE DIFFERENCE IN 2 PAIRED MEANS

**Chapter Links**

* [Chapter 11 Slides (pdf)](http://tysonbarrett.com/EDUC-6600/Slides/u03_Ch11_paired.html#1)

* [Cancer Dataset - SPSS format](https://usu.box.com/s/9c92zof5whb76bphmzxn3vqx5702qgq6)


**Unit Assignment Links**

* Unit 3 Writen Part: [Skeleton - pdf](https://usu.box.com/s/vjcsotiqwu1mwnwgzbfyig6k451ymgow)

* Unit 3 R Part: [Directions - pdf](https://usu.box.com/s/ectr9zx8qfbbm59h0qcexjreje5r9aio) and [Skeleton - Rmd](https://usu.box.com/s/k3vzw6nuq5tw66bxeptcyzth38pj69f9)

* Unit 3 Reading to Summarize: [Article - pdf](https://usu.box.com/s/qmo57s03tbq02ks75p7eb5gad0ap05kg)

* Inho's Dataset: [Excel](https://usu.box.com/s/hyky7eb24l6vvzj2xboedhcx1xolrpw1)



```{r global_options, include=FALSE}
# set global chunk options...  
#  this changes the defaults so you don't have to repeat yourself
knitr::opts_chunk$set(comment     = NA,
                      cache       = TRUE,
                      echo        = TRUE, 
                      warning     = FALSE, 
                      message     = FALSE)
```



Required Packages 

```{r load_libraries}
library(tidyverse)    # Loads several very helpful 'tidy' packages
library(haven)        # Read in SPSS datasets
library(car)          # Companion for Applied Regression (and ANOVA)
```




Example: Cancer Experiment 

The `Cancer` dataset was introduced in [chapter 3][Example: Cancer Experiment].


```{r, include=FALSE}
cancer_raw <- haven::read_spss("data/cancer.sav")

cancer_clean <- cancer_raw %>% 
  dplyr::rename_all(tolower) %>% 
  dplyr::mutate(id = factor(id)) %>% 
  dplyr::mutate(trt = factor(trt,
                             labels = c("Placebo", 
                                        "Aloe Juice"))) %>% 
  dplyr::mutate(stage = factor(stage))
```




-------------------------------------------------------



## Restructure the Data and Run the Test

Before a paired t-test is ran, the dataset must be restructured from WIDE form (variables sitting side-by-side) to LONG form (variable values stacked on-top-of each other).

Notice for this dataset, there are $n = 23$ participants with complete data on the oral condition at weeks 2 and 6, since two out of the 25 do not have scores at the sixth week.


```{r}
# This dataset is in WIDE format: paired variables side-by-side
cancer_clean %>% 
  dplyr::filter(complete.cases(totalcw2, totalcw6))
```




The `tidyr::gather()` function requires the following FOUR options:

* **key** - A new variable name that will store the original variable names:  `key = new_group_var`

* **value** - A new variable name that will store the original variable values: `value = new_continuous_var`

* **variable list** - List the original variable names:  `orig_continous_var1, orig_continuous_var2`

* **na.rm** - Do not get ride of blank values (na.rm = remove the NA or blank values):  `na.rm = FALSE`


```{r}
# This dataset is in LONG format: total oral condiditon (at weeks 2 & 6) is stored in 1 variable, stacked
cancer_clean %>% 
  dplyr::filter(complete.cases(totalcw2, totalcw6)) %>% 
  tidyr::gather(key = time,
                value = totalc,
                totalcw2, totalcw6)
```


The `t.test()` function, needs at least THREE arguments:

* **formula** - The formula specifies the two variabels, where order matters.  The name of the dependent variable  (DV or outcome) is on the left side of the tilda symbol and the independent variable (IV or predictor) is on the right side: `dependent_y_var ~ predictor_x_var`

* **data** - Since the datset is not the first argument in the function, you must use the period to signify that the datset is being piped from above: `data = .` 

* **paired** - The default is independent groups, so include: `paired = TRUE` 


```{r}
cancer_clean %>% 
  dplyr::filter(complete.cases(totalcw2, totalcw6)) %>% 
  tidyr::gather(key = time,
                value = totalc,
                totalcw2, totalcw6,
                na.rm = FALSE) %>% 
  t.test(totalc ~ time,
         data = .,
         paired = TRUE)
```