A Gentle Guide to Tidy Statistics in R

Working your way through a basic analysis

Thomas Mock https://twitter.com/thomas_mock
While data analysis in R can seem intimidating, we will explore how to use it effectively and clearly!


After a great discussion started by Jesse Maegan (@kiersi) on Twitter, I decided to post a workthrough of some (fake) experimental treatment data. These data correspond to a new (fake) research drug called AD-x37, a theoretical drug that has been shown to have beneficial outcomes on cognitive decline in mouse models of Alzheimer’s disease. In the current experiment we will be statistically testing whether the drug was effective in reducing cognitive impairment in dementia patients. See the data HERE.

We will be using MMSE (mini-mental status exam) scores to assess the degree of cognitive impairment. In a real clinical trial, many other variables would be recorded, but for the sake of a straightforward but multi-variate example we will stick to just MMSE.

Source: Folstein et al, 1975, J Psychiatr Res 12:189–198

We will be working through loading, plotting, analyzing, and saving the outputs of our analysis through the tidyverse, an “opinionated collection of R packages” designed for data analysis. We will limit dependence to two packages: tidyverse and broomwhile using base R for the rest. These two packages dramatically improve the data analysis workflow in my opinion. While other stats-heavy packages provide additional statistical testing, base R has a decent ability to perform statistical analyses out of the box. I will use knitr::kable to generate some html tables for a markdown document, but it is not necessary for the workflow.

Additionally, I will be uploading the Excel Sheet used in this example, so that you can re-create the workflow on your own. You can simply copy-paste the code seen here and it will run in R. If you would rather see the entire workflow in an R-Markdown document, please see here. R Markdown is a document created inside R that allows you to write code, execute it inline, and write comments/notes as you go. You could think of it like being able to write R code inside a basic Word document (but it can do a lot more than that!).

Although you may not be interested in the dataset I have provided, this hopefully provides a clear workflow for you to swap in your data of interest and accomplish a basic analysis!

Load the tidyverse, broom, and knitr

Using the library function we will load the tidyverse. If you have never installed it before you can also use the install.packages("tidyverse") call to install it for the first time. This package includes ggplot2 (graphs), dplyr/tidyr (summary statistics, data manipulation), and readxl (reading excel files) as well as the pipe %>%which will make our code much more readable! We will also load the broom package to tidy up some of our statistical outputs. Lastly we will load knitr for making nice html tables via knitr::kable, but not necessary for simply saving the outputs to Excel.

This will output some message about the packages being loaded and any conflicts of function calls.

Loading the data

While I am calling readxl::read_xlsx you could also simply use read_xlsx, but in the interest of transparency, I will be using the full call to begin. The concept of calling a function with the use of :: is important as some packages have conflicts in functions, for example multiple packages include the function select and summarize. As such, we can clarify from which package we want R to call our function from, so package::function ! To read more about the concept of “namespace” when calling functions, please look here.

readxl is unfortunately a funny case, as installing the tidyverse installs readxl, but readxl is not loaded when loading the tidyverse via a library call. As such we must either load readxl like any other package or call both the package and the name as in readxl::read_xlsx. readxl allows us to read .xls, .xlsx files into R. Alternatively, you could convert your Excel sheet into .csv, which can be read by read_csv(). By using the glimpse function from dplyr we can see how the variables were imported, as well as the first few rows.

Rows: 600
Columns: 5
$ age            <int> 80, 85, 82, 80, 83, 79, 82, 79, 80, 79, 80, …
$ sex            <int> 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1,…
$ health_status  <chr> "Healthy", "Healthy", "Healthy", "Healthy", …
$ drug_treatment <chr> "Placebo", "Placebo", "Placebo", "Placebo", …
$ mmse           <dbl> 24.78988, 24.88192, 25.10903, 24.92636, 23.3…

We can collect some information about the dataset now. Namely, we have our 3 categorical/factor variables: sex, health_status, and drug_treatment and 1 dependent variable (DV): mmse. We also have age, but importantly it is recorded as a discrete number instead of as a factor (eg as 85 years, instead of old). Thus we can look at age, but we will not use it as a factor in our ANOVA.

Checking the data distribution

We will use our first ggplot2call to create a graph showing the distribution of age. To break down what we are doing, we need to call ggplot, tell it what data to use, and use the aes or aesthetic call to assign the x coordinate. We then add a + which tells ggplot to include the next line of code. The geom_density tells R that we want to make create a density distribution layer and we want to fillit with a blue color! For more info about ggplot2 please go HERE or here.

The graph shows us that age really only goes from 79–85 years, and that there is really not any age over or underrepresented. We can confirm the age ranges by a dplyr::summarize call or by calling range in base R. As a slight aside, we can now talk about using the pipe or %>%. The pipe passes the results or data from the left of it to the right. For more info about the pipe, please see here.

We can read the following code as take raw_df and then summarize it by taking the min and max of the age variable. Now because we started with raw_df R understands we want to take the column age from this dataframe.

# A tibble: 1 x 2
    min   max
  <int> <int>
1    79    85

Alternatively we could use the base R range function, which requires the use of $ . The dollar sign indicates that R should use the age column from raw_df. Both of these functions give us the same results, the minimum number and maximum number.

[1] 79 85

For more information about using these two syntaxes look here or for cheat sheets look here.

What about the experimental variables levels?

Now while I am very aware of the variables in this dataframe, you might not be without exploring it! To quickly determine drug_treatment groups, health_status groups and how they interact we can do a table call. By calling it on both drug_treatment and health_status, we get a nice table breaking down how many rows are in each of the variable groups.

table(raw_df$drug_treatment, raw_df$health_status)
            Alzheimer's Healthy
  High Dose         100     100
  Low dose          100     100
  Placebo           100     100

Alternatively we can do the same thing in dplyr with the following code.

raw_df %>% 
  group_by(drug_treatment, health_status) %>% 
# A tibble: 6 x 3
# Groups:   drug_treatment, health_status [6]
  drug_treatment health_status     n
  <chr>          <chr>         <int>
1 High Dose      Alzheimer's     100
2 High Dose      Healthy         100
3 Low dose       Alzheimer's     100
4 Low dose       Healthy         100
5 Placebo        Alzheimer's     100
6 Placebo        Healthy         100

Now we know the levels of our variables of interest, and that there are 100 patients per overall treatment group!

Data exploration of dependent variable

Before running our summary statistics we can actually visualize the range, central tendency and quartiles via a geom_boxplot call.

ggplot(data = raw_df, # add the data
       aes(x = drug_treatment, y = mmse, # set x, y coordinates
           color = drug_treatment)) +    # color by treatment
  geom_boxplot() +
  facet_grid(~health_status) # create panes base on health status

We have split the data into separate graph facets (or panes) for healthy and Alzheimer’s patients, as well as into groups within each facet by drug treatment. This graph tells us a few things of interest for later. It definitely looks like we have an effect with our (fake) awesome drug! Let’s explore that with descriptive statistics.

While this is an exploratory graph and we don’t necessarily want to “tweak” it to perfection, we can take note that our drug treatment should be ordered Placebo < Low dose < High Dose and we should have Healthy patients presented first, and Alzheimer’s patients second. This is something we can fix in our next section!

Summary Statistics

We are looking to generate the mean and standard error for mmse scores, this is useful as a measure of central tendency, and for creating our final publication graphs. We have our categorical variables of sex, drug treatment, and health status. However going back to our glimpse call from earlier, we can see that the data is not ‘coded’ properly. Namely, sex is a dbl (number), without a descriptive name, and health_status/drug_treatment are chr (characters)! These need to be converted into factors!

Rows: 600
Columns: 5
$ age            <int> 80, 85, 82, 80, 83, 79, 82, 79, 80, 79, 80, …
$ sex            <int> 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1,…
$ health_status  <chr> "Healthy", "Healthy", "Healthy", "Healthy", …
$ drug_treatment <chr> "Placebo", "Placebo", "Placebo", "Placebo", …
$ mmse           <dbl> 24.78988, 24.88192, 25.10903, 24.92636, 23.3…

We can use the dplyr::mutate function to tell R we want to change (mutate) the rows within a variable of interest. So we will take the data in the sex, drug_treatment, and health_status columns and convert them from either just numbers or characters into a factor variable! dplyr::mutate can also perform math, and many other interesting things. For more information please see here.

We will use the mutate function and the base R factor function to convert our variables into the proper factors, and give them labels (for sex) or reorder the levels of the factors.

We need to be REALLY careful to type the labels EXACTLY as they appear in the column or it will replace those misspelled with a NA. For example, did you notice that High Dose has a capital “D” while Low dose has a lower case “d”?

sum_df <- raw_df %>% 
              sex = factor(sex, 
                  labels = c("Male", "Female")),
              drug_treatment =  f