# Introduction

In part 1, we used the gtsummary package to create a publication-ready demographics table with a few (relatively!) lines of code.

In part 2, we will examine the normality of the data to help chose the right statistical test.

In part 3, we will finally conduct mean testing and export a publication-ready table.

## Dataset information

To complete this tutorial you do not need to understand the response variables being presented, but might be interested nonetheless.

The event-related potentials (ERP) are auditory evoked potentials in response to an auditory chirp stimuli. This stimulus evokes a characteristic EEG response - brain oscillations phase synchronize to the frequency of the auditory stimulus.

Our patient group in this population are individuals with Fragile X Syndrome (FXS), the most common heriditary form of intellectual disability. Individuals with FXS demonstrate a reduction in brain synchronization to the auditory chirp compared to controls.

If you are interested in learning more, see: Ethridge, L. E., De Stefano, L. A., Schmitt, L. M., Woodruff, N. E., Brown, K. L., Tran, M., Wang, J., Pedapati, E. V., Erickson, C. A., & Sweeney, J. A. (2019). Auditory EEG Biomarkers in Fragile X Syndrome: Clinical Relevance. Front Integr Neurosci, 13, 60. https://doi.org/10.3389/fnint.2019.00060

The current dataset is Dr. Ethridge and I attempting to reconstruct cortical sources from scalp electrode encephalography. Since in humans, the auditory cortex is aligned in such a way that the frontal and temporal lobe activity projected to the frontal scalp - scalp level EEG cannot distinguish between source.

Using source localization, we can model the superficial cortical sources that the signal emerge from and answer questions such as 1) does the response to the cortical chirp emerge from the temporal or frontal sources? 2) can we distinguish difference in response from left to right? 3) does group or sex affect where the syncrhonizaton signal emerges from?

## Goals

Our major goal for this lesson is to examine and summarize our response variables. Next, we want to perform group comparisions and summarize everything in a table.

## Dataset

As a reminder from Part 1: The dataset consists of several event-related potential (ERP) responses collected from electroencephalography (EEG). The research cohort of 75 participants consists of those diagnosed with Fragile X Syndrome and so-called typically developing controls (Control). The EEG data was source localized which classifies response variables within a certain brain region.

The data, of course, deidentified and source recording for this data is available publicly from federal NDAR database.

## Setting up the analysis

pacman::p_load(tidyverse, gtsummary, flextable)

# import dataset
mutate(eegid = factor(eegid))

df.select <- df %>% select(
eegid, group, sex, visitage, chan, lobe,
starts_with(c("itc", "ersp"))
)


I’ll point a few highlights:

1. the pacman package makes it simple to install and load packages in a single step. It also allows for multiple packages separated by commas.
2. I’ll again point out the convenience of cloud-hosted data links!
3. Notice the multiple strings in the starts_with command.
4. make sure the eegid column is converted to factor from numeric.

Let’s see the results:

## Off to analyze

The data has gone through a basic data cleaning and so we know there are no missing values and the data itself is organized correctly.

As we will look at mean differences, I am most interested in the distribution of the data. We are expecting a skew in the itc values based on previous results.

Let’s make a graph of the data distribution:

# Checking distribution of variables for skew and need for transformation:
p.skewcheck <- df.source.group %>%
select(starts_with(c("itc","ersp"))) %>%
pivot_longer(everything()) %>%
mutate(name = factor(name, levels = str_sort(unique(name),
numeric = TRUE))) %>%
ggplot() +
geom_histogram(aes(x = value), color="blue", bins = 30) +
facet_wrap(vars(name), scales = "free") +
theme_minimal()


### Examining the plot

There is some data wrangling in this example. We are solely looking at the response variables across all groups. The pivot_longer in this case is very straightforward - it makes a column of the variable names and it puts the values of each within a new column called value.

Looking at the output plot, it is clear that the itc variables are skewed with a right tail. Though at first glance the ersp variables look normally distributed, they do appear to be little narrow.

### Normality Testing in a pipe

Let’s try to get a bit more quantitative by adding some normality testing.

Let’s update our packages list with moments which gives us access to several normality functions:

pacman::p_load(tidyverse, gtsummary, flextable, moments)

# Conduct Normality Tests
# Conduct Normality Tests
df.skewcheck %>%
group_by(name) %>%
summarize(
skew = skewness(value),
kurtosis = kurtosis(value),
ks = ks.test(value, "pnorm") %>% pluck("statistic"),
ks_pval = ks.test(value, "pnorm") %>% pluck("p.value"),
jt = jarque.test(value) %>% pluck("statistic"),
jt_pval = jarque.test(value) %>% pluck("p.value"),
n = n()
)



### Moments: skewness, kurtosis, and Jarque-Bera Test

Here we calculate two additional descriptive variables: skewness and kurtosis (both from the package moments).

You can, for example, learn the “tall” distribution we observed for the ERSP variables is termed “leptokurtic”.

Next, we compute normality significance testing within each variable using two tests:

1. Kolmogorov-Smirnov (stats)
2. Jarque-Bera Test (moments pkg)

Here is a journal article discussing the two tests: https://www.econstor.eu/bitstream/10419/49919/1/668828234.pdf

In this particular case, I felt having two tests (which had valid assumptions on our data) would help bolster our decision making.

### Under the hood: group_by and summarize functions

You have likely used the summarize function to average together rows. I like the present example since it shows how powerful the group_by and summarize can be with other functions in the R universe. group_by creates virtual tibbles/dataframes within a larger dataframe by a grouping variable. This allows operations to be performed across each set, rather than across all the rows in the table.

#### Sanity test with n()

In this case, we run the normality test within a summarize command to consider the distribution of each response variable. The test is calculated “within” the group. Having the n() function to print the number of items for each row is an easy sanity check. In this case 5100 is the correct number of rows for each variables representing the 75 subjects times the 68 cortical regions.

#### Pluck command

The pluck command adds the ability to add results to your data table that may usually not “fit”. For example, the output of the normality tests is an non-standard R object with different variables including a test statistic and a p-value. Let’s look at the output directly from console by running the test on the itc40 variable:

> jarque.test(df.select$itc40) Jarque-Bera Normality Test data: df.select$itc40
JB = 44619, p-value < 2.2e-16
alternative hypothesis: greater

##### Examining the Result Environment

As you can see, these results do not fit neatly into a single cell. Let’s examine the results placed in a variable jt in the environment tab in R-Studio:

Here you can see the underlying environment of the results includes several variables that the function summarizes into statements when you run the test. It also has the names of the values which we can use to pluck them out.

##### Pluck is under used!

So the pluck command automatically extracts a value deep within a result environment and presents that single value. This single value can then be used within a table cell. In our example, we pluck the normality test statisticand the p value. There are a surprising number of places where pluck can tidy up your workflows.

### Examining normality results

The results all point in the same direction - the variables are not normally distributed. This information helps us determine what inferential statistical tests would be appropriate.

#### Transforming the data

Transforming the data may allow it to fit a normal distribution but adds additional complications. For example, since the response is in a different set of units the interpretation of the results is not as straightforward as the difference in means.

That being said, let’s recalculate our table after applying a log transform:

# add log versions of each variable
# create minimum table to account for negative values
df.minvalues <- df.skewcheck %>%
group_by(name) %>%
summarize(minvalue = min(value))
# log transform (minimum = 1)
df.skewcheck.log <- df.skewcheck %>%
left_join(df.minvalues) %>%
mutate(logvalue = value + 1 - minvalue)


As the dataset contains negative values, we also have to linearly transform the variable (+1 - minvalue) for the log calculation to not produce NaNs.

Let’s rerun our normality table on the transformed variable:

Let’s examine the results table: And the associated plots:

As you can see the log transform was not sufficient for this data! If you are more interested in more complex transforms I would refer you to the bestNormalize package (https://github.com/petersonR/bestNormalize).

### Non-parametric testing

A common assumption of most statistical analyses is that of normality. In the face of violating normality assumptions, we can move on to using non-parametric methods.

## Exporting our work

Our normality table and figure may be useful in the supplementary materials to justify our analytic approach.

Creating a nicely formatted version of our table can end up being a time consuming process. So I have a few tricks to speed it up.

### Naming vectors

var.levels <- c("itc40", "itc80", "itconset", "itcoffset", "ersp_alpha", "ersp_gamma1", "ersp_gamma2")
var.labels <- c("ITC: 40 Hz", "ITC: 80 Hz", "ITC: Onset", "ITC: Offset", "ERSP: Alpha", "ERSP: Gamma1", "ERSP: Gamma2")
name = "Measure", mean = "Mean",
median = "Med.", sd = "SD",
skew = "Skew", kurtosis = "Kurtosis",
ks = "KS", ks_pval = "p", jt = "JT", jt_pval = "p"
)


There are various forms of this technique, but essentially strings that you would usually pass to functions through lists should standalone in variables. This makes maintaining the code much easier (edit in one place) and also can align the labels throughout various scripts.

### Creating a formatted flextable to export to Word

ft.normtable <- df.normtable %>%
select(-n) %>%
mutate(name = factor(name,
levels = var.levels,
labels = var.labels
)) %>%
mutate(
across(contains("pval"), .fns = ~ ifelse(.x <= .05, paste0("*", ""))),
across(where(is.numeric), .fns = ~ round(.x, digits = 2))
) %>%
mutate(
ks = paste0(ks, ks_pval),
jt = paste0(jt, jt_pval)
) %>%
select(-contains("pval")) %>%
flextable() %>%
theme_booktabs()


Let’s run over simple steps:

#### Select the final data columns

This step consists for both removing columns, but also the option of combining columns. For example, the two p value columns in our original table take up additional space. We can represent a significant p value with a character instead and combine it with the statistical column.

### Formatting

On this step I am looking on how headers, labels, and data is formatted. This includes proper rounding and abbreviations.

Let’s look at the output table:

## Exporting to Word

One of the reasons I advocate for using flextables is the easy export to Word. In this case, we just have to string together one additional command:

ft.normtable %>% save_as_docx(path = "supplemental_table_normality.docx")

## Summary of Part II

In this tutorial we reviewed the some times tedious process of closely examining the “moments” of our data. Journal and grant reviewers often raise concerns about the appropriateness of a specific statistical test. In this case, normality testing can provide key data in selecting the best analysis for subsequent tests.

In part 3, we will work on conducting group comparisons.

##### Ernest Pedapati, M.D., M.S.
###### Associate Professor of Psychiatry

Physician and Neuroscientist interested in neurodevelopmental conditions.