Describing differences

The previous table and boxplot showed patients’ weights at the start of the study.

There is also a variable in this dataset called weight_lost_end_trt, which shows how much weight people lost between starting and completing FIT or MI. In a previous session we made a boxplot like this:

However, in clinical trials, it’s important to measure participants for longer periods to judge whether the effect of a treatment is sustained.

Interventions for obesity and overweight can be successful, but patients may later regain weight (Hall & Kahan, 2018). And estimating how long weight loss is sustained for is important because it changes the long term prognosis of patients, and so how cost-effective an intervention is.

The funimagery data come from a study which followed people for 6 months after completing treatment (12 months after joining the study). The kg1 column records weights at baseline, and thekg3 columns records observations made at the end of follow-up

This means we can calculate weight loss from baseline to follow-up (not just the end of treatment, which has already been done for us).

To do this we need to create a new column in our dataset. Let’s call this weight_lost_end_followup.

To calculate this new column we need to subtract weight at baseline (kg1) from weight at the end of follow-up (kg3).

In R, we can do this with the mutate function:

# use `mutate` to create a NEW COLUMN of data
# this code shows the result just below the code chunk
funimagery %>%
  mutate(weight_lost_end_followup = kg3 - kg1)

What mutate does is to make a copy of our dataset, but with a new column in. That is, it always gives us back a new dataset.

We almost always want to STORE this new copy of the dataset so we can use the new column that was created. To do this we assign the result of mutate funimagery dataset by assigning the result of mutate()) to a new variable (the ‘container’ type of variable).

The assignment operator is the left hand arrow, <-:

funimagery.edited <- funimagery %>%
  mutate(weight_lost_end_followup = kg3 - kg1)

So the code above:

• takes the funimagery data and pipes it to the mutate() function, which
• adds a new column, called weight_lost_end_followup
• this new column is made by subtracting kg1 (baseline) from kg3 (end of followup); it then
• stores this new copy of the dataset (with the extra column) in a new variable called funimagery.edited:

We can then use this new variable, funimagery.edited, to do more work, like making a boxplot:

# boxploot of weight lost at end of follow-up using new column
funimagery.edited %>%
  ggplot(aes(intervention, weight_lost_end_followup)) +
  geom_boxplot()

If anything, it looks like the difference between groups is even BIGGER after follow-up than it was at the end of treatment, which is very promising for FIT.

Using count()

To count the frequency of different responses we can use the count function, which is again from the tidyverse package. [load tidyverse now]

For example, the following statement counts the total number of responses in our sample:

# this gives us the total number of rows
earnings %>% count()

However, we often want to count the number of observations by-group. For example, if we write:

# numbers of men and women
earnings %>%
  count(gender)

Here we added gender inside count() so R knows to count the responses from each group separately.

Note, this does the same thing as writing this, although one line shorter:

earnings %>%
  group_by(gender) %>%
  count()

We can do arithmetic on these numbers to get the percentage of women in the sample:

2353 / 4483 * 100

[1] 52.48717

Later on you’ll find ways to create a new column containing percentages (using mutate), but this is fine for now.

Multiple subgroups

What’s neat about count() is that we can add more than one variable at once, and we get a count for each sub-grouping that is formed. For example:

earnings %>%
  count(job, gender)

You can re-order the table by changing the order in which you include gender and job.

Correlation

A correlation is a single number which describes how related two continuous variables are.

For a correlation to work the relationship between the variables must be linear. That is, the line on the graph has to be (fairly) straight (as it is in the example above).

To calculate a correlation we use the correlate() function in the corrr library.

First we load the library:

library(corrr)

Next we need to select the columns we want to correlate. In this case we want to use kg1, kg2, and kg3 in the funimagery dataset.

We can use select() to choose only these columns, and then use another pipe to send just those columns to correlate():

# select weight at baseline and follow-up an correlate them
funimagery %>%
  select(kg1, kg2, kg3) %>%
  correlate()

The result of correlate() is a new dataset.

It has one column for each of the variables we selected, plus an extra column called term for the variable being correlated.

The numbers represent the correlation coefficient for each pair of variables. The correlation between a variable and itself is always perfect, so the numbers on the diagonal of the table are not shown (they are NA).

We can see here that the correlations are all above 0.9, which is very high.

This isn’t surprising though. Even when trying to lose weight if we measure the same person twice these observations are likely to be quite closely related.

Summary

Both plots and descriptive statistics are valuable ways of answering questions from the data. Psychologists sometimes neglect them (especially plots) but they are important steps in developing understanding.

• Boxplots are useful for describing the differences between groups
• Scatterplots and smoothed-line plots help describe relationships