Attach packages

library(groupdata2)
library(dplyr) # %>%
library(knitr) # kable

Data

3 participants were asked to solve a task. They had to take turns but could go for multiple runs of the task before taking a break and letting the next participant take over. They had 2 turns (called sessions) each, meaning there were 6 sessions in total with multiple runs per session. A team of experts would rate how well the participant did throughout the entire session, meaning that if the participant had some bad runs, they would have to make a choice whether to save energy for the other session or whether to try and correct the rating of the current session.

For each run of the task, we recorded how many errors the participant made.

df_observations <- data.frame(
  "run" = 1:30,
  "participant" = c(
    1, 1, 1, 1, 
    2, 2, 2, 2, 2, 2, 
    3, 3, 3, 3, 
    1, 1, 1, 1, 1, 1, 1, 
    2, 2, 2, 
    3, 3, 3, 3, 3, 3), 
  "errors" = c(
    3, 2, 5, 3, 
    0, 0, 1, 1, 0, 1, 
    6, 4, 3, 1,
    2, 1, 3, 2, 1, 1, 0, 
    0, 0, 1,
    3, 3, 4, 2, 2, 1)
)

# Show the first 20 rows of data frame
df_observations %>% head(20) %>%  kable()

df_ratings <- data.frame(
  "session" = c(1:6), 
  "rating" = c(3, 8, 2, 5, 9, 4)
)

df_ratings %>% kable()

We would like to get the expert ratings into the data frame with observations. For this, we will first create a session column and then get the ratings for the sessions.

As the participants had differing numbers of runs, we must start a new session group whenever the participant column changes. This can be done with group() using the l_starts method. This methods takes group start values, finds those values in a specified column, and creates groups that begin at the start values. To show this, let’s try it out with some manually entered start values before having group() find them automatically.

group(
  data = df_observations,
  n = c(1, 2, 3, 1, 2, 3),  # Starting values
  method = 'l_starts',
  starts_col = 'participant',
  col_name = 'session'
) %>%
  kable()

Note how each session only has observations from a single participant.

group() went through the participant column and found one value from n at a time. When it encountered the value, it noted down the row index and continued down the column searching for the next value in n. In the end, it started groups at the found row indices from top to bottom.

Since our data has the same value in the participant column for the entire session, we can actually get group() to find these group starts automatically. It will go through the given column and whenever it encounters a new value, i.e. one that is different from the previous row, it starts a new group.

df_observations <- group(
  data = df_observations,
  n = 'auto',
  method = 'l_starts',
  starts_col = 'participant',
  col_name = 'session'
) 

df_observations %>% 
  kable()

And it works! :)

If you just want to find the group starts, you can use the find_starts() function. Alternatively, the differs_from_previous() function allows setting a threshold for how much the value must differ from the previous value.

Now that we have the session information, we can transfer the ratings from the ratings data frame.

df_merged <- merge(df_observations, df_ratings, by = 'session')

# Show head of df_merged
df_merged %>% head(15) %>% kable()

Now, we can find the average number of errors per session and see if they correlate with the experts’ ratings.

avg_errors <- df_merged %>%
  group_by(session) %>%
  dplyr::summarize("avg_errors" = mean(errors))

avg_errors %>% kable()

Let’s transfer the averages back to the merged data frame. Once again, we use merge(). Note that you may prefer to use one of the join functions from dplyr instead (e.g. dplyr::left_join()).

Since we have just one average rating per session, we extract the first row of each session and remove the original error count column.

df_summarized <- merge(df_merged, avg_errors, by = 'session') %>% 
  group_by(session) %>%  # For each session
  filter(row_number() == 1) %>%  # Get first row
  select(-errors) # Remove errors column as we use avg_errors now

df_summarized %>% kable()

We have 1 row per session with the participant, the rating and the average number of errors. If we wanted to know how many runs a session contained, we could extract it from the run column.

Let’s check if there’s a correlation between ratings and average errors.

cor(df_summarized$rating, df_summarized$avg_errors)
#> [1] -0.9739425

It seems they are highly negatively correlated, so participants with fewer errors have higher ratings and vice versa.