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 each. Let’s call each turn a session, i.e. there was 6 sessions. A team of experts would rate how well the participant did throughout the entire session, meaning that if the participant had some bad runs, he/she would have to make a choice of 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 dataframe
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 ratings into the dataframes with observations. For this we will first create a session column, and then get the ratings for the sessions. To do this we will use group() with 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 start values before having group() find them automatically.

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

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(df_observations, n = 'auto', 
                         method = 'l_starts',
                         starts_col = 'participant', 
                         col_name = 'session') 

df_observations %>% 
  kable()

And it works! :)
If you just want the group starts, you can use the function find_starts().

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

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 to the merged dataframe. Once again, we just use merge(). Since we have just one rating per session, we will get only the first row of each session.

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 errors. If we wanted to know how many runs a session contained, we could extract it from the ‘run’ column.

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

summary(lm(rating~avg_errors, df_summarized))
#> 
#> Call:
#> lm(formula = rating ~ avg_errors, data = df_summarized)
#> 
#> Residuals:
#>        1        2        3        4        5        6 
#>  0.47205  0.02158 -0.03245 -1.13800  0.69125 -0.01444 
#> 
#> Coefficients:
#>             Estimate Std. Error t value Pr(>|t|)    
#> (Intercept)   8.9694     0.5285  16.973 7.07e-05 ***
#> avg_errors   -1.9820     0.2308  -8.589  0.00101 ** 
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> Residual standard error: 0.7067 on 4 degrees of freedom
#> Multiple R-squared:  0.9486, Adjusted R-squared:  0.9357 
#> F-statistic: 73.77 on 1 and 4 DF,  p-value: 0.00101

It seems like they follow each other pretty neatly.