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Week 11 · Grouping and Summarizing Across Participants

How to use these notes: Create a new Quarto file named reports/npt_group.qmd. Copy the sections below into that file in order. All fenced code chunks use Quarto syntax so you can render immediately.

YAML header for `reports/npt_group.qmd`

Copy this header to the very top of your Quarto file:

---
title: "Grouping and Summarizing Across Participants"
format: html
execute:
  echo: true
  warning: true
  message: false
---

0 · Overview

We now have a clean study-level dataset where each row is one participant. In this report, we will summarize across participants to create group-level values that we can interpret and later visualize.

Goals for today:

Load and inspect the study-level data.
Create derived variables that clarify comparisons.
Compute summaries across participants.
Compare groups based on a questionnaire measure of focus (High vs Low using tef10_score).
Save a compact summary table to output/tables/.

What are derived variables?
Derived variables are new columns we calculate from existing ones. They help us express a question more directly than raw variables alone. For example, a difference score captures parity minus magnitude reaction time, which is easier to interpret than two separate means.

1 · Load and inspect

#### Load and Inspect Group Level Data Data
```{r}
# Load here::here robustly
if (!require(here)) install.packages("here")
library(here)

# Load the study-level dataset built in our previous workflow
study_level <- read.csv(here("data/cleaned/study_level.csv"))

# Quick inspection
head(study_level)
str(study_level)
summary(study_level)
```

Let's get rid of the behavior. prefix in our variable names so it's easier to type out.

```{r}
## Replace Column Names
names(study_level) <- c("subject_id", "tef10_score", "practice_mean_rt", "practice_acc", "magnitude_mean_rt", "magnitude_acc", "parity_mean_rt", "parity_acc", "practice_sd_rt", "magnitude_sd_rt", "parity_sd_rt")
write.csv(study_level, here::here("data/cleaned/study_level.csv"), row.names = FALSE)
```

2 · Derived variables (participant-level)

We will add variables that make interpretation easier.

A. Reaction time difference: parity mean RT minus magnitude mean RT.
B. Accuracy difference: parity accuracy minus magnitude accuracy.
C. Overall averages across conditions (magnitude + parity) for each participant.

#### Calculate Difference Scores
```{r}
# A) Reaction time difference (complete this line together)
# hint: subtract magnitude mean RT from parity mean RT
study_level$rt_diff <-

# B) Accuracy difference (complete together)
study_level$acc_diff <-

# C) Overall averages across conditions
study_level$mean_rt_overall  <- rowMeans(
  study_level[, c("magnitude_mean_rt", "parity_mean_rt")],
  na.rm = TRUE
)
study_level$mean_acc_overall <- rowMeans(
  study_level[, c("magnitude_acc", "parity_acc")],
  na.rm = TRUE
)

# Peek at the new columns
head(study_level[, c("subject_id", "rt_diff", "acc_diff",
                     "mean_rt_overall", "mean_acc_overall")])
```

Interpretation prompt

If rt_diff is positive, what does that imply about parity vs magnitude reaction times?
What does a negative acc_diff imply?

3 · Summaries across participants

We summarize across participants to understand overall trends in the class. We will start with simple vectorized summaries, then use aggregate() to summarize by groups.
Why aggregate()? It computes a summary (like a mean) for each level of a grouping variable. This is useful when we want to compare the same measures for different subgroups (for example, High vs Low Focus).

3A · Vectorized summaries

#### Summarize Across Participants
```{r}
# Class-level means
colMeans(study_level[, c("magnitude_mean_rt",
                         "parity_mean_rt",
                         "rt_diff")],
         na.rm = TRUE)

# Class-level variability (standard deviations)
sapply(study_level[, c("magnitude_mean_rt",
                       "parity_mean_rt",
                       "rt_diff")],
       sd, na.rm = TRUE)
```

You can also write brief inline summaries in prose. For example:
Parity mean RT is r round(mean(study_level$parity_mean_rt, na.rm = TRUE), 2) ms, plus or minus r round(sd(study_level$parity_mean_rt, na.rm = TRUE), 2) ms.

3B · Group summaries with `aggregate()`

Sometimes we are curious whether performance depends on a participant characteristic. Maybe accuracy or reaction time depends on how focused a participant reported being. We can categorize participants by tef10_score into High Focus and Low Focus using the class mean as a cut point, then compare groups.

#### Grouping using aggregate
```{r}
# Create a focus grouping variable from tef10_score
focus_cut <- mean(study_level$tef10_score, na.rm = TRUE)
study_level$focus_group <- ifelse(study_level$tef10_score >= focus_cut,
                                  "High Focus", "Low Focus")

# Check group counts
table(study_level$focus_group)

# Aggregate reaction times and differences by focus group
rt_by_focus <- aggregate(
  study_level[, c("magnitude_mean_rt",
                  "parity_mean_rt",
                  "rt_diff")],
  by = list(Focus = study_level$focus_group),
  FUN = mean
)
rt_by_focus

# Aggregate accuracies and differences by focus group
acc_by_focus <- aggregate(
  study_level[, c("magnitude_acc",
                  "parity_acc",
                  "acc_diff")],
  by = list(Focus = study_level$focus_group),
  FUN = mean
)
acc_by_focus

str(study_level)
# What do we notice here?

```

Example of inline reporting:

For High Focus participants, parity mean RT is approximately `r {
hf <- subset(study_level, focus_group == "High Focus");
round(mean(hf$parity_mean_rt, na.rm = TRUE), 2) }` ms, plus or minus `r {
hf <- subset(study_level, focus_group == "High Focus");
round(sd(hf$parity_mean_rt, na.rm = TRUE), 2) }` ms.
For Low Focus participants, parity mean RT is approximately `r {
lf <- subset(study_level, focus_group == "Low Focus");
round(mean(lf$parity_mean_rt, na.rm = TRUE), 2) }` ms, plus or minus `r {
lf <- subset(study_level, focus_group == "Low Focus");
round(sd(lf$parity_mean_rt, na.rm = TRUE), 2) }` ms.

This is a mean difference of `r round(
  mean(study_level$parity_mean_rt[study_level$focus_group == "High Focus"], na.rm = TRUE) -
  mean(study_level$parity_mean_rt[study_level$focus_group == "Low Focus"], na.rm = TRUE),
  2
)` ms between the High and Low focus group on the parity trials.

For High Focus participants, magnitude mean RT is approximately `r {
hf <- subset(study_level, focus_group == "High Focus");
round(mean(hf$magnitude_mean_rt, na.rm = TRUE), 2) }` ms, plus or minus `r {
hf <- subset(study_level, focus_group == "High Focus");
round(sd(hf$magnitude_mean_rt, na.rm = TRUE), 2) }` ms.
For Low Focus participants, magnitude mean RT is approximately `r {
lf <- subset(study_level, focus_group == "Low Focus");
round(mean(lf$magnitude_mean_rt, na.rm = TRUE), 2) }` ms, plus or minus `r {
lf <- subset(study_level, focus_group == "Low Focus");
round(sd(lf$magnitude_mean_rt, na.rm = TRUE), 2) }` ms.

This is a mean difference of `r round(
  mean(study_level$magnitude_mean_rt[study_level$focus_group == "High Focus"], na.rm = TRUE) -
  mean(study_level$magnitude_mean_rt[study_level$focus_group == "Low Focus"], na.rm = TRUE),
  2
)` ms between the High and Low focus group on the magnitude trials.

Discussion prompt

Do the group means suggest that more focused participants were faster, more accurate, both, or neither?
What additional information would help interpret these differences?

4 · Explore and interpret

#### Exploring and Interpreting
```{r}
# Summaries for key variables
summary(study_level[, c("magnitude_mean_rt",
                        "parity_mean_rt",
                        "rt_diff",
                        "magnitude_acc",
                        "parity_acc",
                        "acc_diff")])

# Optional exploration: association between overall RT and overall accuracy
cor(study_level$mean_rt_overall, study_level$mean_acc_overall, use = "complete.obs")
```