Superpowered Instructor’s Kit

The executable statements below reproduce the original completed teaching solution; the short # NOTE comments are additional and do not change program behaviour.

# NOTE: Show the result in the Console (or display a ggplot object).
print(6 + 1)                              # Addition returns 7.
# NOTE: Show the result in the Console (or display a ggplot object).
print(2 * (1 + 3))                      # Parentheses evaluated first; returns 8.
# NOTE: Show the result in the Console (or display a ggplot object).
print(5 + 3 * 2)                        # Multiplication precedes addition: 11.


# ============================================================================

# EXPECTED OUTPUT — Exact, deterministic example:
# [1] 7
# [1] 8
# [1] 11
# Data-dependent previews are templates, not verified Console output.

[1] 7
[1] 8
[1] 11

print [print(x)]: Display an object or calculated value in the R Console.

The executable statements below reproduce the original completed teaching solution; the short # NOTE comments are additional and do not change program behaviour.

# NOTE: Assign the computed expression to x for reuse.
x <- sum(1:10)                          # 1:10 is an inclusive integer sequence; sum gives 55.
# NOTE: Show the result in the Console (or display a ggplot object).
print(x / 10)                           # Stored result re-used; expected 5.5.
# NOTE: Show the result in the Console (or display a ggplot object).
print(ls())                             # List current objects; not the same as printing values.


# ============================================================================

# EXPECTED OUTPUT — Exact values where deterministic; otherwise preview:
# [1] 5.5
# # ls() also lists current object names; that list depends on the R session.
# Data-dependent previews are templates, not verified Console output.

[1] 5.5
# ls() also lists current object names; that list depends on the R session.

sum [sum(x, na.rm=FALSE)]: Add numeric values; optionally ignore missing values. print [print(x)]: Display an object or calculated value in the R Console. ls [ls()]: List names of objects currently in the R environment. <- [name <- expression]: Assign the result of the right-hand expression to an object name.

The executable statements below reproduce the original completed teaching solution; the short # NOTE comments are additional and do not change program behaviour.

# NOTE: Create a named value or vector that later steps can inspect.
course_label <- "PALS practice"          # Character/string is enclosed in quotes.
# NOTE: Create a named value or vector that later steps can inspect.
participants <- 66L                      # L makes an integer literal.
# NOTE: Create a named value or vector that later steps can inspect.
sleep_hours <- c(6, 8, 7, 5)            # c() combines values into a numeric vector.
# NOTE: Show the result in the Console (or display a ggplot object).
print(sleep_hours[1])                    # R indices start at 1, not 0.
# NOTE: Show the result in the Console (or display a ggplot object).
print(sleep_hours[sleep_hours > 6])      # Logical indexing -> c(8, 7).
# NOTE: Show the result in the Console (or display a ggplot object).
print(mean(sleep_hours))                 # Expected 6.5 hours, for illustrative data.


# ============================================================================

# EXPECTED OUTPUT — Exact, deterministic example:
# [1] 6
# [1] 8 7
# [1] 6.5
# Data-dependent previews are templates, not verified Console output.

[1] 6
[1] 8 7
[1] 6.5

c [c(a, b, ...)]: Combine multiple values into a vector. print [print(x)]: Display an object or calculated value in the R Console. mean [mean(x, na.rm=FALSE)]: Calculate an arithmetic average. [ ] [x[i]]: Select one or more values by 1-based position or logical mask.

The executable statements below reproduce the original completed teaching solution; the short # NOTE comments are additional and do not change program behaviour.

# NOTE: Assign a built-in teaching data frame to a working object.
crime <- USArrests                        # Built-in public teaching dataset, no CSV needed.
# NOTE: Show the result in the Console (or display a ggplot object).
print(dim(crime))                         # Rows and columns: 50 by 4.
# NOTE: Show the result in the Console (or display a ggplot object).
print(names(crime))                       # Murder, Assault, UrbanPop, Rape.
# NOTE: Show the result in the Console (or display a ggplot object).
print(head(crime))                        # Display the first six rows.


# ============================================================================

# EXPECTED OUTPUT — Exact values where deterministic; otherwise preview:
# [1] 50 4
# [1] "Murder" "Assault" "UrbanPop" "Rape"
# # head(crime) prints six state rows with four columns.
# Data-dependent previews are templates, not verified Console output.

[1] 50 4
[1] "Murder" "Assault" "UrbanPop" "Rape"
# head(crime) prints six state rows with four columns.

print [print(x)]: Display an object or calculated value in the R Console. dim [dim(x)]: Return dimensions, usually rows and columns. names [names(data)]: Get or assign column or element names. head [head(x, n=6)]: Show the first n elements or rows.

The executable statements below reproduce the original completed teaching solution; the short # NOTE comments are additional and do not change program behaviour.

# NOTE: Show the result in the Console (or display a ggplot object).
print(max(c(2, 4, 6)))                   # max() needs a vector or individual numbers.
# NOTE: Show the result in the Console (or display a ggplot object).
print(crime$Murder)                       # $ extracts the column named Murder.
# NOTE: Show the result in the Console (or display a ggplot object).
print(max(crime$Murder))                  # Expected 17.4 in USArrests.
# NOTE: Show the result in the Console (or display a ggplot object).
print(max(crime$Assault))                 # Expected 337 in USArrests.
# Interactive help: type ?max or help("max") in the RStudio Console.


# ============================================================================

# EXPECTED OUTPUT — Exact values where deterministic; otherwise preview:
# [1] 6
# # print(crime$Murder) shows all 50 values (truncated here).
# [1] 17.4
# [1] 337
# Data-dependent previews are templates, not verified Console output.

[1] 6
# print(crime$Murder) shows all 50 values (truncated here).
[1] 17.4
[1] 337

print [print(x)]: Display an object or calculated value in the R Console. max [max(x, na.rm=FALSE)]: Return the largest value. c [c(a, b, ...)]: Combine multiple values into a vector.

The executable statements below reproduce the original completed teaching solution; the short # NOTE comments are additional and do not change program behaviour.

# NOTE: Remove the named object from the R environment.
rm(crime)                                # Remove only this named object from Environment.
# NOTE: Show the result in the Console (or display a ggplot object).
print(exists("crime"))                   # FALSE: object no longer exists.


# ============================================================================

# EXPECTED OUTPUT — Exact, deterministic example:
# [1] FALSE
# Data-dependent previews are templates, not verified Console output.

[1] FALSE

rm [rm(object)]: Remove an object from the current R environment. print [print(x)]: Display an object or calculated value in the R Console. exists [exists("x")]: Check whether an object of the specified name exists.

The executable statements below reproduce the original completed teaching solution; the short # NOTE comments are additional and do not change program behaviour.

# NOTE: Assign the computed result to a named R object.
question <- "Does sleep predict response time?"  # A question is not a causal conclusion.
# NOTE: Define an illustrative vector of fictional reaction times.
rt_demo <- c(620, 610, 590, 605)         # Fictional reaction times in milliseconds.
# NOTE: Show the result in the Console (or display a ggplot object).
print(data.frame(trial=seq_along(rt_demo), rt_ms=rt_demo))

# EXPECTED OUTPUT — Exact, deterministic example:
#   trial rt_ms
# 1     1   620
# 2     2   610
# 3     3   590
# 4     4   605
# Data-dependent previews are templates, not verified Console output.

  trial rt_ms
1     1   620
2     2   610
3     3   590
4     4   605

c [c(a, b, ...)]: Combine multiple values into a vector. print [print(x)]: Display an object or calculated value in the R Console. data.frame [data.frame(x=..., y=...)]: Build a rectangular data frame from named columns. seq_along [seq_along(x)]: Create integer indices from 1 through length(x).

The executable statements below reproduce the original completed teaching solution; the short # NOTE comments are additional and do not change program behaviour.

# Run install.packages("tidyverse") ONCE in Console if not installed.
# library(tidyverse) loads dplyr, tidyr, ggplot2 etc. from your R library.
# NOTE: Read an input CSV into a data frame; check the working directory.
pinfo <- read.csv("data/participant-info.csv", stringsAsFactors=FALSE)
# NOTE: Read an input CSV into a data frame; check the working directory.
responses <- read.csv("data/ahi-cesd.csv", stringsAsFactors=FALSE)
# NOTE: Show the result in the Console (or display a ggplot object).
print(c(n_participants=nrow(pinfo), n_responses=nrow(responses)))


# ============================================================================

# EXPECTED OUTPUT — Output format / checks (not fabricated values):
# n_participants n_responses
# # Numeric counts depend on the included fictional public CSV files.
# Data-dependent previews are templates, not verified Console output.

n_participants n_responses
# Numeric counts depend on the included fictional public CSV files.

read.csv [read.csv("data/file.csv", stringsAsFactors=FALSE)]: Read a comma-separated file into a data frame. print [print(x)]: Display an object or calculated value in the R Console. c [c(a, b, ...)]: Combine multiple values into a vector. nrow [nrow(data)]: Count the number of rows in a table.

The executable statements below reproduce the original completed teaching solution; the short # NOTE comments are additional and do not change program behaviour.

# NOTE: Join matching records using the specified key columns.
all_data <- dplyr::inner_join(pinfo, responses, by=c("id","intervention"))
# NOTE: Show the result in the Console (or display a ggplot object).
print(c(rows=nrow(all_data), unique_ids=dplyr::n_distinct(all_data$id)))
# NOTE: Assert that a data-quality or numerical check is true; stop on failure.
stopifnot(nrow(all_data) <= nrow(responses))  # Key matching must not explode rows.


# ============================================================================

# EXPECTED OUTPUT — Output format / checks (not fabricated values):
# rows unique_ids
# # Two named counts; values depend on the loaded public datasets.
# Data-dependent previews are templates, not verified Console output.

rows unique_ids
# Two named counts; values depend on the loaded public datasets.

inner_join [dplyr::inner_join(x, y, by="id")]: Keep and combine rows whose keys match in both tables. c [c(a, b, ...)]: Combine multiple values into a vector. print [print(x)]: Display an object or calculated value in the R Console. nrow [nrow(data)]: Count the number of rows in a table. n_distinct [dplyr::n_distinct(x)]: Count distinct values in a vector. stopifnot [stopifnot(condition)]: Stop execution with an error if a logical condition is not true.

The executable statements below reproduce the original completed teaching solution; the short # NOTE comments are additional and do not change program behaviour.

# NOTE: Choose or rename variables; this does not filter rows.
selected_vars <- dplyr::select(all_data, id, intervention, ahiTotal, cesdTotal,
# NOTE: Continue this R expression with its arguments, values or formatting.
                                sex, age, educ, income, occasion)
# NOTE: Show the result in the Console (or display a ggplot object).
print(names(selected_vars))               # Exactly nine specified columns.


# ============================================================================

# EXPECTED OUTPUT — Exact, deterministic example:
# [1] "id" "intervention" "ahiTotal" "cesdTotal" "sex"
# [6] "age" "educ" "income" "occasion"
# Data-dependent previews are templates, not verified Console output.

[1] "id" "intervention" "ahiTotal" "cesdTotal" "sex"
[6] "age" "educ" "income" "occasion"

select [dplyr::select(data, col1, col2)]: Choose or rename columns in a data frame. print [print(x)]: Display an object or calculated value in the R Console. names [names(data)]: Get or assign column or element names.

The executable statements below reproduce the original completed teaching solution; the short # NOTE comments are additional and do not change program behaviour.

# MOODLE CORRECTION: worksheet says 1/2 are pre/post; codebook is authoritative:
# occasion 0 = pretest; 1 = posttest; 2 = one-week follow-up.
# NOTE: Retain only observations that meet the filter condition.
pre_post <- dplyr::filter(selected_vars, occasion %in% c(0,1))
# NOTE: Show the result in the Console (or display a ggplot object).
print(table(pre_post$occasion))           # Inspect sample size/attrition per occasion.


# ============================================================================

# EXPECTED OUTPUT — Output format / checks (not fabricated values):
# 0   1
# # Counts for baseline and posttest; public fictional data values vary.
# Data-dependent previews are templates, not verified Console output.

0   1
# Counts for baseline and posttest; public fictional data values vary.

filter [dplyr::filter(data, condition)]: Keep rows satisfying the specified logical condition. c [c(a, b, ...)]: Combine multiple values into a vector. print [print(x)]: Display an object or calculated value in the R Console. table [table(x)]: Count frequencies of unique values. %in% [x %in% c(0,1)]: Return TRUE when each element belongs to the specified set of values.

The executable statements below reproduce the original completed teaching solution; the short # NOTE comments are additional and do not change program behaviour.

# NOTE: Sort rows by the given variable without changing their values.
pre_post_asc <- dplyr::arrange(pre_post, ahiTotal)
# NOTE: Show the result in the Console (or display a ggplot object).
print(head(dplyr::select(pre_post_asc, id, occasion, ahiTotal)))


# ============================================================================

# EXPECTED OUTPUT — Output format / checks (not fabricated values):
#   id occasion ahiTotal
# # First six rows after ascending sorting; exact values are data-dependent.
# Data-dependent previews are templates, not verified Console output.

  id occasion ahiTotal
# First six rows after ascending sorting; exact values are data-dependent.

arrange [dplyr::arrange(data, col)]: Sort rows by one or more columns. print [print(x)]: Display an object or calculated value in the R Console. head [head(x, n=6)]: Show the first n elements or rows. select [dplyr::select(data, col1, col2)]: Choose or rename columns in a data frame.

The executable statements below reproduce the original completed teaching solution; the short # NOTE comments are additional and do not change program behaviour.

# NOTE: Reduce each group to its aggregate statistics.
overall_summary <- dplyr::summarise(pre_post,
# NOTE: Compute an arithmetic mean of the selected numbers.
  n=dplyr::n(), mean_ahi=mean(ahiTotal,na.rm=TRUE),
# NOTE: Compute an arithmetic mean of the selected numbers.
  mean_cesd=mean(cesdTotal,na.rm=TRUE))
# NOTE: Show the result in the Console (or display a ggplot object).
print(overall_summary)


# ============================================================================

# EXPECTED OUTPUT — Output format / checks (not fabricated values):
#   n mean_ahi mean_cesd
# # One row with three summary columns; numbers depend on input CSVs.
# Data-dependent previews are templates, not verified Console output.

  n mean_ahi mean_cesd
# One row with three summary columns; numbers depend on input CSVs.

summarise [dplyr::summarise(data, metric=mean(x))]: Produce summary statistics for the whole table or each group. n [dplyr::n()]: Return the number of rows in the active dplyr group. mean [mean(x, na.rm=FALSE)]: Calculate an arithmetic average. print [print(x)]: Display an object or calculated value in the R Console.

The executable statements below reproduce the original completed teaching solution; the short # NOTE comments are additional and do not change program behaviour.

# NOTE: Assign the computed result to a named R object.
occasion_summary <- pre_post_asc |>
# NOTE: Define the groups to be summarised independently.
  dplyr::group_by(occasion) |>
# NOTE: Reduce each group to its aggregate statistics.
  dplyr::summarise(n=dplyr::n(), mean_ahi=mean(ahiTotal),
# NOTE: Compute an arithmetic mean of the selected numbers.
                   mean_cesd=mean(cesdTotal), .groups="drop")
# NOTE: Show the result in the Console (or display a ggplot object).
print(occasion_summary)


# ============================================================================

# EXPECTED OUTPUT — Output format / checks (not fabricated values):
#   occasion   n mean_ahi mean_cesd
# # One summary row per occasion (0 and 1).
# Data-dependent previews are templates, not verified Console output.

  occasion   n mean_ahi mean_cesd
# One summary row per occasion (0 and 1).

group_by [dplyr::group_by(data, group)]: Set the grouping keys used by later operations. summarise [dplyr::summarise(data, metric=mean(x))]: Produce summary statistics for the whole table or each group. n [dplyr::n()]: Return the number of rows in the active dplyr group. mean [mean(x, na.rm=FALSE)]: Calculate an arithmetic average. print [print(x)]: Display an object or calculated value in the R Console. |> [data |> function()]: Pass the preceding result to the next function call.

The executable statements below reproduce the original completed teaching solution; the short # NOTE comments are additional and do not change program behaviour.

# NOTE: Create or recode columns while retaining row-level observations.
pre_post <- dplyr::mutate(pre_post, sadness=cesdTotal-ahiTotal)
# NOTE: Show the result in the Console (or display a ggplot object).
print(head(dplyr::select(pre_post, sadness, cesdTotal, ahiTotal)))
# DO NOT interpret "sadness" clinically: AHI/CES-D scales have different constructs/ranges.


# ============================================================================

# EXPECTED OUTPUT — Output format / checks (not fabricated values):
#   sadness cesdTotal ahiTotal
# # First six rows; sadness = cesdTotal - ahiTotal.
# Data-dependent previews are templates, not verified Console output.

  sadness cesdTotal ahiTotal
# First six rows; sadness = cesdTotal - ahiTotal.

mutate [dplyr::mutate(data, new=x+y)]: Create or alter one or more columns. print [print(x)]: Display an object or calculated value in the R Console. head [head(x, n=6)]: Show the first n elements or rows. select [dplyr::select(data, col1, col2)]: Choose or rename columns in a data frame.

The executable statements below reproduce the original completed teaching solution; the short # NOTE comments are additional and do not change program behaviour.

# MOODLE CORRECTION: worksheet labels conflict with source codebook.
# Correct coding in code-book.pdf: 1=Female, 2=Male.
# NOTE: Create or recode columns while retaining row-level observations.
pre_post <- dplyr::mutate(pre_post,
# NOTE: Map numeric category codes to readable factor levels.
    sex_label=factor(sex,levels=c(1,2),labels=c("Female","Male")))
# NOTE: Show the result in the Console (or display a ggplot object).
print(table(pre_post$sex_label, useNA="ifany"))


# ============================================================================

# EXPECTED OUTPUT — Output format / checks (not fabricated values):
# Female Male
# # Category frequencies; an NA row appears if unmatched/missing values occur.
# Data-dependent previews are templates, not verified Console output.

Female Male
# Category frequencies; an NA row appears if unmatched/missing values occur.

mutate [dplyr::mutate(data, new=x+y)]: Create or alter one or more columns. factor [factor(x, levels=..., labels=...)]: Represent categorical values with ordered levels and labels. c [c(a, b, ...)]: Combine multiple values into a vector. print [print(x)]: Display an object or calculated value in the R Console. table [table(x)]: Count frequencies of unique values.

The executable statements below reproduce the original completed teaching solution; the short # NOTE comments are additional and do not change program behaviour.

# NOTE: Keep baseline observations and preserve identifiers for later pairing.
paired_pre <- dplyr::filter(all_data, occasion==0) |>
# NOTE: Choose or rename variables; this does not filter rows.
 dplyr::select(id,intervention,ahi_pre=ahiTotal)
# NOTE: Keep posttest observations and preserve identifiers for later pairing.
paired_post <- dplyr::filter(all_data, occasion==1) |>
# NOTE: Choose or rename variables; this does not filter rows.
 dplyr::select(id,intervention,ahi_post=ahiTotal)
# NOTE: Join matching records using the specified key columns.
paired_data <- dplyr::inner_join(paired_pre,paired_post,by=c("id","intervention")) |>
# NOTE: Create or recode columns while retaining row-level observations.
 dplyr::mutate(change_ahi=ahi_post-ahi_pre)
# NOTE: Show the result in the Console (or display a ggplot object).
print(dplyr::summarise(paired_data, paired_n=dplyr::n(), mean_change=mean(change_ahi)))

# EXPECTED OUTPUT — Output format / checks (not fabricated values):
#   paired_n mean_change
# # One row: count of matched pairs and their average ahi_post - ahi_pre.
# Data-dependent previews are templates, not verified Console output.

  paired_n mean_change
# One row: count of matched pairs and their average ahi_post - ahi_pre.

filter [dplyr::filter(data, condition)]: Keep rows satisfying the specified logical condition. select [dplyr::select(data, col1, col2)]: Choose or rename columns in a data frame. inner_join [dplyr::inner_join(x, y, by="id")]: Keep and combine rows whose keys match in both tables. c [c(a, b, ...)]: Combine multiple values into a vector. mutate [dplyr::mutate(data, new=x+y)]: Create or alter one or more columns. print [print(x)]: Display an object or calculated value in the R Console. summarise [dplyr::summarise(data, metric=mean(x))]: Produce summary statistics for the whole table or each group. n [dplyr::n()]: Return the number of rows in the active dplyr group. mean [mean(x, na.rm=FALSE)]: Calculate an arithmetic average.

The executable statements below reproduce the original completed teaching solution; the short # NOTE comments are additional and do not change program behaviour.

# NOTE: Read an input CSV into a data frame; check the working directory.
qformats <- read.csv("data/Qformats.csv", stringsAsFactors=FALSE)
# NOTE: Read an input CSV into a data frame; check the working directory.
scoring <- read.csv("data/Scoring.csv", stringsAsFactors=FALSE)
# NOTE: Read an input CSV into a data frame; check the working directory.
aq_responses <- read.csv("data/AQ.csv", stringsAsFactors=FALSE)
# NOTE: Show the result in the Console (or display a ggplot object).
print(c(participants=nrow(aq_responses),questions=nrow(qformats),rules=nrow(scoring)))


# ============================================================================

# EXPECTED OUTPUT — Output format / checks (not fabricated values):
# participants questions rules
# # Three named counts; original private AQ source had 66 respondents and 10 items.
# Data-dependent previews are templates, not verified Console output.

participants questions rules
# Three named counts; original private AQ source had 66 respondents and 10 items.

read.csv [read.csv("data/file.csv", stringsAsFactors=FALSE)]: Read a comma-separated file into a data frame. print [print(x)]: Display an object or calculated value in the R Console. c [c(a, b, ...)]: Combine multiple values into a vector. nrow [nrow(data)]: Count the number of rows in a table.

The executable statements below reproduce the original completed teaching solution; the short # NOTE comments are additional and do not change program behaviour.

# NOTE: Pivot Q1–Q10 columns into long-form question/response rows.
aq_long <- tidyr::pivot_longer(aq_responses,
# NOTE: Generate exact field names Q1 through Q10 without separators.
  cols=dplyr::all_of(paste0("Q",1:10)),names_to="Question",values_to="Response")
# NOTE: Show the result in the Console (or display a ggplot object).
print(dim(aq_long))                       # Real source: 66*10=660 rows; public demo differs.


# ============================================================================

# EXPECTED OUTPUT — Output format / checks (not fabricated values):
# [1] <participants × 10> <column count after pivot>
# # In original private data, there were 66 × 10 = 660 long-form rows.
# Data-dependent previews are templates, not verified Console output.

[1] <participants × 10> <column count after pivot>
# In original private data, there were 66 × 10 = 660 long-form rows.

pivot_longer [tidyr::pivot_longer(data, cols=..., names_to=..., values_to=...)]: Reshape many columns into a smaller number of key/value columns. all_of [dplyr::all_of(names)]: Select columns identified by a character vector of names. paste0 [paste0("Q", 1:10)]: Join text and values without separators. print [print(x)]: Display an object or calculated value in the R Console. dim [dim(x)]: Return dimensions, usually rows and columns.

The executable statements below reproduce the original completed teaching solution; the short # NOTE comments are additional and do not change program behaviour.

# NOTE: Join matching records using the specified key columns.
aq_with_format <- dplyr::inner_join(aq_long,qformats,by="Question")
# NOTE: Join matching records using the specified key columns.
aq_scored <- dplyr::inner_join(aq_with_format,scoring,by=c("QFormat","Response"))
# NOTE: Assert that a data-quality or numerical check is true; stop on failure.
stopifnot(nrow(aq_scored)==nrow(aq_long), !anyNA(aq_scored$Score))
# NOTE: Show the result in the Console (or display a ggplot object).
print(head(dplyr::select(aq_scored,Id,Question,Response,QFormat,Score)))


# ============================================================================

# EXPECTED OUTPUT — Output format / checks (not fabricated values):
#   Id Question Response QFormat Score
# # First six matched response rows, each with a binary Score (0 or 1).
# Data-dependent previews are templates, not verified Console output.

  Id Question Response QFormat Score
# First six matched response rows, each with a binary Score (0 or 1).

inner_join [dplyr::inner_join(x, y, by="id")]: Keep and combine rows whose keys match in both tables. c [c(a, b, ...)]: Combine multiple values into a vector. stopifnot [stopifnot(condition)]: Stop execution with an error if a logical condition is not true. nrow [nrow(data)]: Count the number of rows in a table. anyNA [anyNA(x)]: Check whether an object contains missing values. print [print(x)]: Display an object or calculated value in the R Console. head [head(x, n=6)]: Show the first n elements or rows. select [dplyr::select(data, col1, col2)]: Choose or rename columns in a data frame.

The executable statements below reproduce the original completed teaching solution; the short # NOTE comments are additional and do not change program behaviour.

# NOTE: Compute one AQ-10 total for each participant.
aq_scores <- aq_scored |>
# NOTE: Define the groups to be summarised independently.
  dplyr::group_by(Id) |>
# NOTE: Reduce each group to its aggregate statistics.
  dplyr::summarise(AQTotal=sum(Score),.groups="drop")
# NOTE: Assert that a data-quality or numerical check is true; stop on failure.
stopifnot(all(aq_scores$AQTotal >= 0 & aq_scores$AQTotal <= 10))
# NOTE: Show the result in the Console (or display a ggplot object).
print(head(aq_scores))


# ============================================================================

# EXPECTED OUTPUT — Output format / checks (not fabricated values):
#   Id AQTotal
# # First six participants with integer totals from 0 to 10.
# Data-dependent previews are templates, not verified Console output.

  Id AQTotal
# First six participants with integer totals from 0 to 10.

group_by [dplyr::group_by(data, group)]: Set the grouping keys used by later operations. summarise [dplyr::summarise(data, metric=mean(x))]: Produce summary statistics for the whole table or each group. sum [sum(x, na.rm=FALSE)]: Add numeric values; optionally ignore missing values. stopifnot [stopifnot(condition)]: Stop execution with an error if a logical condition is not true. all [all(logical)]: Return TRUE only if every tested value is TRUE. print [print(x)]: Display an object or calculated value in the R Console. head [head(x, n=6)]: Show the first n elements or rows.

The executable statements below reproduce the original completed teaching solution; the short # NOTE comments are additional and do not change program behaviour.

# NOTE: Perform the whole AQ workflow through one chained pipeline.
aq_pipe <- aq_responses |>
# NOTE: Pivot Q1–Q10 columns into long-form question/response rows.
 tidyr::pivot_longer(cols=dplyr::all_of(paste0("Q",1:10)),
# NOTE: Continue this R expression with its arguments, values or formatting.
                     names_to="Question",values_to="Response") |>
# NOTE: Join matching records using the specified key columns.
 dplyr::inner_join(qformats,by="Question") |>
# NOTE: Join matching records using the specified key columns.
 dplyr::inner_join(scoring,by=c("QFormat","Response")) |>
# NOTE: Define the groups to be summarised independently.
 dplyr::group_by(Id) |>
# NOTE: Reduce each group to its aggregate statistics.
 dplyr::summarise(AQTotal=sum(Score),.groups="drop")
# NOTE: Assert that a data-quality or numerical check is true; stop on failure.
stopifnot(identical(aq_scores,aq_pipe))   # Native |> parallels tidyverse %>% for these operations.


# ============================================================================

# EXPECTED OUTPUT — Exact, deterministic example:
# # No printed output when stopifnot(identical(...)) passes.
# # If it fails, R stops with an error.
# Data-dependent previews are templates, not verified Console output.

# No printed output when stopifnot(identical(...)) passes.
# If it fails, R stops with an error.

pivot_longer [tidyr::pivot_longer(data, cols=..., names_to=..., values_to=...)]: Reshape many columns into a smaller number of key/value columns. all_of [dplyr::all_of(names)]: Select columns identified by a character vector of names. paste0 [paste0("Q", 1:10)]: Join text and values without separators. inner_join [dplyr::inner_join(x, y, by="id")]: Keep and combine rows whose keys match in both tables. c [c(a, b, ...)]: Combine multiple values into a vector. group_by [dplyr::group_by(data, group)]: Set the grouping keys used by later operations. summarise [dplyr::summarise(data, metric=mean(x))]: Produce summary statistics for the whole table or each group. sum [sum(x, na.rm=FALSE)]: Add numeric values; optionally ignore missing values. stopifnot [stopifnot(condition)]: Stop execution with an error if a logical condition is not true. identical [identical(x, y)]: Test strict equality, including data types and attributes. |> [data |> transform()]: Compose data-processing steps in readable left-to-right order.

The executable statements below reproduce the original completed teaching solution; the short # NOTE comments are additional and do not change program behaviour.

# NOTE: Reduce each group to its aggregate statistics.
aq_summary <- dplyr::summarise(aq_scores,
# NOTE: Compute an arithmetic mean of the selected numbers.
  n=dplyr::n(), mean=mean(AQTotal), sd=sd(AQTotal),
# NOTE: Continue this R expression with its arguments, values or formatting.
  min=min(AQTotal), max=max(AQTotal), above6=sum(AQTotal>6))
# NOTE: Show the result in the Console (or display a ggplot object).
print(aq_summary)
# NOTE: Show the result in the Console (or display a ggplot object).
print(dplyr::filter(aq_scores,AQTotal>6))


# ============================================================================

# EXPECTED OUTPUT — Output format / checks (not fabricated values):
#   n mean sd min max above6
# # One summary row; followed by rows with AQTotal > 6.
# Data-dependent previews are templates, not verified Console output.

  n mean sd min max above6
# One summary row; followed by rows with AQTotal > 6.

summarise [dplyr::summarise(data, metric=mean(x))]: Produce summary statistics for the whole table or each group. n [dplyr::n()]: Return the number of rows in the active dplyr group. mean [mean(x, na.rm=FALSE)]: Calculate an arithmetic average. sd [sd(x)]: Calculate the sample standard deviation. min [min(x, na.rm=FALSE)]: Return the smallest value. max [max(x, na.rm=FALSE)]: Return the largest value. sum [sum(x, na.rm=FALSE)]: Add numeric values; optionally ignore missing values. print [print(x)]: Display an object or calculated value in the R Console. filter [dplyr::filter(data, condition)]: Keep rows satisfying the specified logical condition.

The executable statements below reproduce the original completed teaching solution; the short # NOTE comments are additional and do not change program behaviour.

# NOTE: Build a plot and specify how data map to visual variables.
p_aq <- ggplot2::ggplot(aq_scores,ggplot2::aes(x=AQTotal)) +
# NOTE: Add a visual layer; ggplot layers are combined with +.
 ggplot2::geom_histogram(binwidth=1,boundary=-0.5,colour="white") +
# NOTE: Apply a plot theme; styling does not change source data.
 ggplot2::scale_x_continuous(breaks=0:10) + ggplot2::theme_classic() +
# NOTE: Set interpretable axis labels and titles.
 ggplot2::labs(x="AQ-10 score",y="Number of participants",title="AQ-10 score distribution")
# NOTE: Show the result in the Console (or display a ggplot object).
print(p_aq)


# ============================================================================

# EXPECTED OUTPUT — Expected visual output:
# [Plot] Ten-point integer-scale histogram; x-axis 0–10, y-axis participant counts.
# Data-dependent previews are templates, not verified Console output.

[Plot] Ten-point integer-scale histogram; x-axis 0–10, y-axis participant counts.

ggplot [ggplot2::ggplot(data, aes(...))]: Start a layered grammar-of-graphics plot. aes [ggplot2::aes(x=..., y=..., colour=...)]: Map data variables to graphical features such as x, y or colour. geom_histogram [ggplot2::geom_histogram(binwidth=...)]: Draw bins showing a distribution of numeric values. scale_x_continuous [ggplot2::scale_x_continuous(breaks=...)]: Control the continuous x-axis scale and tick marks. theme_classic [ggplot2::theme_classic()]: Apply a simple plotting theme with minimal background decoration. labs [ggplot2::labs(x="...", y="...", title="...")]: Set plot titles, axis labels and legend text. print [print(x)]: Display an object or calculated value in the R Console.

The executable statements below reproduce the original completed teaching solution; the short # NOTE comments are additional and do not change program behaviour.

# NOTE: Compute sample variance (square of SD).
variance_aq <- var(aq_scores$AQTotal)    # Sample variance (n-1 denominator).
# NOTE: Compute a sample standard deviation.
se_aq <- sd(aq_scores$AQTotal)/sqrt(nrow(aq_scores))
# NOTE: Show the result in the Console (or display a ggplot object).
print(c(sample_variance=variance_aq, standard_error=se_aq))

# EXPECTED OUTPUT — Output format / checks (not fabricated values):
# sample_variance standard_error
# # Two positive numeric values; data-dependent.
# Data-dependent previews are templates, not verified Console output.

sample_variance standard_error
# Two positive numeric values; data-dependent.

var [var(x)]: Calculate the sample variance. sd [sd(x)]: Calculate the sample standard deviation. sqrt [sqrt(x)]: Calculate the non-negative square root. nrow [nrow(data)]: Count the number of rows in a table. print [print(x)]: Display an object or calculated value in the R Console. c [c(a, b, ...)]: Combine multiple values into a vector.

The executable statements below reproduce the original completed teaching solution; the short # NOTE comments are additional and do not change program behaviour.

# NOTE: Build a plot and specify how data map to visual variables.
p_hist <- ggplot2::ggplot(all_data,ggplot2::aes(x=ahiTotal)) +
# NOTE: Add a visual layer; ggplot layers are combined with +.
 ggplot2::geom_histogram(binwidth=5,colour="white") +
# NOTE: Set interpretable axis labels and titles.
 ggplot2::labs(x="AHI total",y="Count",title="AHI distribution")
# NOTE: Show the result in the Console (or display a ggplot object).
print(p_hist)
# NOTE: Show the result in the Console (or display a ggplot object).
print(ggplot2::ggplot(all_data,ggplot2::aes(x=ahiTotal)) +
# NOTE: Add a visual layer; ggplot layers are combined with +.
 ggplot2::geom_histogram(binwidth=1,colour="white") +
# NOTE: Set interpretable axis labels and titles.
 ggplot2::labs(x="AHI total",y="Count",title="AHI distribution: binwidth 1"))


# ============================================================================

# EXPECTED OUTPUT — Expected visual output:
# [Plot 1] AHI histogram with binwidth 5.
# [Plot 2] The same distribution with binwidth 1.
# Data-dependent previews are templates, not verified Console output.

[Plot 1] AHI histogram with binwidth 5.
[Plot 2] The same distribution with binwidth 1.

ggplot [ggplot2::ggplot(data, aes(...))]: Start a layered grammar-of-graphics plot. aes [ggplot2::aes(x=..., y=..., colour=...)]: Map data variables to graphical features such as x, y or colour. geom_histogram [ggplot2::geom_histogram(binwidth=...)]: Draw bins showing a distribution of numeric values. labs [ggplot2::labs(x="...", y="...", title="...")]: Set plot titles, axis labels and legend text. print [print(x)]: Display an object or calculated value in the R Console. + [ggplot(...) + geom_histogram(...)]: Add a graphics layer; here + combines plot components, not numbers.

The executable statements below reproduce the original completed teaching solution; the short # NOTE comments are additional and do not change program behaviour.

# NOTE: Create or recode columns while retaining row-level observations.
all_data <- dplyr::mutate(all_data,
# NOTE: Map numeric category codes to readable factor levels.
 sex_label=factor(sex,levels=c(1,2),labels=c("Female","Male")))
# NOTE: Build a plot and specify how data map to visual variables.
p_scatter <- ggplot2::ggplot(all_data,
# NOTE: Apply the ggplot operation to the current visualisation.
 ggplot2::aes(x=ahiTotal,y=cesdTotal,colour=sex_label)) +
# NOTE: Add a visual layer; ggplot layers are combined with +.
 ggplot2::geom_point(alpha=0.48) +
# NOTE: Set interpretable axis labels and titles.
 ggplot2::labs(x="AHI total",y="CES-D total",colour="Sex")
# NOTE: Show the result in the Console (or display a ggplot object).
print(p_scatter)


# ============================================================================

# EXPECTED OUTPUT — Expected visual output:
# [Plot] AHI on x-axis; CES-D on y-axis; coloured points and a Female/Male legend.
# Data-dependent previews are templates, not verified Console output.

[Plot] AHI on x-axis; CES-D on y-axis; coloured points and a Female/Male legend.

mutate [dplyr::mutate(data, new=x+y)]: Create or alter one or more columns. factor [factor(x, levels=..., labels=...)]: Represent categorical values with ordered levels and labels. c [c(a, b, ...)]: Combine multiple values into a vector. ggplot [ggplot2::ggplot(data, aes(...))]: Start a layered grammar-of-graphics plot. aes [ggplot2::aes(x=..., y=..., colour=...)]: Map data variables to graphical features such as x, y or colour. geom_point [ggplot2::geom_point()]: Plot individual observations as points. labs [ggplot2::labs(x="...", y="...", title="...")]: Set plot titles, axis labels and legend text. print [print(x)]: Display an object or calculated value in the R Console.

The executable statements below reproduce the original completed teaching solution; the short # NOTE comments are additional and do not change program behaviour.

# NOTE: Map numeric category codes to readable factor levels.
p_box <- ggplot2::ggplot(all_data,ggplot2::aes(x=factor(occasion),y=ahiTotal)) +
# NOTE: Add a visual layer; ggplot layers are combined with +.
 ggplot2::geom_boxplot(fill="#7cccd2",outlier.alpha=.4) +
# NOTE: Set interpretable axis labels and titles.
 ggplot2::labs(x="Occasion code",y="AHI total")
# NOTE: Show the result in the Console (or display a ggplot object).
print(p_box)
# NOTE: Map numeric category codes to readable factor levels.
p_violin <- ggplot2::ggplot(all_data,ggplot2::aes(x=factor(occasion),y=ahiTotal)) +
# NOTE: Add a visual layer; ggplot layers are combined with +.
 ggplot2::geom_violin(fill="#c3aaf5",alpha=.55) +
# NOTE: Add a visual layer; ggplot layers are combined with +.
 ggplot2::geom_boxplot(width=.13,outlier.shape=NA) +
# NOTE: Add a visual layer; ggplot layers are combined with +.
 ggplot2::geom_jitter(width=.1,alpha=.15,size=.45)
# NOTE: Show the result in the Console (or display a ggplot object).
print(p_violin)


# ============================================================================

# EXPECTED OUTPUT — Expected visual output:
# [Plot 1] AHI boxplot by occasion.
# [Plot 2] Violin + narrow boxplot + jittered individual points.
# Data-dependent previews are templates, not verified Console output.

[Plot 1] AHI boxplot by occasion.
[Plot 2] Violin + narrow boxplot + jittered individual points.

ggplot [ggplot2::ggplot(data, aes(...))]: Start a layered grammar-of-graphics plot. aes [ggplot2::aes(x=..., y=..., colour=...)]: Map data variables to graphical features such as x, y or colour. factor [factor(x, levels=..., labels=...)]: Represent categorical values with ordered levels and labels. geom_boxplot [ggplot2::geom_boxplot()]: Draw median, quartile and whisker summaries. labs [ggplot2::labs(x="...", y="...", title="...")]: Set plot titles, axis labels and legend text. print [print(x)]: Display an object or calculated value in the R Console. geom_violin [ggplot2::geom_violin()]: Draw smoothed density shapes by group. geom_jitter [ggplot2::geom_jitter(width=...)]: Add small position offsets to reveal overlapping points.

The executable statements below reproduce the original completed teaching solution; the short # NOTE comments are additional and do not change program behaviour.

# NOTE: Create human-readable labels for coded intervention groups.
intervention_labels <- c("Signature strengths","Three good things",
# NOTE: Continue this R expression with its arguments, values or formatting.
                         "Gratitude visit","Early memories (control)")
# NOTE: Create or recode columns while retaining row-level observations.
all_data <- dplyr::mutate(all_data, intervention_label=factor(intervention,
# NOTE: Continue this R expression with its arguments, values or formatting.
 levels=1:4,labels=intervention_labels))
# NOTE: Assign the computed result to a named R object.
means_occasion <- all_data |>
# NOTE: Define the groups to be summarised independently.
 dplyr::group_by(occasion) |>
# NOTE: Reduce each group to its aggregate statistics.
 dplyr::summarise(mean_ahi=mean(ahiTotal),.groups="drop")
# NOTE: Show the result in the Console (or display a ggplot object).
print(ggplot2::ggplot(means_occasion,ggplot2::aes(x=factor(occasion),y=mean_ahi))+
# NOTE: Add a visual layer; ggplot layers are combined with +.
 ggplot2::geom_col(fill="#9fd8c2"))
# NOTE: Assign the computed result to a named R object.
means_groups <- all_data |>
# NOTE: Define the groups to be summarised independently.
 dplyr::group_by(occasion,intervention_label) |>
# NOTE: Reduce each group to its aggregate statistics.
 dplyr::summarise(n=dplyr::n(),mean_ahi=mean(ahiTotal),sd_ahi=sd(ahiTotal),
# NOTE: Specify how groups, missing values or join keys are handled.
 .groups="drop")
# NOTE: Show the result in the Console (or display a ggplot object).
print(ggplot2::ggplot(means_groups,ggplot2::aes(x=factor(occasion),y=mean_ahi,
# NOTE: Add a visual layer; ggplot layers are combined with +.
 fill=intervention_label)) + ggplot2::geom_col(position="dodge"))


# ============================================================================

# EXPECTED OUTPUT — Expected visual output:
# [Plot 1] One mean-AHI bar per occasion.
# [Plot 2] Side-by-side intervention mean bars per occasion.
# Data-dependent previews are templates, not verified Console output.

[Plot 1] One mean-AHI bar per occasion.
[Plot 2] Side-by-side intervention mean bars per occasion.

mutate [dplyr::mutate(data, new=x+y)]: Create or alter one or more columns. factor [factor(x, levels=..., labels=...)]: Represent categorical values with ordered levels and labels. group_by [dplyr::group_by(data, group)]: Set the grouping keys used by later operations. summarise [dplyr::summarise(data, metric=mean(x))]: Produce summary statistics for the whole table or each group. mean [mean(x, na.rm=FALSE)]: Calculate an arithmetic average. ggplot [ggplot2::ggplot(data, aes(...))]: Start a layered grammar-of-graphics plot. aes [ggplot2::aes(x=..., y=..., colour=...)]: Map data variables to graphical features such as x, y or colour. geom_col [ggplot2::geom_col()]: Draw bars using already-calculated y values. n [dplyr::n()]: Return the number of rows in the active dplyr group. sd [sd(x)]: Calculate the sample standard deviation. |> [data |> group_by(...)]: Pass a data frame through consecutive transformations.

The executable statements below reproduce the original completed teaching solution; the short # NOTE comments are additional and do not change program behaviour.

# NOTE: Build a plot and specify how data map to visual variables.
p_line <- ggplot2::ggplot(means_groups,
# NOTE: Apply the ggplot operation to the current visualisation.
 ggplot2::aes(x=occasion,y=mean_ahi,colour=intervention_label,group=intervention_label)) +
# NOTE: Add a visual layer; ggplot layers are combined with +.
 ggplot2::geom_line() + ggplot2::geom_point() +
# NOTE: Add a visual layer; ggplot layers are combined with +.
 ggplot2::geom_errorbar(ggplot2::aes(ymin=mean_ahi-sd_ahi,ymax=mean_ahi+sd_ahi),
# NOTE: Specify how groups, missing values or join keys are handled.
 width=.13,na.rm=TRUE) + ggplot2::coord_cartesian(ylim=c(24,120)) +
# NOTE: Set interpretable axis labels and titles.
 ggplot2::labs(x="Measurement occasion (0=pre, 1=post)",y="Mean AHI ± 1 SD")
# NOTE: Show the result in the Console (or display a ggplot object).
print(p_line)


# ============================================================================

# EXPECTED OUTPUT — Expected visual output:
# [Plot] Intervention mean-AHI trajectories across occasions with vertical ±1 SD error bars.
# Data-dependent previews are templates, not verified Console output.

[Plot] Intervention mean-AHI trajectories across occasions with vertical ±1 SD error bars.

ggplot [ggplot2::ggplot(data, aes(...))]: Start a layered grammar-of-graphics plot. aes [ggplot2::aes(x=..., y=..., colour=...)]: Map data variables to graphical features such as x, y or colour. geom_line [ggplot2::geom_line()]: Connect points in x-axis order within groups. geom_point [ggplot2::geom_point()]: Plot individual observations as points. geom_errorbar [ggplot2::geom_errorbar(aes(ymin=..., ymax=...))]: Draw uncertainty or variability intervals between ymin and ymax. coord_cartesian [ggplot2::coord_cartesian(ylim=c(lo, hi))]: Zoom a plot to a selected viewing range without discarding data. c [c(a, b, ...)]: Combine multiple values into a vector. labs [ggplot2::labs(x="...", y="...", title="...")]: Set plot titles, axis labels and legend text. print [print(x)]: Display an object or calculated value in the R Console.

The executable statements below reproduce the original completed teaching solution; the short # NOTE comments are additional and do not change program behaviour.

# NOTE: Show the result in the Console (or display a ggplot object).
print(p_scatter + ggplot2::theme_classic() +
# NOTE: Set interpretable axis labels and titles.
 ggplot2::labs(title="Happiness and depressive symptoms"))
# NOTE: Show the result in the Console (or display a ggplot object).
print(p_scatter + ggplot2::theme_bw() + ggplot2::facet_wrap(~sex_label))
# NOTE: Show the result in the Console (or display a ggplot object).
print(ggplot2::ggplot(all_data,ggplot2::aes(x=ahiTotal,y=cesdTotal)) +
# NOTE: Add a visual layer; ggplot layers are combined with +.
 ggplot2::geom_point(colour="purple",size=2,shape=17,alpha=.3) +
# NOTE: Set interpretable axis labels and titles.
 ggplot2::labs(title="Styled scatterplot",x="AHI",y="CES-D"))


# ============================================================================

# EXPECTED OUTPUT — Expected visual output:
# [Plot 1] Classic scatter with title.
# [Plot 2] Black-and-white faceted scatter by sex.
# [Plot 3] Purple triangle scatter.
# Data-dependent previews are templates, not verified Console output.

[Plot 1] Classic scatter with title.
[Plot 2] Black-and-white faceted scatter by sex.
[Plot 3] Purple triangle scatter.

print [print(x)]: Display an object or calculated value in the R Console. theme_classic [ggplot2::theme_classic()]: Apply a simple plotting theme with minimal background decoration. labs [ggplot2::labs(x="...", y="...", title="...")]: Set plot titles, axis labels and legend text. theme_bw [ggplot2::theme_bw()]: Apply a black-and-white plotting theme. facet_wrap [ggplot2::facet_wrap(~ group)]: Split a plot into small panels by one or more grouping variables. ggplot [ggplot2::ggplot(data, aes(...))]: Start a layered grammar-of-graphics plot. aes [ggplot2::aes(x=..., y=..., colour=...)]: Map data variables to graphical features such as x, y or colour. geom_point [ggplot2::geom_point()]: Plot individual observations as points.

The executable statements below reproduce the original completed teaching solution; the short # NOTE comments are additional and do not change program behaviour.

# NOTE: Compute the Pearson linear correlation coefficient.
cor_ahi_cesd <- cor(all_data$ahiTotal,all_data$cesdTotal,use="complete.obs")
# NOTE: Show the result in the Console (or display a ggplot object).
print(c(correlation=cor_ahi_cesd))
# NOTE: Read an input CSV into a data frame; check the working directory.
atsq <- read.csv("data/atsq_scores.csv",stringsAsFactors=FALSE)
# NOTE: Read an input CSV into a data frame; check the working directory.
p_background <- read.csv("data/p_info.csv",stringsAsFactors=FALSE)
# NOTE: Join matching records using the specified key columns.
atsq_joint <- dplyr::inner_join(atsq,p_background,by="id")
# NOTE: Show the result in the Console (or display a ggplot object).
print(c(atsq_rows=nrow(atsq),background_rows=nrow(p_background),joined=nrow(atsq_joint)))

# EXPECTED OUTPUT — Output format / checks (not fabricated values):
# correlation
# # One coefficient in [-1,1].
# atsq_rows background_rows joined
# # Three data-dependent row counts.
# Data-dependent previews are templates, not verified Console output.

correlation
# One coefficient in [-1,1].
atsq_rows background_rows joined
# Three data-dependent row counts.

cor [cor(x, y, use="complete.obs")]: Calculate a correlation coefficient, Pearson by default. print [print(x)]: Display an object or calculated value in the R Console. c [c(a, b, ...)]: Combine multiple values into a vector. read.csv [read.csv("data/file.csv", stringsAsFactors=FALSE)]: Read a comma-separated file into a data frame. inner_join [dplyr::inner_join(x, y, by="id")]: Keep and combine rows whose keys match in both tables. nrow [nrow(data)]: Count the number of rows in a table.

The executable statements below reproduce the original completed teaching solution; the short # NOTE comments are additional and do not change program behaviour.

# NOTE: Define an illustrative vector of fictional reaction times.
rt_demo <- c(620,610,590,605,615,600,625,595,608,612,598,603)
# NOTE: Assign the computed result to a named R object.
rt_n <- length(rt_demo)
# NOTE: Compute an arithmetic mean of the selected numbers.
rt_mean <- mean(rt_demo)
# NOTE: Compute a sample standard deviation.
rt_sd <- sd(rt_demo)
# NOTE: Assign the computed result to a named R object.
rt_se <- rt_sd / sqrt(rt_n)
# NOTE: Show the result in the Console (or display a ggplot object).
print(c(n=rt_n,mean_ms=rt_mean,sd_ms=rt_sd,se_ms=rt_se))


# ============================================================================

# EXPECTED OUTPUT — Exact, deterministic example:
# n = 12
# mean_ms = 606.75
# sd_ms ≈ 10.3320
# se_ms ≈ 2.9826
# Data-dependent previews are templates, not verified Console output.

n = 12
mean_ms = 606.75
sd_ms ≈ 10.3320
se_ms ≈ 2.9826

c [c(a, b, ...)]: Combine multiple values into a vector. length [length(x)]: Return the number of elements in a vector. mean [mean(x, na.rm=FALSE)]: Calculate an arithmetic average. sd [sd(x)]: Calculate the sample standard deviation. sqrt [sqrt(x)]: Calculate the non-negative square root. print [print(x)]: Display an object or calculated value in the R Console.

The executable statements below reproduce the original completed teaching solution; the short # NOTE comments are additional and do not change program behaviour.

# NOTE: Fix the R pseudorandom sequence for reproducible simulation.
set.seed(46)                              # Fix pseudo-random seed for reproducibility.
# NOTE: Compute an arithmetic mean of the selected numbers.
means_n4 <- replicate(1000,mean(sample(rt_demo,4,replace=TRUE)))
# NOTE: Compute an arithmetic mean of the selected numbers.
means_n10 <- replicate(1000,mean(sample(rt_demo,10,replace=TRUE)))
# NOTE: Show the result in the Console (or display a ggplot object).
print(c(sd_n4=sd(means_n4),sd_n10=sd(means_n10)))
# NOTE: Compute an arithmetic mean of the selected numbers.
bootstrap_means <- replicate(1000,mean(sample(rt_demo,rt_n,replace=TRUE)))
# NOTE: Extract specified percentile values from the resampling distribution.
bootstrap_ci <- quantile(bootstrap_means,c(.025,.975))
# NOTE: Show the result in the Console (or display a ggplot object).
print(bootstrap_ci)


# ============================================================================

# EXPECTED OUTPUT — Output format / checks (not fabricated values):
# sd_n4 sd_n10
# # Two simulation SDs (typically sd_n10 < sd_n4).
# 2.5% 97.5%
# # Two bootstrap percentile endpoints; exact values require running R.
# Data-dependent previews are templates, not verified Console output.

sd_n4 sd_n10
# Two simulation SDs (typically sd_n10 < sd_n4).
2.5% 97.5%
# Two bootstrap percentile endpoints; exact values require running R.

set.seed [set.seed(46)]: Fix the pseudorandom generator state for reproducible output. replicate [replicate(B, expression)]: Evaluate an expression repeatedly and collect the results. mean [mean(x, na.rm=FALSE)]: Calculate an arithmetic average. sample [sample(x, size, replace=TRUE)]: Draw elements with or without replacement. print [print(x)]: Display an object or calculated value in the R Console. c [c(a, b, ...)]: Combine multiple values into a vector. sd [sd(x)]: Calculate the sample standard deviation. quantile [quantile(x, probs=c(.025,.975))]: Calculate the requested percentiles of a vector. replace=TRUE [sample(x, n, replace=TRUE)]: Allow an observed data point to appear more than once in a resample.

The executable statements below reproduce the original completed teaching solution; the short # NOTE comments are additional and do not change program behaviour.

# NOTE: Configure the base-R plotting layout.
par(mfrow=c(1,2))
# NOTE: Draw a histogram of the supplied numeric vector.
hist(means_n4,main="Resample size 4",xlab="Mean RT (ms)")
# NOTE: Draw a histogram of the supplied numeric vector.
hist(means_n10,main="Resample size 10",xlab="Mean RT (ms)")
# NOTE: Configure the base-R plotting layout.
par(mfrow=c(1,1))

# EXPECTED OUTPUT — Expected visual output:
# [Plot] Two side-by-side resampled-mean histograms: n=4 and n=10.
# Data-dependent previews are templates, not verified Console output.

[Plot] Two side-by-side resampled-mean histograms: n=4 and n=10.

par [par(mfrow=c(1,2))]: Set graphical parameters such as the plot-panel layout. c [c(a, b, ...)]: Combine multiple values into a vector. hist [hist(x, main="...", xlab="...")]: Draw a Base R histogram.

The executable statements below reproduce the original completed teaching solution; the short # NOTE comments are additional and do not change program behaviour.

# NOTE: Assign the computed result to a named R object.
mu0 <- 600                               # Hypothesised population mean, milliseconds.
# NOTE: Compute t from a mean difference divided by its standard error.
t_manual <- (rt_mean-mu0)/(rt_sd/sqrt(rt_n))
# NOTE: Assign the computed result to a named R object.
df_manual <- rt_n-1
# NOTE: Assign the computed result to a named R object.
two_sided_p <- 2*pt(-abs(t_manual),df=df_manual)
# NOTE: Show the result in the Console (or display a ggplot object).
print(c(t=t_manual,df=df_manual,p=two_sided_p))
# NOTE: Run a one-sample t test and request its confidence interval.
model_t <- t.test(rt_demo,mu=mu0,alternative="two.sided",conf.level=.95)
# NOTE: Show the result in the Console (or display a ggplot object).
print(model_t)


# ============================================================================

# EXPECTED OUTPUT — Exact values where deterministic; otherwise preview:
# t ≈ 2.2631   df = 11   p ≈ 0.04484
# # t.test() additionally prints the 95% confidence interval and sample mean.
# Data-dependent previews are templates, not verified Console output.

t ≈ 2.2631   df = 11   p ≈ 0.04484
# t.test() additionally prints the 95% confidence interval and sample mean.

sqrt [sqrt(x)]: Calculate the non-negative square root. pt [pt(t, df)]: Evaluate the cumulative probability for a Student t distribution. abs [abs(x)]: Return the absolute value of each number. print [print(x)]: Display an object or calculated value in the R Console. c [c(a, b, ...)]: Combine multiple values into a vector. t.test [t.test(x, mu=600)]: Perform a Student t test and report a confidence interval. p-value [2 * pt(-abs(t), df)]: Compute the two-sided tail probability under the null model.

The executable statements below reproduce the original completed teaching solution; the short # NOTE comments are additional and do not change program behaviour.

# NOTE: Assign the computed result to a named R object.
critical_t <- qt(.975,df=rt_n-1)
# NOTE: Construct the t interval as mean ± critical t × SE.
ci_manual <- rt_mean + c(-1,1)*critical_t*rt_se
# NOTE: Standardise the mean difference using the sample SD.
cohens_d <- (rt_mean-mu0)/rt_sd
# NOTE: Show the result in the Console (or display a ggplot object).
print(c(ci_lower=ci_manual[1],ci_upper=ci_manual[2],cohens_d=cohens_d))
# NOTE: Assert that a data-quality or numerical check is true; stop on failure.
stopifnot(isTRUE(all.equal(as.numeric(ci_manual),as.numeric(model_t$conf.int),tolerance=1e-8)))


# ============================================================================

# EXPECTED OUTPUT — Exact values where deterministic; otherwise preview:
# ci_lower ≈ 600.1854
# ci_upper ≈ 613.3146
# cohens_d ≈ 0.6533
# # stopifnot() prints nothing if the two CI calculations agree.
# Data-dependent previews are templates, not verified Console output.

ci_lower ≈ 600.1854
ci_upper ≈ 613.3146
cohens_d ≈ 0.6533
# stopifnot() prints nothing if the two CI calculations agree.

qt [qt(.975, df)]: Get a quantile (critical value) of a Student t distribution. c [c(a, b, ...)]: Combine multiple values into a vector. print [print(x)]: Display an object or calculated value in the R Console. stopifnot [stopifnot(condition)]: Stop execution with an error if a logical condition is not true. all.equal [all.equal(x, y)]: Compare objects approximately, allowing small numeric tolerances. as.numeric [as.numeric(x)]: Convert values to numeric form when conversion is meaningful.

The executable statements below reproduce the original completed teaching solution; the short # NOTE comments are additional and do not change program behaviour.

# NOTE: Fit an ordinary least-squares linear model.
fit <- lm(cesdTotal~ahiTotal,data=all_data)
# NOTE: Show the result in the Console (or display a ggplot object).
print(summary(fit)$coefficients)
# NOTE: Show the result in the Console (or display a ggplot object).
print(c(r=cor(all_data$ahiTotal,all_data$cesdTotal),
# NOTE: Continue this R expression with its arguments, values or formatting.
        r_squared=summary(fit)$r.squared))
# Assumptions: independence, approximately linear relationship, conditional errors.


# END OF THE SIX-WEEK COURSE.

# EXPECTED OUTPUT — Output format / checks (not fabricated values):
#                Estimate Std. Error t value Pr(>|t|)
# (Intercept)      ...      ...    ...      ...
# ahiTotal         ...      ...    ...      ...
# r = ... ; r_squared = ...
# # Coefficient values depend on the public dataset.
# Data-dependent previews are templates, not verified Console output.

               Estimate Std. Error t value Pr(>|t|)
(Intercept)      ...      ...    ...      ...
ahiTotal         ...      ...    ...      ...
r = ... ; r_squared = ...
# Coefficient values depend on the public dataset.

lm [lm(y ~ x, data=data)]: Fit a linear statistical model using a formula. print [print(x)]: Display an object or calculated value in the R Console. summary [summary(model)]: Show a descriptive or model-specific statistical summary. c [c(a, b, ...)]: Combine multiple values into a vector. cor [cor(x, y, use="complete.obs")]: Calculate a correlation coefficient, Pearson by default.