K-Group One-Way ANOVA

Between-groups ANOVA with 3+ groups, LSD/HSD post-hoc comparisons

Overview

When the independent variable has three or more groups, a significant omnibus F-test must be followed by pairwise comparisons. psych350lab handles the full workflow: omnibus ANOVA, LSD and Tukey’s HSD minimum mean differences, pairwise comparisons with effect sizes, and power assessment.

1. Run the Analysis

anova_kgroup_answers() performs the omnibus ANOVA, calculates LSD/HSD thresholds, and runs all pairwise comparisons automatically.

library(psych350lab)
library(psych350data)
library(dplyr)

data(superman, package = "psych350data")

# Run k-group ANOVA
kgroup_result <- anova_kgroup_answers(
  data         = superman,
  dv           = "box_office_mil",
  iv           = "decade",
  group_labels = c("1950s", "1970-80s", "2000s", "2010s")
)

# Omnibus results
kgroup_result$ANOVA

# Group descriptives
kgroup_result$Descriptives

# LSD/HSD thresholds
kgroup_result$LSD

# Pairwise comparisons
kgroup_result$Pairwise

What `anova_kgroup_answers()` returns

Element	Contents
`$ANOVA`	`F`, `p_value`, `df_between`, `df_within`, `mse`, `total_n`, `k`, `mean_n`
`$Descriptives`	Tibble with `iv`, `mean`, `sd`, `n`, `group_label` per group
`$LSD`	`lsd_mmd`, `hsd_mmd`, `need_posthoc` (TRUE if p < .05)
`$Pairwise`	List of comparison results, each with `comparison`, `mean_diff`, `lsd_result`, `error_type`, `effect_size`, `power_problem`
`$group_labels`	Character vector of display labels

2. Understanding Pairwise Comparisons

Each element in $Pairwise contains:

comparison — which groups are being compared (e.g., “1950s vs 2000s”)
mean_diff — raw difference between group means
lsd_result — ">", "<", or "=" based on whether |mean_diff| > LSD MMD
error_type — “Type I & III” if significant, “Type II” if not
effect_size — r effect size for the comparison
power_problem — assessment of whether non-significant results may reflect a power issue

3. LSD and HSD Calculation

lsd_hsd_calculator() is called internally but can also be used directly:

lsd_hsd_calculator(
  k              = 4,        # number of groups
  n_per_group    = 8,        # average n per group
  mse            = 1250.5,   # mean square error from omnibus ANOVA
  df_error_input = 28        # df_within from omnibus ANOVA
)

4. Format Results for Worksheets

The k-group ANOVA uses the same format_bg_anova_results() function for the omnibus portion, plus additional pairwise display functions.

# Omnibus results for worksheet
format_bg_anova_results(
  rh_name            = "RH1",
  vars               = c("Decade", "Box Office (millions)"),
  anova_results_list = kgroup_result,
  iv_labels          = c("1950s", "1970-80s", "2000s", "2010s"),
  KEY                = TRUE
)

5. Create APA Tables

# Descriptives table with group means
create_bg_anova_table(
  anova_results_list = kgroup_result,
  iv_name            = "Decade",
  dv_name            = "Box Office (millions)",
  group_labels       = c("1950s", "1970-80s", "2000s", "2010s"),
  KEY                = TRUE,
  table_title        = "Descriptive Statistics for Box Office by Decade"
)

# ANOVA source table
create_anova_source_table(
  anova_results_list = kgroup_result,
  KEY                = TRUE,
  table_title        = "ANOVA Source Table for Box Office by Decade"
)

# LSD pairwise comparisons (answer key)
lsd_pairwise_KEY(kgroup_result)

6. Generate APA Write-Up

apa_kgroup_anova_writeup() produces a write-up that includes the omnibus test, post-hoc comparisons (if significant), and effect size interpretation.

writeup <- apa_kgroup_anova_writeup(
  kgroup_results_list = kgroup_result,
  dv_name             = "box office revenue",
  iv_name             = "decade",
  group_labels        = c("1950s", "1970-80s", "2000s", "2010s"),
  hypothesis          = list(
    direction = "different",
    rh_text   = "box office revenue would differ across decades"
  ),
  posthoc_tests       = c("LSD", "Tukey's HSD")
)

# cat(writeup)

7. Hypothesis Support Evaluation

create_rh_support_text() generates text evaluating whether pairwise results support the research hypothesis:

create_rh_support_text(kgroup_result)

Complete Lab Setup Example

library(psych350lab)
library(psych350data)
library(dplyr)

data(superman, package = "psych350data")

# ── Analysis ─────────────────────────────────────────────
RH1_kgroup <- anova_kgroup_answers(
  data         = superman,
  dv           = "box_office_mil",
  iv           = "decade",
  group_labels = c("1950s", "1970-80s", "2000s", "2010s")
)

# ── Worksheet Output ─────────────────────────────────────
RH1_omnibus_KEY <- format_bg_anova_results(
  rh_name = "RH1",
  vars = c("Decade", "Box Office (millions)"),
  anova_results_list = RH1_kgroup,
  iv_labels = c("1950s", "1970-80s", "2000s", "2010s"),
  KEY = TRUE
)

# ── APA Tables ───────────────────────────────────────────
RH1_desc_table <- create_bg_anova_table(
  anova_results_list = RH1_kgroup,
  iv_name = "Decade", dv_name = "Box Office (millions)",
  group_labels = c("1950s", "1970-80s", "2000s", "2010s"),
  KEY = TRUE,
  table_title = "Descriptive Statistics for Box Office by Decade"
)

RH1_source_table <- create_anova_source_table(
  anova_results_list = RH1_kgroup, KEY = TRUE
)

# ── Write-Up ─────────────────────────────────────────────
RH1_writeup <- apa_kgroup_anova_writeup(
  kgroup_results_list = RH1_kgroup,
  dv_name = "box office revenue",
  iv_name = "decade",
  group_labels = c("1950s", "1970-80s", "2000s", "2010s"),
  hypothesis = list(
    direction = "different",
    rh_text = "box office revenue would differ across decades"
  )
)

Key Functions Reference

Function	Purpose
`anova_kgroup_answers()`	K-group ANOVA with LSD/HSD and pairwise comparisons
`lsd_hsd_calculator()`	Compute LSD and HSD minimum mean differences
`pr_means_to_r()`	Pairwise r effect size from means and MSE
`create_rh_support_text()`	Hypothesis support evaluation text
`format_bg_anova_results()`	Markdown output for worksheets (KEY/BLANK)
`create_bg_anova_table()`	APA descriptives table (flextable)
`create_anova_source_table()`	ANOVA source table (flextable)
`lsd_pairwise_KEY()`	Pairwise comparison answer key
`apa_kgroup_anova_writeup()`	Full APA write-up with post-hoc results