Executive Summary

Does reaction ms differ across the 10 days deprived conditions?

Subjects

Conditions

F Statistic

18.703

Headline Test

Greenhouse-Geisser corrected

Headline p-value

< 0.001

Partial Eta-Squared

0.524

Sphericity

violated

Significant Pairs

reaction ms does change across days deprived: the greenhouse-geisser corrected test gives p < 0.001. Mauchly's test rejects sphericity (p < 0.001) and the estimated epsilon is 0.369, below 0.75, so the Greenhouse-Geisser correction is the result to lead with. The condition means run from day_00 at 256.65 to day_09 at 350.85, a spread of 94.20. Partial eta-squared is 0.524 (large effect within subjects); generalized eta-squared, which keeps the subject-to-subject variation in the denominator and is therefore the number comparable to a between-subjects study, is 0.293. 21 of 45 pairwise comparisons survive the Holm correction; the largest is day_00 vs day_09, a difference of -94.20 (95% CI -122.76 to -65.64). Because the same subjects were measured throughout, this is a within-subject comparison, not evidence that days deprived caused the change.

What this means— written from the computed numbers · yours to edit

Reaction time degrades across the 10 days of sleep deprivation: the Greenhouse-Geisser corrected test gives p < 0.001. Sphericity was violated (Mauchly's p < 0.001, epsilon 0.369), so the corrected result is the one to report, and it reaches the same verdict as the uncorrected test. Reaction time rises from 256.65 ms on day_00 to 350.85 ms on day_09, a degradation of 94.20 ms. Partial eta-squared is 0.524 (large effect); generalized eta-squared is 0.293 (the comparable figure for a between-subjects study). 21 of 45 pairwise comparisons survive multiplicity correction, with day_00 vs day_09 showing the largest difference. Because the same subjects were measured throughout, this is a within-subject comparison and does not establish that days of deprivation caused the change—order, practice, fatigue, and other factors that moved with the days remain confounded.

Overview

Analysis Overview

Repeated-measures ANOVA of reaction ms across 10 days deprived conditions on 18 subjects.

N Subjects18

N Conditions10

F Statistic18.703

Partial Eta Squared0.524

What this means— written from the computed numbers · yours to edit

Reaction time was measured across 10 consecutive days of sleep deprivation in 18 subjects, each providing a response under all 10 conditions. A repeated-measures ANOVA separates the stable between-subject differences from the within-subject test, making it more sensitive than comparing independent groups of the same size. This design assumes sphericity—that every pair of conditions has the same variance of within-subject differences—which is tested explicitly and corrected when violated. The F-statistic is 18.703 with partial eta-squared of 0.524, indicating a large effect within subjects.

Data Preparation

Data Quality

Which subjects entered the model, and which could not.

Initial Rows180

Final Rows180

Rows Removed0

Subjects Dropped0

What this means— written from the computed numbers · yours to edit

All 180 rows across 18 subjects and 10 conditions were complete and entered the model; no subjects were dropped for missing data. The conditions are read in temporal order from day_00 through day_09. Because subjects without a complete set of conditions would have been removed entirely rather than imputed, the analysed set could differ systematically from the original if incompleteness was related to reaction time itself—though in this case, all 18 subjects had complete data, so no bias from listwise deletion applies here.

Visualization

Condition Means

Mean reaction ms under each days deprived condition, with 95% confidence intervals.

What this means— written from the computed numbers · yours to edit

Reaction time rises monotonically across the 10 days. Day_00 shows the fastest mean response at 256.652 ms and day_09 the slowest at 350.851 ms, a gap of 94.20 ms. The error bars (95% confidence intervals on each condition's own mean) carry the full between-subject spread and overlap considerably, as they do in repeated-measures designs; the within-subject test works on each subject's own change and never sees this spread. For the narrower intervals that match the actual pairwise comparisons tested, consult the post-hoc table, where each interval is on a within-subject difference. The monotonic rise from day_00 to day_09 is consistent with progressive degradation of reaction time across consecutive days of deprivation.

Visualization

Per-Subject Profiles

Every subject's reaction ms across the days deprived conditions, one row per subject.

What this means— written from the computed numbers · yours to edit

The short answer

Reaction time consistently deteriorates as sleep deprivation deepens across the 10-day period. All 18 subjects showed the same directional pattern, with slowest times appearing at day_09 (the endpoint of the deprivation period). The effect is uniform across individuals rather than driven by a subset.

The detail

Each subject's profile spans day_00 through day_09. The vertical color gradient represents between-subject variation in baseline speed; the horizontal gradient within rows shows the condition effect. 94.44% of subjects move in the same direction from day_00 to day_09 as the group average, confirming a consistent effect. The coldest (fastest) cells cluster in the early days; the hottest (slowest) cells appear in the later days, particularly day_09. For example, subject S309 moved from 222.734 ms at day_00 to 237.314 ms at day_09; subject S310 moved from 199.054 ms to 247.515 ms.

What this can't tell you

This profile chart shows the pattern exists and is consistent across subjects, but does not quantify the size of the effect or test whether it exceeds chance. The statistical test and effect size appear in the methods and posthoc cards.

Data Table

Repeated-Measures ANOVA

Sources of variation, the F test, and the effect sizes.

Source	Df	Sum Sq	F Statistic	P Value	Partial Eta Sq
Subjects (between subjects)	17	2.506e+05	—	n/a	—
days deprived (within subjects)	9	1.662e+05	18.7	< 0.001	0.524
Residual (within subjects)	153	1.511e+05	—	n/a	—

What this means— written from the computed numbers · yours to edit

The repeated-measures table splits variation into the between-subject stratum (sum of squares 250618.108, df 17), the within-subject effect of days deprived (sum of squares 166235.123, df 9), and residual error (sum of squares 151101.039, df 153). The days deprived row carries the test: F(9.00, 153.00) = 18.703, p < 0.001 before sphericity correction. Partial eta-squared is 0.524, representing the share of within-subject variation explained by days deprived; generalized eta-squared is 0.293, which restores the between-subject variance to the denominator and is the figure comparable to a between-subjects study. The sums of squares were independently reproduced from the condition means as a check (relative disagreement 0.00000000).

Data Table

Sphericity & Corrections

Mauchly's test, both epsilon estimates, and the corrected p-values.

Quantity	Value	Interpretation
Mauchly's W	0.000	Likelihood-ratio statistic for sphericity across the 10 conditions; 1 means the pairwise differences all have the same variance.
Mauchly p-value	< 0.001	Sphericity is rejected — read a corrected p-value, not the uncorrected one.
Greenhouse-Geisser epsilon	0.369	How far the covariance departs from sphericity, on a scale from the lower bound 0.111 (worst case) to 1 (perfect). Degrees of freedom are multiplied by it.
Huynh-Feldt epsilon	0.469	A less conservative estimate of the same quantity; preferred when the Greenhouse-Geisser epsilon is at or above 0.75.
Uncorrected p-value	< 0.001	The F test read at 9.00 and 153.00 degrees of freedom.
Greenhouse-Geisser p-value	< 0.001	The same F read at 3.32 and 56.46 degrees of freedom.
Huynh-Feldt p-value	< 0.001	The same F read at 4.22 and 71.81 degrees of freedom.

What this means— written from the computed numbers · yours to edit

Mauchly's test rejects sphericity: W = 0.000, p < 0.001. The Greenhouse-Geisser epsilon is 0.369 (well below the lower bound of 0.111 and the perfect value of 1), indicating substantial departure from the sphericity assumption. Degrees of freedom are multiplied by this epsilon; the corrected test reads F at 3.32 and 56.46 degrees of freedom instead of 9.00 and 153.00. The Huynh-Feldt epsilon is 0.469, a less conservative estimate. Critically, the verdict survives correction: uncorrected p < 0.001, Greenhouse-Geisser p < 0.001, Huynh-Feldt p < 0.001. The conclusion does not depend on the assumption, though the corrected p-value is the honest one to quote. Mauchly's test itself is sensitive to sample size and non-normality, so a non-significant result would be weak evidence rather than proof of sphericity.

Data Table

Which Conditions Differ

Pairwise comparisons across days deprived, corrected for multiplicity.

Comparison	Difference	CI Low	CI High	T Statistic	P Value	P Adjusted	Cohens Dz	Significant
day_00 vs day_09	-94.2	-122.8	-65.64	-6.958	< 0.001	< 0.001	-1.64	yes
day_01 vs day_09	-86.36	-114.3	-58.41	-6.52	< 0.001	< 0.001	-1.537	yes
day_02 vs day_09	-85.49	-115.7	-55.3	-5.975	< 0.001	< 0.001	-1.408	yes
day_00 vs day_08	-79.98	-108.9	-51.05	-5.834	< 0.001	< 0.001	-1.375	yes
day_01 vs day_08	-72.13	-100	-44.22	-5.452	< 0.001	0.002	-1.285	yes
day_02 vs day_08	-71.27	-98.73	-43.8	-5.474	< 0.001	0.002	-1.29	yes
day_03 vs day_09	-67.86	-95.33	-40.39	-5.211	< 0.001	0.003	-1.228	yes
day_04 vs day_09	-62.2	-85.62	-38.78	-5.603	< 0.001	0.001	-1.321	yes
day_00 vs day_07	-62.1	-84.09	-40.11	-5.957	< 0.001	< 0.001	-1.404	yes
day_00 vs day_06	-55.53	-87.46	-23.6	-3.669	0.002	0.048	-0.865	yes
day_01 vs day_07	-54.26	-76.67	-31.84	-5.106	< 0.001	0.003	-1.203	yes
day_03 vs day_08	-53.64	-77.73	-29.55	-4.698	< 0.001	0.007	-1.107	yes
day_02 vs day_07	-53.39	-73.5	-33.28	-5.601	< 0.001	0.001	-1.32	yes
day_00 vs day_05	-51.87	-76.61	-27.13	-4.423	< 0.001	0.011	-1.043	yes
day_04 vs day_08	-47.98	-68	-27.96	-5.057	< 0.001	0.003	-1.192	yes

What this means— written from the computed numbers · yours to edit

All 45 pairwise comparisons of days deprived were tested on each subject's own difference and corrected for multiplicity using the Holm method. 21 comparisons remain significant after correction. The largest effect is day_00 vs day_09: mean within-subject difference −94.199 ms (95% CI −122.764 to −65.635), t(17) = −6.958, p < 0.001, Cohen's dz = −1.64 (large effect). Other substantial differences include day_01 vs day_09 (−86.355 ms, dz −1.537), day_02 vs day_09 (−85.489 ms, dz −1.408), and day_00 vs day_08 (−79.978 ms, dz −1.375). These confidence intervals are much narrower than the error bars on the condition means chart because they reflect within-subject differences, not the full between-subject spread. The overall test was significant, making these comparisons a legitimate follow-up rather than exploratory.

Data Table

Methods & Disclosure

The exact model, formulas, and what the design does not establish.

Item	Detail
Model	aov(reaction ms ~ days deprived with Error(subject / days deprived)) — the within-subject error stratum is separated from the subject stratum, which is what removes the stable subject-to-subject differences from the test.
Subjects analysed	18 subject(s) with a complete set of all 10 conditions; 0 subject(s) dropped as incomplete. Replicate measurements in the same subject-condition cell were averaged (0 cell(s) affected).
Sphericity test	Mauchly's likelihood-ratio test computed directly from the covariance of the repeated measures: W = det(T) divided by the mean-of-eigenvalues to the power 9, where T is the covariance projected onto an orthonormal basis of the 9 contrasts orthogonal to the unit vector, with the standard chi-square approximation and its second-order refinement.
Epsilon corrections	Greenhouse-Geisser epsilon is the squared trace of T divided by 9 times the trace of T squared; Huynh-Feldt rescales it using the 18 subject(s) and 1 between-subjects group(s). Both multiply the numerator and denominator degrees of freedom before the F is read.
Effect sizes	Partial eta-squared is the effect's sum of squares over itself plus its own error stratum (0.524 here). Generalized eta-squared puts the subject variance back into the denominator (0.293), which is why it is much smaller and is the one comparable to a between-subjects study.
Post-hoc comparisons	All 45 pairs of conditions compared with a paired t-test on each subject's own difference, corrected for multiplicity with base p.adjust using the Holm method.
Sums-of-squares cross-check	The condition sum of squares from aov was reproduced from first principles (n times the squared deviations of the condition means); relative disagreement 0.00000000.
What this does not establish	A repeated-measures design removes stable differences between subjects, but it does not make the comparison causal. Anything else that changed alongside 'days deprived' — practice, fatigue, maturation, the order the conditions were run in — remains confounded with it.

What this means— written from the computed numbers · yours to edit

The short answer

The analysis used a repeated-measures ANOVA model that isolates the within-subject effect of days deprived while removing stable differences between subjects. Sphericity assumptions were tested directly from the covariance matrix, and post-hoc comparisons were corrected for 45 pairwise tests using the Holm method. The model is valid for detecting whether reaction time changed across the deprivation period in the same subjects, but cannot rule out confounding from practice, fatigue, or order effects.

The detail

Model: aov(reaction ms ~ days deprived with Error(subject / days deprived)). Subjects analysed: 18 with complete data across all 10 conditions; 0 dropped as incomplete. Sphericity tested via Mauchly's likelihood-ratio (W = det(T) / mean-of-eigenvalues^9). Epsilon corrections applied: partial eta-squared = 0.524; generalized eta-squared = 0.293. Post-hoc: all 45 condition pairs tested with paired t-tests, corrected via Holm method. Sums-of-squares cross-check: relative disagreement 0.00000000.

What this can't tell you

The repeated-measures design controls for stable subject differences but does not establish causation. Anything that changed alongside days deprived—practice, fatigue, order of presentation—remains confounded with the condition effect and could partly or wholly explain the observed slowdown.

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How this was computed method · R source · citation

The code that did it

Repeated-Measures ANOVA — The Same Subjects Across Several Conditions

Every subject is measured under three or more conditions (timepoints, treatments, tasks). Comparing those condition means with an ordinary ANOVA would be wrong: the measurements share a subject, so they are correlated. A repeated-measures ANOVA splits the stable subject-to-subject differences out of the error term, which is what makes the test both correct and far more powerful than the between-subjects version.

Why This Method?

Removing the between-subject variance shrinks the error term, so a real condition effect shows up with far fewer subjects. The price is a new assumption — sphericity, that all pairwise differences between conditions have the same variance. When it fails the F test is anti-conservative (the p-value is too small), so this module tests it (Mauchly) and reports the Greenhouse-Geisser and Huynh-Feldt corrected p-values, leading with the corrected result whenever the assumption is rejected.

What This Analysis Covers

Condition means with confidence intervals (bar chart with error bars)
Per-subject profiles across the conditions (profile grid)
The repeated-measures ANOVA table with partial and generalized eta-squared
Mauchly's test of sphericity plus both epsilon corrections
Pairwise post-hoc comparisons with a multiplicity correction

Standard Library

Platform standard-library module (LAT-1441): runs on ANY dataset via the semantic mapping {subject, condition, value, group}. All narrative is derived from the user's own column names and computed values.

suppressPackageStartupMessages(library(DT))
suppressPackageStartupMessages(library(htmlwidgets))
suppressPackageStartupMessages(library(arrow))
suppressPackageStartupMessages(library(knitr))
suppressPackageStartupMessages(library(rmarkdown))
suppressPackageStartupMessages(library(dplyr))
suppressPackageStartupMessages(library(tidyr))
suppressPackageStartupMessages(library(ggplot2))
suppressPackageStartupMessages(library(stringr))
suppressPackageStartupMessages(library(lubridate))
suppressPackageStartupMessages(library(broom))
suppressPackageStartupMessages(library(Matrix))
suppressPackageStartupMessages(library(cluster))
suppressPackageStartupMessages(library(data.table))

Core Analysis Pipeline

compute_shared <- function(df, params, col_map = list()) {
  # === SHARED EXPORTS ===
  #   initial_rows/final_rows/rows_removed  $ row accounting
  #   subject_h/condition_h/value_h/group_h $ humanized user column names
  #   n_subjects / n_dropped_subjects       $ complete subjects used / dropped
  #   n_conditions / cond_levels            $ the within factor, in reading order
  #   n_replicate_cells                     $ subject-condition cells averaged
  #   f_stat/df1/df2/p_uncorr               $ the within-subject F test
  #   mauchly_W/mauchly_p/sphericity_ok     $ Mauchly's test of sphericity
  #   eps_gg/eps_hf/eps_lb                  $ epsilon corrections + lower bound
  #   p_gg/p_hf                             $ corrected p-values
  #   headline_label/headline_p             $ the result the narrative leads with
  #   partial_eta2/generalized_eta2         $ effect sizes
  #   mixed / group_levels / inter_*        $ optional between-subjects factor
  #   anova_df/sphericity_df/posthoc_df     $ card tables
  #   condition_means_df/profiles_df        $ chart datasets
  #   methods_df                            $ disclosure table
  #   metrics / json_output
  # === /SHARED EXPORTS ===

Step 1: Resolve the mapped columns (humanized for every sentence)

initial_rows <- nrow(df)
  subject_h   <- humanize_semantic("subject", col_map)
  condition_h <- humanize_semantic("condition", col_map)
  value_h     <- humanize_semantic("value", col_map)
  group_h     <- humanize_semantic("group", col_map)

  missing_keys <- setdiff(c("subject", "condition", "value"), names(df))
  if (length(missing_keys) > 0) {
    stop(sprintf("A repeated-measures analysis needs three mapped columns: the subject identifier(&#x27;%s'), the within-subject condition ('%s'), and the measured value ('%s'). Missing: %s.",
                 subject_h, condition_h, value_h,
                 paste(humanize_semantic(missing_keys, col_map), collapse = ", ")))
  }

Step 2: Coerce the measurement to numeric with the 95% rule

v <- df$value
  if (!is.numeric(v)) {
    ch <- as.character(v)
    non_blank <- !is.na(ch) & trimws(ch) != ""
    conv <- suppressWarnings(as.numeric(ch))
    if (sum(non_blank) == 0 ||
        sum(!is.na(conv[non_blank])) < 0.95 * sum(non_blank)) {
      stop(sprintf("The measurement column &#x27;%s' does not look numeric — fewer than 95%% of its values parse as numbers. Map a numeric column as the measurement.",
                   value_h))
    }
    v <- conv
  }
  df$value <- as.numeric(v)

Step 3: Clean the identifiers; blank subject or condition is unusable

sid <- trimws(as.character(df$subject))
  cnd <- trimws(as.character(df$condition))
  bad_id <- is.na(sid) | sid == "" | is.na(cnd) | cnd == ""
  n_blank_id <- sum(bad_id)
  df <- df[!bad_id, , drop = FALSE]
  sid <- sid[!bad_id]; cnd <- cnd[!bad_id]
  if (nrow(df) == 0) {
    stop(sprintf("Every row is missing either &#x27;%s' or '%s', so no repeated measurement could be assembled.",
                 subject_h, condition_h))
  }

Step 4: Sanity-check the within-subject factor before anything else

cond_levels_raw <- unique(cnd)
  k_raw <- length(cond_levels_raw)
  if (k_raw < 2) {
    stop(sprintf("&#x27;%s' has only one distinct value ('%s'), so there is nothing to compare across conditions. A repeated-measures design needs three or more conditions measured on the same subjects.",
                 condition_h, cond_levels_raw[1]))
  }
  if (k_raw == 2) {
    stop(sprintf("&#x27;%s' has exactly two levels ('%s' and '%s'). That is a two-condition design, not a repeated-measures ANOVA — use the paired comparison tool (Before vs After), which gives you the paired t-test, the Wilcoxon signed-rank cross-check, and a confidence interval on the change.",
                 condition_h, order_levels(cond_levels_raw)[1], order_levels(cond_levels_raw)[2]))
  }
  if (k_raw > 12) {
    stop(sprintf("&#x27;%s' has %s distinct values. A repeated-measures factor is a handful of conditions or timepoints measured on every subject; %s values looks like an identifier or a continuous measurement rather than a condition. Map the column that names the condition.",
                 condition_h, fmt_n(k_raw), fmt_n(k_raw)))
  }

Step 5: Average replicate subject-condition cells (reported)

cell_key <- paste(sid, "\r", cnd)
  n_replicate_cells <- sum(duplicated(cell_key))
  n_rows_missing_value <- sum(is.na(df$value))
  agg <- stats::aggregate(list(value = df$value),
                          by = list(subject = sid, condition = cnd),
                          FUN = function(x) if (all(is.na(x))) NA_real_ else mean(x, na.rm = TRUE))

Carry the optional between-subjects group along (first non-blank per subject)

has_group_col <- "group" %in% names(df)
  subj_group <- NULL
  if (has_group_col) {
    gvals <- trimws(as.character(df$group))
    gvals[is.na(gvals) | gvals == ""] <- "Missing"
    first_g <- tapply(gvals, sid, function(x) x[1])
    subj_group <- setNames(as.character(first_g), names(first_g))
  }

Step 6: Completeness — a subject needs every condition, non-missing

cond_levels <- order_levels(cond_levels_raw)
  k <- length(cond_levels)
  ok_cells <- agg[!is.na(agg$value), , drop = FALSE]
  per_subj <- table(ok_cells$subject)
  n_subjects_seen <- length(unique(agg$subject))
  complete_subj <- names(per_subj)[per_subj == k]
  n_subjects <- length(complete_subj)
  n_dropped_subjects <- n_subjects_seen - n_subjects
  max_cells <- if (length(per_subj) > 0) max(as.integer(per_subj)) else 0L

  if (n_subjects == 0) {
    if (max_cells <= 1) {
      stop(sprintf("No value of &#x27;%s' appears under more than one '%s' — every row is a different subject. That is a between-subjects design, not repeated measures: use the group comparison tool, which compares independent groups with ANOVA, Kruskal-Wallis, and pairwise tests.",
                   subject_h, condition_h))
    }
    stop(sprintf("Not one of the %s values of &#x27;%s' has a measurement under all %s levels of '%s'. Repeated-measures ANOVA needs a complete set of conditions per subject; the most any subject has here is %s.",
                 fmt_n(n_subjects_seen), subject_h, fmt_n(k), condition_h, fmt_n(max_cells)))
  }
  if (n_subjects < 5) {
    stop(sprintf("Only %s value(s) of &#x27;%s' have a complete set of all %s '%s' conditions (%s were dropped as incomplete). At least 5 complete subjects are needed for a repeated-measures ANOVA.",
                 fmt_n(n_subjects), subject_h, fmt_n(k), condition_h,
                 fmt_n(n_dropped_subjects)))
  }

Step 7: Build the balanced subject-by-condition matrix

keep <- ok_cells$subject %in% complete_subj
  long <- ok_cells[keep, , drop = FALSE]
  long$subject   <- factor(long$subject, levels = sort(complete_subj))
  long$condition <- factor(long$condition, levels = cond_levels)
  long <- long[order(long$subject, long$condition), , drop = FALSE]
  Y <- matrix(long$value, nrow = n_subjects, ncol = k, byrow = TRUE,
              dimnames = list(levels(long$subject), cond_levels))
  final_rows <- nrow(long)
  rows_removed <- initial_rows - final_rows

  if (isTRUE(stats::var(as.numeric(Y)) == 0) || is.na(stats::var(as.numeric(Y)))) {
    stop(sprintf("&#x27;%s' is constant — every one of the %s retained measurements is the same value (%s). There is no variation to attribute to '%s'.",
                 value_h, fmt_n(final_rows), r3(Y[1, 1]), condition_h))
  }

Step 8: The optional between-subjects factor (mixed design)

mixed <- FALSE
  group_levels <- character(0)
  group_note <- ""
  gvec <- NULL
  if (!is.null(subj_group)) {
    gv <- unname(subj_group[levels(long$subject)])
    gv[is.na(gv)] <- "Missing"
    tabg <- sort(table(gv), decreasing = TRUE)
    if (length(tabg) > 8) {
      gv[gv %in% names(tabg)[-(1:8)]] <- "Other"
      tabg <- sort(table(gv), decreasing = TRUE)
    }
    tiny <- names(tabg)[tabg < 2]
    if (length(tiny) > 0) gv[gv %in% tiny] <- NA_character_
    if (length(unique(stats::na.omit(gv))) >= 2 && !anyNA(gv)) {
      gvec <- factor(gv, levels = order_levels(unique(gv)))
      group_levels <- levels(gvec)
      mixed <- TRUE
      long$group <- rep(gvec, each = k)
    } else {
      group_note <- sprintf("The between-subjects column &#x27;%s' was mapped but did not split the complete subjects into two or more usable groups, so the analysis was run as a pure within-subject design. ",
                            group_h)
    }
  }
  n_between_groups <- if (mixed) length(group_levels) else 1L

Step 9: The repeated-measures ANOVA, via base aov with an Error stratum

fit <- if (mixed)
    suppressWarnings(stats::aov(value ~ group * condition + Error(subject / condition),
                                data = long))
  else
    suppressWarnings(stats::aov(value ~ condition + Error(subject / condition),
                                data = long))
  s <- summary(fit)

  find_term <- function(s, term) {
    for (st in names(s)) {
      tb <- s[[st]][[1]]
      rn <- trimws(rownames(tb))
      if (term %in% rn) {
        i <- which(rn == term)[1]
        j <- which(rn == "Residuals")[1]
        return(list(
          df = tb[["Df"]][i], ss = tb[["Sum Sq"]][i],
          f = tb[["F value"]][i], p = tb[["Pr(>F)"]][i],
          res_df = if (!is.na(j)) tb[["Df"]][j] else NA_real_,
          res_ss = if (!is.na(j)) tb[["Sum Sq"]][j] else NA_real_
        ))
      }
    }
    NULL
  }

  cond_eff <- find_term(s, "condition")
  if (is.null(cond_eff) || is.na(cond_eff$f)) {
    stop(sprintf("The repeated-measures F test for &#x27;%s' could not be computed from the %s complete subjects — the design may be degenerate (for example every subject identical across conditions).",
                 condition_h, fmt_n(n_subjects)))
  }

Subject stratum residual = the between-subject variance the design removes

subj_res_ss <- {
    tb <- s[[1]][[1]]
    rn <- trimws(rownames(tb))
    j <- which(rn == "Residuals")[1]
    if (!is.na(j)) tb[["Sum Sq"]][j] else NA_real_
  }

  f_stat <- cond_eff$f
  df1 <- cond_eff$df
  df2 <- cond_eff$res_df
  p_uncorr <- cond_eff$p
  ss_cond <- cond_eff$ss
  ss_err  <- cond_eff$res_ss

Independent cross-check of the same sums of squares from first principles

grand <- mean(Y)
  ss_cond_direct <- n_subjects * sum((colMeans(Y) - grand)^2)
  ss_check <- if (!mixed && is.finite(ss_cond) && ss_cond > 0)
    abs(ss_cond - ss_cond_direct) / ss_cond else NA_real_

  partial_eta2 <- if (is.finite(ss_cond) && is.finite(ss_err) && (ss_cond + ss_err) > 0)
    ss_cond / (ss_cond + ss_err) else NA_real_
  gen_denom <- sum(c(ss_cond, subj_res_ss, ss_err), na.rm = TRUE)
  generalized_eta2 <- if (is.finite(gen_denom) && gen_denom > 0)
    ss_cond / gen_denom else NA_real_

  inter_eff <- if (mixed) find_term(s, "group:condition") else NULL
  group_eff <- if (mixed) find_term(s, "group") else NULL
  inter_p <- if (!is.null(inter_eff)) inter_eff$p else NA_real_
  inter_peta2 <- if (!is.null(inter_eff) && is.finite(inter_eff$ss) && is.finite(ss_err) &&
                     (inter_eff$ss + ss_err) > 0)
    inter_eff$ss / (inter_eff$ss + ss_err) else NA_real_

Step 10: Sphericity — Mauchly's W and the epsilon corrections,

computed directly from the covariance of the repeated measures. M is an orthonormal basis of the contrast space orthogonal to 1, T = M' SSCP M, and everything below is a function of T only.

p_dim <- k - 1
  df_e_cov <- n_subjects - n_between_groups
  mauchly_W <- NA_real_; mauchly_p <- NA_real_
  eps_gg <- NA_real_; eps_hf <- NA_real_
  eps_lb <- 1 / p_dim
  sph_note <- ""
  if (df_e_cov >= p_dim) {
    SSCP <- if (mixed) {
      Reduce(`+`, lapply(group_levels, function(l) {
        Yi <- Y[gvec == l, , drop = FALSE]
        if (nrow(Yi) < 2) matrix(0, k, k) else (nrow(Yi) - 1) * stats::cov(Yi)
      }))
    } else {
      (n_subjects - 1) * stats::cov(Y)
    }
    M <- qr.Q(qr(matrix(1 / sqrt(k), nrow = k, ncol = 1)), complete = TRUE)[, -1, drop = FALSE]
    Tm <- t(M) %*% SSCP %*% M
    detT <- suppressWarnings(det(Tm))
    trT  <- sum(diag(Tm))
    if (is.finite(detT) && detT > 0 && is.finite(trT) && trT > 0) {

Mauchly's likelihood-ratio statistic with the standard chi-square approximation and its second-order (w2) refinement.

logW <- log(detT) - p_dim * log(trT / p_dim)
      mauchly_W <- exp(logW)
      rho <- 1 - (2 * p_dim^2 + p_dim + 2) / (6 * p_dim * df_e_cov)
      z <- -df_e_cov * rho * logW
      f_df <- p_dim * (p_dim + 1) / 2 - 1
      w2 <- (p_dim + 2) * (p_dim - 1) * (p_dim - 2) *
        (2 * p_dim^3 + 6 * p_dim^2 + 3 * p_dim + 2) / (288 * (df_e_cov * p_dim * rho)^2)
      pr1 <- stats::pchisq(z, f_df, lower.tail = FALSE)
      pr2 <- stats::pchisq(z, f_df + 4, lower.tail = FALSE)
      mauchly_p <- min(1, max(0, pr1 + w2 * (pr2 - pr1)))

Greenhouse-Geisser epsilon from the eigenvalues of T

ev <- suppressWarnings(eigen(Tm, symmetric = TRUE, only.values = TRUE)$values)
      ev <- ev[is.finite(ev)]
      if (length(ev) == p_dim && sum(ev^2) > 0) {
        eps_gg <- min(1, max(eps_lb, sum(ev)^2 / (p_dim * sum(ev^2))))

Huynh-Feldt epsilon (N subjects, g between-subjects groups)

hf_num <- n_subjects * p_dim * eps_gg - 2
        hf_den <- p_dim * (n_subjects - n_between_groups - p_dim * eps_gg)
        eps_hf <- if (is.finite(hf_den) && hf_den > 0)
          min(1, max(eps_lb, hf_num / hf_den)) else NA_real_
      }
    } else {
      sph_note <- sprintf("The covariance of the repeated measures is singular(often because two &#x27;%s' levels carry identical values), so the sphericity test and its corrections could not be computed. ",
                          condition_h)
    }
  } else {
    sph_note <- sprintf("Sphericity needs at least as many subjects as conditions to estimate; with %s complete subjects and %s conditions it is not estimable, so no correction could be applied. ",
                        fmt_n(n_subjects), fmt_n(k))
  }

  p_gg <- if (!is.na(eps_gg))
    stats::pf(f_stat, eps_gg * df1, eps_gg * df2, lower.tail = FALSE) else NA_real_
  p_hf <- if (!is.na(eps_hf))
    stats::pf(f_stat, eps_hf * df1, eps_hf * df2, lower.tail = FALSE) else NA_real_

  sphericity_ok <- !is.na(mauchly_p) && mauchly_p >= 0.05
  sphericity_known <- !is.na(mauchly_p)

Girden's rule: below 0.75 the Greenhouse-Geisser correction, at or above it the less conservative Huynh-Feldt.

if (!sphericity_known) {
    headline_label <- "Uncorrected F test"; headline_p <- p_uncorr
    headline_reason <- sph_note
  } else if (sphericity_ok) {
    headline_label <- "Uncorrected F test"; headline_p <- p_uncorr
    headline_reason <- sprintf("Mauchly&#x27;s test does not reject sphericity (%s), so the uncorrected F test is the one to read. ",
                               fmt_pp(mauchly_p))
  } else if (!is.na(eps_gg) && eps_gg < 0.75) {
    headline_label <- "Greenhouse-Geisser corrected"; headline_p <- p_gg
    headline_reason <- sprintf("Mauchly&#x27;s test rejects sphericity (%s) and the estimated epsilon is %s, below 0.75, so the Greenhouse-Geisser correction is the result to lead with. ",
                               fmt_pp(mauchly_p), r3(eps_gg))
  } else if (!is.na(eps_hf)) {
    headline_label <- "Huynh-Feldt corrected"; headline_p <- p_hf
    headline_reason <- sprintf("Mauchly&#x27;s test rejects sphericity (%s) but the estimated epsilon is %s, at or above 0.75, so the less conservative Huynh-Feldt correction is the result to lead with. ",
                               fmt_pp(mauchly_p), r3(eps_gg))
  } else {
    headline_label <- "Uncorrected F test"; headline_p <- p_uncorr
    headline_reason <- sph_note
  }
  headline_sig <- !is.na(headline_p) && headline_p < 0.05
  flips <- !is.na(p_uncorr) && !is.na(headline_p) &&
    ((p_uncorr < 0.05) != (headline_p < 0.05))

Step 11: Post-hoc pairwise comparisons with a multiplicity correction

adj_method <- tolower(as.character(params$p_adjust %||% "holm"))
  if (!(adj_method %in% c("holm", "bonferroni", "bh", "by", "hochberg", "hommel", "none"))) {
    adj_method <- "holm"
  }
  adj_arg <- switch(adj_method, bh = "BH", by = "BY", adj_method)
  adj_label <- switch(adj_method,
                      holm = "Holm", bonferroni = "Bonferroni",
                      bh = "Benjamini-Hochberg", by = "Benjamini-Yekutieli",
                      hochberg = "Hochberg", hommel = "Hommel",
                      none = "none(raw p-values)")

  pairs <- utils::combn(k, 2)
  pw <- lapply(seq_len(ncol(pairs)), function(i) {
    ia <- pairs[1, i]; ib <- pairs[2, i]
    d <- Y[, ia] - Y[, ib]
    sd_d <- stats::sd(d)
    tt <- tryCatch(stats::t.test(d), error = function(e) NULL)
    data.frame(
      comparison = paste0(cond_levels[ia], " vs ", cond_levels[ib]),
      difference = round(mean(d), 3),
      ci_low  = if (!is.null(tt)) round(as.numeric(tt$conf.int)[1], 3) else NA_real_,
      ci_high = if (!is.null(tt)) round(as.numeric(tt$conf.int)[2], 3) else NA_real_,
      t_statistic = if (!is.null(tt)) round(unname(tt$statistic), 3) else NA_real_,
      p_raw_num = if (!is.null(tt)) tt$p.value else NA_real_,
      cohens_dz = if (!is.na(sd_d) && sd_d > 0) round(mean(d) / sd_d, 3) else NA_real_,
      stringsAsFactors = FALSE
    )
  })
  posthoc_all <- do.call(rbind, pw)
  posthoc_all$p_adj_num <- if (adj_method == "none") posthoc_all$p_raw_num else
    stats::p.adjust(posthoc_all$p_raw_num, method = adj_arg)
  n_sig_pairs <- sum(!is.na(posthoc_all$p_adj_num) & posthoc_all$p_adj_num < 0.05)
  n_pairs <- nrow(posthoc_all)
  ord <- order(-abs(posthoc_all$difference))
  posthoc_ranked <- posthoc_all[ord, , drop = FALSE]
  posthoc_df <- head(posthoc_ranked, 15)
  posthoc_df <- data.frame(
    comparison = posthoc_df$comparison,
    difference = posthoc_df$difference,
    ci_low = posthoc_df$ci_low, ci_high = posthoc_df$ci_high,
    t_statistic = posthoc_df$t_statistic,
    p_value = sapply(posthoc_df$p_raw_num, fmt_p),
    p_adjusted = sapply(posthoc_df$p_adj_num, fmt_p),
    cohens_dz = posthoc_df$cohens_dz,
    significant = ifelse(is.na(posthoc_df$p_adj_num), "",
                         ifelse(posthoc_df$p_adj_num < 0.05, "yes", "no")),
    stringsAsFactors = FALSE
  )
  rownames(posthoc_df) <- NULL
  top_pair <- posthoc_ranked[1, ]

Step 12: Condition means with confidence intervals (the bar chart)

condition_means_df <- do.call(rbind, lapply(seq_len(k), function(j) {
    x <- Y[, j]
    m <- mean(x); sdev <- stats::sd(x)
    half <- if (!is.na(sdev) && sdev > 0 && n_subjects > 1)
      stats::qt(0.975, n_subjects - 1) * sdev / sqrt(n_subjects) else 0
    data.frame(condition = cond_levels[j], mean_value = round(m, 3),
               ci_low = round(m - half, 3), ci_high = round(m + half, 3),
               sd_value = round(if (is.na(sdev)) 0 else sdev, 3),
               n = n_subjects, stringsAsFactors = FALSE)
  }))
  rownames(condition_means_df) <- NULL

NA-safe extremes — never which.max over a possibly-all-NA vector

fin <- which(is.finite(condition_means_df$mean_value))
  hi_i <- if (length(fin) > 0) fin[which.max(condition_means_df$mean_value[fin])] else 1L
  lo_i <- if (length(fin) > 0) fin[which.min(condition_means_df$mean_value[fin])] else 1L
  highest_cond <- condition_means_df$condition[hi_i]
  lowest_cond  <- condition_means_df$condition[lo_i]
  spread <- condition_means_df$mean_value[hi_i] - condition_means_df$mean_value[lo_i]

Step 13: Per-subject profile grid — up to 60 subjects, seeded sample

subj_means <- rowMeans(Y)
  show_n <- min(60, n_subjects)
  set.seed(42)
  pick <- if (n_subjects > show_n) sort(sample(n_subjects, show_n)) else seq_len(n_subjects)
  pick <- pick[order(subj_means[pick])]
  profiles_df <- do.call(rbind, lapply(pick, function(i) {
    data.frame(condition = cond_levels,
               subject_label = rownames(Y)[i],
               value = round(as.numeric(Y[i, ]), 3),
               stringsAsFactors = FALSE)
  }))
  rownames(profiles_df) <- NULL

How consistent are the profiles? The share of subjects whose own change from the lowest-mean to the highest-mean condition runs the same way.

same_dir <- mean((Y[, hi_i] - Y[, lo_i]) * sign(spread) > 0)
  pct_same_dir <- 100 * (if (is.finite(same_dir)) same_dir else 0)

Step 14: The ANOVA table

anova_rows <- list()
  add_anova <- function(source, dfv, ssv, fv, pv, peta) {
    anova_rows[[length(anova_rows) + 1]] <<- data.frame(
      source = source,
      df = as.numeric(dfv),
      sum_sq = round(as.numeric(ssv), 3),
      f_statistic = if (is.na(fv)) NA_real_ else round(as.numeric(fv), 3),
      p_value = fmt_p(pv),
      partial_eta_sq = if (is.na(peta)) NA_real_ else round(as.numeric(peta), 3),
      stringsAsFactors = FALSE
    )
  }
  if (mixed && !is.null(group_eff)) {
    g_peta <- if (is.finite(group_eff$ss) && is.finite(group_eff$res_ss) &&
                  (group_eff$ss + group_eff$res_ss) > 0)
      group_eff$ss / (group_eff$ss + group_eff$res_ss) else NA_real_
    add_anova(sprintf("%s(between subjects)", group_h), group_eff$df, group_eff$ss,
              group_eff$f, group_eff$p, g_peta)
    add_anova("Subjects within groups(error)", group_eff$res_df, group_eff$res_ss,
              NA_real_, NA_real_, NA_real_)
  } else {
    add_anova("Subjects(between subjects)",
              if (is.finite(subj_res_ss)) n_subjects - 1 else NA_real_,
              subj_res_ss, NA_real_, NA_real_, NA_real_)
  }
  add_anova(sprintf("%s(within subjects)", condition_h), df1, ss_cond,
            f_stat, p_uncorr, partial_eta2)
  if (mixed && !is.null(inter_eff)) {
    add_anova(sprintf("%s by %s(interaction)", group_h, condition_h),
              inter_eff$df, inter_eff$ss, inter_eff$f, inter_eff$p, inter_peta2)
  }
  add_anova("Residual(within subjects)", df2, ss_err, NA_real_, NA_real_, NA_real_)
  anova_df <- do.call(rbind, anova_rows)
  rownames(anova_df) <- NULL

Step 15: The sphericity table

sph_rows <- list()
  add_sph <- function(quantity, value, interpretation) {
    sph_rows[[length(sph_rows) + 1]] <<- data.frame(
      quantity = quantity, value = value, interpretation = interpretation,
      stringsAsFactors = FALSE)
  }
  add_sph("Mauchly&#x27;s W",
          if (is.na(mauchly_W)) "not estimable" else r3(mauchly_W),
          sprintf("Likelihood-ratio statistic for sphericity across the %s conditions; 1 means the pairwise differences all have the same variance.",
                  fmt_n(k)))
  add_sph("Mauchly p-value",
          if (is.na(mauchly_p)) "not estimable" else fmt_p(mauchly_p),
          if (!sphericity_known) "Sphericity could not be tested on this data."
          else if (sphericity_ok) "Sphericity is not rejected — the uncorrected F test is appropriate."
          else "Sphericity is rejected — read a corrected p-value, not the uncorrected one.")
  add_sph("Greenhouse-Geisser epsilon",
          if (is.na(eps_gg)) "not estimable" else r3(eps_gg),
          sprintf("How far the covariance departs from sphericity, on a scale from the lower bound %s(worst case) to 1 (perfect). Degrees of freedom are multiplied by it.",
                  r3(eps_lb)))
  add_sph("Huynh-Feldt epsilon",
          if (is.na(eps_hf)) "not estimable" else r3(eps_hf),
          "A less conservative estimate of the same quantity; preferred when the Greenhouse-Geisser epsilon is at or above 0.75.")
  add_sph("Uncorrected p-value", fmt_p(p_uncorr),
          sprintf("The F test read at %s and %s degrees of freedom.", r2(df1), r2(df2)))
  add_sph("Greenhouse-Geisser p-value",
          if (is.na(p_gg)) "not estimable" else fmt_p(p_gg),
          if (is.na(eps_gg)) "Not available." else
            sprintf("The same F read at %s and %s degrees of freedom.",
                    r2(eps_gg * df1), r2(eps_gg * df2)))
  add_sph("Huynh-Feldt p-value",
          if (is.na(p_hf)) "not estimable" else fmt_p(p_hf),
          if (is.na(eps_hf)) "Not available." else
            sprintf("The same F read at %s and %s degrees of freedom.",
                    r2(eps_hf * df1), r2(eps_hf * df2)))
  sphericity_df <- do.call(rbind, sph_rows)
  rownames(sphericity_df) <- NULL

Step 16: Methods and disclosure

methods_df <- data.frame(
    item = c(
      "Model",
      "Subjects analysed",
      "Sphericity test",
      "Epsilon corrections",
      "Effect sizes",
      "Post-hoc comparisons",
      "Sums-of-squares cross-check",
      "What this does not establish"),
    detail = c(
      if (mixed)
        sprintf("aov(%s ~ %s by %s with Error(%s / %s)) — a mixed design with &#x27;%s' between subjects and '%s' within subjects.",
                value_h, group_h, condition_h, subject_h, condition_h, group_h, condition_h)
      else
        sprintf("aov(%s ~ %s with Error(%s / %s)) — the within-subject error stratum is separated from the subject stratum, which is what removes the stable subject-to-subject differences from the test.",
                value_h, condition_h, subject_h, condition_h),
      sprintf("%s subject(s) with a complete set of all %s conditions; %s subject(s) dropped as incomplete. Replicate measurements in the same subject-condition cell were averaged(%s cell(s) affected).",
              fmt_n(n_subjects), fmt_n(k), fmt_n(n_dropped_subjects), fmt_n(n_replicate_cells)),
      sprintf("Mauchly&#x27;s likelihood-ratio test computed directly from the covariance of the repeated measures: W = det(T) divided by the mean-of-eigenvalues to the power %s, where T is the covariance projected onto an orthonormal basis of the %s contrasts orthogonal to the unit vector, with the standard chi-square approximation and its second-order refinement.",
              fmt_n(p_dim), fmt_n(p_dim)),
      sprintf("Greenhouse-Geisser epsilon is the squared trace of T divided by %s times the trace of T squared; Huynh-Feldt rescales it using the %s subject(s) and %s between-subjects group(s). Both multiply the numerator and denominator degrees of freedom before the F is read.",
              fmt_n(p_dim), fmt_n(n_subjects), fmt_n(n_between_groups)),
      sprintf("Partial eta-squared is the effect&#x27;s sum of squares over itself plus its own error stratum (%s here). Generalized eta-squared puts the subject variance back into the denominator (%s), which is why it is much smaller and is the one comparable to a between-subjects study.",
              r3(partial_eta2), r3(generalized_eta2)),
      sprintf("All %s pairs of conditions compared with a paired t-test on each subject&#x27;s own difference, corrected for multiplicity with base p.adjust using the %s method.",
              fmt_n(n_pairs), adj_label),
      if (is.na(ss_check)) "Not applicable to this design."
      else sprintf("The condition sum of squares from aov was reproduced from first principles(n times the squared deviations of the condition means); relative disagreement %s.",
                   formatC(ss_check, format = "f", digits = 8)),
      sprintf("A repeated-measures design removes stable differences between subjects, but it does not make the comparison causal. Anything else that changed alongside &#x27;%s' — practice, fatigue, maturation, the order the conditions were run in — remains confounded with it.",
              condition_h))
    , stringsAsFactors = FALSE)

Step 17: Metrics + the one-paragraph computed answer

metrics <- list(
    `Subjects`            = n_subjects,
    `Conditions`          = k,
    `F Statistic`         = round(f_stat, 3),
    `Headline Test`       = headline_label,
    `Headline p-value`    = fmt_p(headline_p),
    `Partial Eta-Squared` = if (is.na(partial_eta2)) NA_real_ else round(partial_eta2, 3),
    `Sphericity`          = if (!sphericity_known) "not estimable"
                            else if (sphericity_ok) "not rejected" else "violated",
    `Significant Pairs`   = as.integer(n_sig_pairs)
  )

  verdict <- if (headline_sig)
    sprintf("%s differs across the %s levels of %s", value_h, fmt_n(k), condition_h)
  else
    sprintf("no reliable difference in %s across the %s levels of %s was found",
            value_h, fmt_n(k), condition_h)

  json_output <- list(
    answer = paste0(
      "Repeated-measures ANOVA of ", value_h, " across ", fmt_n(k), " ", condition_h,
      " conditions measured on the same ", fmt_n(n_subjects), " subjects: ",
      verdict, " (F(", r2(df1), ", ", r2(df2), ") = ", r2(f_stat), ", ",
      headline_label, ", ", fmt_pp(headline_p), "). ",
      "Partial eta-squared is ", r3(partial_eta2), " (", eta_word(partial_eta2),
      ") and generalized eta-squared ", r3(generalized_eta2), ". ",
      if (!sphericity_known) sph_note
      else if (sphericity_ok)
        paste0("Mauchly&#x27;s test does not reject sphericity (", fmt_pp(mauchly_p),
               "), so the uncorrected F test stands. ")
      else
        paste0("Mauchly&#x27;s test rejects sphericity (", fmt_pp(mauchly_p),
               ", Greenhouse-Geisser epsilon ", r3(eps_gg),
               "), so the corrected p-value is the one to read. "),
      fmt_n(n_sig_pairs), " of ", fmt_n(n_pairs),
      " pairwise comparisons remain significant after the ", adj_label, " correction",
      if (n_sig_pairs > 0) paste0(", the largest being ", top_pair$comparison,
                                  " (difference ", r2(top_pair$difference), ")") else "",
      "."
    ),
    cards = lapply(
      c("tldr", "overview", "preprocessing", "condition_means", "subject_profiles",
        "anova_table", "sphericity", "posthoc", "methods"),
      function(cid) list(id = cid, metrics = metrics)
    )
  )

  list(
    initial_rows = initial_rows, final_rows = final_rows, rows_removed = rows_removed,
    subject_h = subject_h, condition_h = condition_h, value_h = value_h, group_h = group_h,
    n_subjects = n_subjects, n_subjects_seen = n_subjects_seen,
    n_dropped_subjects = n_dropped_subjects, n_replicate_cells = n_replicate_cells,
    n_rows_missing_value = n_rows_missing_value, n_blank_id = n_blank_id,
    n_conditions = k, cond_levels = cond_levels,
    f_stat = f_stat, df1 = df1, df2 = df2, p_uncorr = p_uncorr,
    ss_cond = ss_cond, ss_err = ss_err, subj_res_ss = subj_res_ss, ss_check = ss_check,
    partial_eta2 = partial_eta2, generalized_eta2 = generalized_eta2,
    mauchly_W = mauchly_W, mauchly_p = mauchly_p,
    sphericity_ok = sphericity_ok, sphericity_known = sphericity_known,
    sph_note = sph_note, group_note = group_note,
    eps_gg = eps_gg, eps_hf = eps_hf, eps_lb = eps_lb, p_gg = p_gg, p_hf = p_hf,
    headline_label = headline_label, headline_p = headline_p,
    headline_sig = headline_sig, headline_reason = headline_reason, flips = flips,
    mixed = mixed, group_levels = group_levels, n_between_groups = n_between_groups,
    inter_p = inter_p, inter_peta2 = inter_peta2,
    adj_label = adj_label, n_pairs = n_pairs, n_sig_pairs = n_sig_pairs,
    top_pair = top_pair, posthoc_df = posthoc_df,
    anova_df = anova_df, sphericity_df = sphericity_df, methods_df = methods_df,
    condition_means_df = condition_means_df, profiles_df = profiles_df,
    highest_cond = highest_cond, lowest_cond = lowest_cond, spread = spread,
    pct_same_dir = pct_same_dir, n_profiles_shown = length(pick),
    metrics = metrics, json_output = json_output
  )
}

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What's wrong with this card?

Executive Summary

Analysis Overview

Data Quality

Condition Means

Per-Subject Profiles

The short answer

The detail

What this can't tell you

Repeated-Measures ANOVA

Sphericity & Corrections

Which Conditions Differ

Methods & Disclosure

The short answer

The detail

What this can't tell you

Repeated-Measures ANOVA — The Same Subjects Across Several Conditions

Why This Method?

What This Analysis Covers

Standard Library

Core Analysis Pipeline

Step 1: Resolve the mapped columns (humanized for every sentence)

Step 2: Coerce the measurement to numeric with the 95% rule

Step 3: Clean the identifiers; blank subject or condition is unusable

Step 4: Sanity-check the within-subject factor before anything else

Step 5: Average replicate subject-condition cells (reported)

Step 6: Completeness — a subject needs every condition, non-missing

Step 7: Build the balanced subject-by-condition matrix

Step 8: The optional between-subjects factor (mixed design)

Step 9: The repeated-measures ANOVA, via base aov with an Error stratum

Step 10: Sphericity — Mauchly's W and the epsilon corrections,

Step 11: Post-hoc pairwise comparisons with a multiplicity correction

Step 12: Condition means with confidence intervals (the bar chart)

Step 13: Per-subject profile grid — up to 60 subjects, seeded sample

Step 14: The ANOVA table

Step 15: The sphericity table

Step 16: Methods and disclosure

Step 17: Metrics + the one-paragraph computed answer

Cite this analysis

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