library(readxl)
library(purrr)
library(dplyr)
library(DT)
library(gt)

# ── Load all result tables from the exported Excel workbook ──────────────────
xlsx_path <- "figs/R/PanelCheck_results.xlsx"

table_names <- c(
  "descriptive_stats",
  "descriptive_stats_overall",
  "Table5_perf_counts",
  "Table6_anova_Fratios",
  "panel_performance",
  "assessor_discrimination",
  "assessor_agreement",
  "panel_anova",
  "repeatability_anova",
  "mixed_model_fixed",
  "mixed_model_random",
  "tukey_contrasts",
  "tukey_cld",
  "tukey_emmeans",
  "pca_sample_coords",
  "pca_variable_coords"
)

tables <- map(table_names, \(t) read_xlsx(xlsx_path, sheet = t))
names(tables) <- table_names

Introduction

This report presents the outputs of the PanelCheck R translation — a clean, modular reimplementation of the PanelCheck sensory panel analysis pipeline in R. All analyses were executed via R/run_all.R on the included example dataset (Data_Bread.xlsx), which comprises ratings from 8 assessors across 5 bread samples, collected over 2 replicates and 10 sensory attributes.

The analyses cover four broad areas:

Area	Scripts
Panel performance & ANOVA	`01_panel_performance.R`
Profile visualisation	`02_profile_plots.R`, `05_fvalue_overview.R`
Mixed model & post-hoc testing	`03_mixed_model.R`
Consensus PCA	`04_pca.R`

Tabular results are loaded directly from figs/R/PanelCheck_results.xlsx; figures are embedded from figs/R/.

Descriptive Statistics

Descriptive statistics summarise the distribution of sensory scores across all attributes. The by-sample table breaks scores down per product, whilst the overall table collapses across samples to give panel-wide summaries.

By Sample

Each row represents one attribute–sample combination. Columns report the minimum, maximum, mean, standard deviation (SD), standard error of the mean (SEM), and coefficient of variation (CV%).

tables[["descriptive_stats"]] |>
  mutate(across(where(is.numeric), \(x) round(x, 2))) |>
  datatable(
    filter    = "top",
    rownames  = FALSE,
    extensions = "Buttons",
    options   = list(
      dom        = "Bfrtip",
      buttons    = c("csv", "excel"),
      pageLength = 15,
      scrollX    = TRUE
    ),
    caption = "Table 1. Descriptive statistics per attribute and sample."
  )

Overall

Panel-wide descriptive statistics collapsed across all samples and replicates.

tables[["descriptive_stats_overall"]] |>
  mutate(across(where(is.numeric), \(x) round(x, 2))) |>
  datatable(
    filter    = "top",
    rownames  = FALSE,
    extensions = "Buttons",
    options   = list(
      dom        = "Bfrtip",
      buttons    = c("csv", "excel"),
      pageLength = 15,
      scrollX    = TRUE
    ),
    caption = "Table 2. Overall descriptive statistics per attribute (collapsed across samples)."
  )

Panel Performance

Panel performance is evaluated per assessor and attribute using three complementary metrics:

Discrimination — ability to distinguish between samples (F-value from one-way ANOVA per assessor)
Repeatability — consistency across replicates (CV%)
Agreement — correlation of individual scores with the panel mean

Summary Table

The panel performance table combines all three metrics into a single summary per assessor and attribute. Higher discrimination F-values and agreement correlations, combined with lower repeatability CVs, indicate a well-performing assessor.

tables[["panel_performance"]] |>
  mutate(across(where(is.numeric), \(x) round(x, 2))) |>
  datatable(
    filter    = "top",
    rownames  = FALSE,
    extensions = "Buttons",
    options   = list(
      dom        = "Bfrtip",
      buttons    = c("csv", "excel"),
      pageLength = 15,
      scrollX    = TRUE
    ),
    caption = "Table 3. Combined panel performance metrics per assessor and attribute."
  )

Performance Counts

The counts table summarises how many attributes each assessor performs well, moderately, or poorly on — providing a quick overview of overall panel reliability.

tables[["Table5_perf_counts"]] |>
  gt() |>
  tab_header(
    title    = "Table 4. Panel Performance Count Summary",
    subtitle = "Number of attributes per assessor meeting performance thresholds"
  ) |>
  tab_spanner_delim(delim = "_") |>
  fmt_number(decimals = 2) |>
  opt_row_striping() |>
  opt_table_font(font = google_font("Source Sans Pro")) |>
  tab_options(
    table.font.size    = px(13),
    heading.align      = "left",
    column_labels.font.weight = "bold"
  )

Metric	AS1	AS2	AS3	AS4	AS5	AS6	AS7	AS8
Table 4. Panel Performance Count Summary
Number of attributes per assessor meeting performance thresholds
Discrimination	2.00	7.00	5.00	2.00	4.00	4.00	4.00	7.00
Repeatability	10.00	9.00	9.00	9.00	8.00	10.00	9.00	8.00
No interaction	5.00	5.00	4.00	8.00	6.00	5.00	7.00	9.00
Total	17.00	21.00	18.00	19.00	18.00	19.00	20.00	24.00

Mean Score Plot

The panel mean score plot displays the average rating for each sample across all attributes, providing an at-a-glance view of product differentiation at the panel level.

knitr::include_graphics("figs/R/panel_mean_scores.png")

Assessor Discrimination

Discrimination is assessed via a one-way ANOVA per assessor per attribute. The resulting F-value indicates how well each assessor distinguishes between samples on that attribute — a higher F-value reflects stronger discrimination.

Discrimination Table

tables[["assessor_discrimination"]] |>
  mutate(across(where(is.numeric), \(x) round(x, 2))) |>
  datatable(
    filter    = "top",
    rownames  = FALSE,
    extensions = "Buttons",
    options   = list(
      dom        = "Bfrtip",
      buttons    = c("csv", "excel"),
      pageLength = 15,
      scrollX    = TRUE
    ),
    caption = "Table 5. One-way ANOVA F-values per assessor and attribute (sample discrimination)."
  )

Significance key: *** p < 0.001 · ** p < 0.01 · * p < 0.05 · ns p ≥ 0.05

Discrimination Bars

Each bar represents an assessor’s F-value for a given attribute. Bar colour reflects the significance of the one-way ANOVA for that assessor–attribute combination.

knitr::include_graphics("figs/R/discrimination_bars.png")

Panel ANOVA

A two-way ANOVA is run per attribute at the panel level using car::Anova() (Type II sums of squares). This decomposes variance into four effects:

Sample — significant product differences (the primary goal of profiling)
Assessor — systematic differences in scale use between panellists
Replicate — variation between repeat sessions, nested within assessor; a significant effect indicates poor panel repeatability
Sample × Assessor — interaction indicating disagreement in how assessors rank samples relative to one another

F-ratios are computed as the mean square for each effect divided by the residual mean square. Significance is evaluated against an F-distribution with the corresponding degrees of freedom.

ANOVA F-Ratios

tables[["Table6_anova_Fratios"]] |>
  mutate(across(where(is.numeric), \(x) round(x, 2))) |>
  datatable(
    filter    = "top",
    rownames  = FALSE,
    extensions = "Buttons",
    options   = list(
      dom        = "Bfrtip",
      buttons    = c("csv", "excel"),
      pageLength = 15,
      scrollX    = TRUE
    ),
    caption = "Table 6. Two-way ANOVA F-ratios per attribute (Sample, Assessor, Replicate, Sample × Assessor). F-ratios computed via Type II sums of squares (car::Anova())."
  )

Significance key: *** p < 0.001 · ** p < 0.01 · * p < 0.05 · ns p ≥ 0.05

Panel ANOVA Detail

tables[["panel_anova"]] |>
  mutate(across(where(is.numeric), \(x) round(x, 2))) |>
  datatable(
    filter    = "top",
    rownames  = FALSE,
    extensions = "Buttons",
    options   = list(
      dom        = "Bfrtip",
      buttons    = c("csv", "excel"),
      pageLength = 15,
      scrollX    = TRUE
    ),
    caption = "Table 7. Full two-way ANOVA results per attribute."
  )

Significance key: *** p < 0.001 · ** p < 0.01 · * p < 0.05 · ns p ≥ 0.05

F-Value Heatmap

The heatmap displays F-values for each effect (rows) across all attributes (columns). Warm colours indicate higher F-values and stronger effects.

knitr::include_graphics("figs/R/fvalue_heatmap.png")

F-Value Dotplot

The dotplot provides an alternative view of the same F-values, ordered by magnitude per effect, making it easier to identify the most discriminating attributes.

knitr::include_graphics("figs/R/fvalue_dotplot.png")

P-Value Heatmap

The p-value heatmap highlights which attribute–effect combinations are statistically significant. Each cell is labelled with a significance symbol derived from the two-way ANOVA p-value for that attribute × effect combination.

knitr::include_graphics("figs/R/pvalue_heatmap.png")

Panel ANOVA F-Values Plot

knitr::include_graphics("figs/R/panel_anova_fvalues.png")

Repeatability & Agreement

Repeatability ANOVA

Repeatability is evaluated using a two-way ANOVA (Sample + Replicate) per assessor per attribute. A significant Replicate effect indicates inconsistency across repeat sessions, suggesting poor repeatability for that assessor–attribute combination.

tables[["repeatability_anova"]] |>
  mutate(across(where(is.numeric), \(x) round(x, 2))) |>
  datatable(
    filter    = "top",
    rownames  = FALSE,
    extensions = "Buttons",
    options   = list(
      dom        = "Bfrtip",
      buttons    = c("csv", "excel"),
      pageLength = 15,
      scrollX    = TRUE
    ),
    caption = "Table 8. Repeatability ANOVA (Sample + Replicate effects) per assessor and attribute."
  )

Significance key: *** p < 0.001 · ** p < 0.01 · * p < 0.05 · ns p ≥ 0.05

Assessor Agreement

Agreement is quantified as the Pearson correlation between each assessor’s scores and the panel mean. Values approaching 1 indicate the assessor aligns closely with the consensus; values near 0 or negative indicate systematic disagreement.

tables[["assessor_agreement"]] |>
  mutate(across(where(is.numeric), \(x) round(x, 2))) |>
  datatable(
    filter    = "top",
    rownames  = FALSE,
    extensions = "Buttons",
    options   = list(
      dom        = "Bfrtip",
      buttons    = c("csv", "excel"),
      pageLength = 15,
      scrollX    = TRUE
    ),
    caption = "Table 9. Assessor agreement (correlation with panel mean) per attribute."
  )

Significance key: *** p < 0.001 · ** p < 0.01 · * p < 0.05 · ns p ≥ 0.05

Profile Plots

Profile plots show how each assessor scores samples across all attributes relative to the panel mean (bold line). Deviations from the panel mean reveal individual biases in scale use or perception.

Note: One representative assessor profile (AS1) is shown below. Profiles for all eight assessors are available in figs/R/ and were generated using 02_profile_plots.R.

Assessor Profile (AS1)

knitr::include_graphics("figs/R/profile_AS1.png")

All Assessors Overview

The combined overview plot displays all assessors on a single figure, facilitating rapid identification of outliers or systematic scale deviations.

knitr::include_graphics("figs/R/profile_all_assessors.png")

Spider Plot

The spider (radar) chart displays panel mean scores for each sample across all attributes simultaneously, making it straightforward to compare overall sensory profiles between products.

knitr::include_graphics("figs/R/spider_plot.png")

Mixed Model ANOVA

A linear mixed model is fitted per attribute using lmerTest, with Sample as a fixed effect and Assessor, Assessor:Replicate, and Assessor:Sample as random effects. This approach accounts for the hierarchical structure of panel data and provides more accurate inference than a standard ANOVA.

Model formula:

score ~ Sample + (1 | Assessor) + (1 | Assessor:Replicate) + (1 | Assessor:Sample)

Fixed Effects

The fixed effects table reports the estimated sample means, standard errors, t-values, and p-values for each attribute. A significant Sample effect confirms that the panel reliably distinguishes between products on that attribute.

tables[["mixed_model_fixed"]] |>
  mutate(across(where(is.numeric), \(x) round(x, 2))) |>
  gt() |>
  tab_header(
    title    = "Table 10. Mixed Model Fixed Effects",
    subtitle = "Sample effect estimates per attribute"
  ) |>
  fmt_number(decimals = 2) |>
  tab_style(
    style = cell_text(weight = "bold"),
    locations = cells_column_labels()
  ) |>
  opt_row_striping() |>
  opt_table_font(font = google_font("Source Sans Pro")) |>
  tab_options(
    table.font.size    = px(13),
    heading.align      = "left"
  )

Attribute	F_value	df_num	df_den	p_value	sig
Table 10. Mixed Model Fixed Effects
Sample effect estimates per attribute
Bread-od	0.97	4.00	28.00	0.44	ns
Yeast-od	8.54	4.00	28.00	0.00	***
Off-flav	5.51	4.00	28.00	0.00	**
Colour	15.60	4.00	60.00	0.00	***
Moisture	27.98	4.00	28.00	0.00	***
Tough	44.40	4.00	28.00	0.00	***
Salt-t	57.11	4.00	28.00	0.00	***
Sweet-t	22.30	4.00	28.00	0.00	***
Yeast-t	9.60	4.00	28.00	0.00	***
Other-t	23.12	4.00	28.00	0.00	***

Significance key: *** p < 0.001 · ** p < 0.01 · * p < 0.05 · ns p ≥ 0.05

Random Effects

The random effects table quantifies the variance attributable to each random component (Assessor, Assessor:Replicate, Assessor:Sample, Residual). Large Assessor:Sample variance indicates that panellists disagree on the relative ranking of products.

tables[["mixed_model_random"]] |>
  mutate(across(where(is.numeric), \(x) round(x, 2))) |>
  datatable(
    filter    = "top",
    rownames  = FALSE,
    extensions = "Buttons",
    options   = list(
      dom        = "Bfrtip",
      buttons    = c("csv", "excel"),
      pageLength = 15,
      scrollX    = TRUE
    ),
    caption = "Table 11. Mixed model random effects variance components per attribute."
  )

Post-hoc Analysis — Tukey HSD

Where the mixed model identifies a significant Sample effect, a Tukey HSD post-hoc test is applied to determine which specific sample pairs differ. Compact letter display (CLD) groups are assigned such that samples sharing a letter do not differ significantly at α = 0.05.

Estimated Marginal Means

Estimated marginal means (EMMs) are model-adjusted sample means that account for imbalance and random effects. They provide the best estimates of true sample differences per attribute.

tables[["tukey_emmeans"]] |>
  mutate(across(where(is.numeric), \(x) round(x, 2))) |>
  datatable(
    filter    = "top",
    rownames  = FALSE,
    extensions = "Buttons",
    options   = list(
      dom        = "Bfrtip",
      buttons    = c("csv", "excel"),
      pageLength = 15,
      scrollX    = TRUE
    ),
    caption = "Table 12. Estimated marginal means (EMMs) per sample and attribute."
  )

Compact Letter Display

Each row assigns a CLD group letter to a sample–attribute combination. Samples sharing the same letter do not differ significantly; samples with no shared letters are significantly different.

tables[["tukey_cld"]] |>
  mutate(across(where(is.numeric), \(x) round(x, 2))) |>
  datatable(
    filter    = "top",
    rownames  = FALSE,
    extensions = "Buttons",
    options   = list(
      dom        = "Bfrtip",
      buttons    = c("csv", "excel"),
      pageLength = 15,
      scrollX    = TRUE
    ),
    caption = "Table 13. Compact letter display (CLD) groups from Tukey HSD."
  )

Pairwise Contrasts

Full pairwise contrast table showing estimated differences, standard errors, t-ratios, and adjusted p-values for every sample pair per attribute.

tables[["tukey_contrasts"]] |>
  mutate(across(where(is.numeric), \(x) round(x, 2))) |>
  datatable(
    filter    = "top",
    rownames  = FALSE,
    extensions = "Buttons",
    options   = list(
      dom        = "Bfrtip",
      buttons    = c("csv", "excel"),
      pageLength = 15,
      scrollX    = TRUE
    ),
    caption = "Table 14. Tukey HSD pairwise contrasts per attribute."
  )

Significance key: *** p < 0.001 · ** p < 0.01 · * p < 0.05 · ns p ≥ 0.05

Means & CLD Plot

Points represent estimated marginal means ± 95% confidence intervals. CLD letters appear above each point; samples sharing a letter are not significantly different.

knitr::include_graphics("figs/R/tukey_means_cld.png")

Pairwise P-value Heatmap

The heatmap displays Tukey-adjusted p-values for all pairwise sample comparisons per attribute. Each cell is labelled with a significance symbol; only the lower triangle is shown as comparisons are symmetric.

knitr::include_graphics("figs/R/tukey_heatmap.png")

Variance Components

Variance Breakdown Plot

The stacked bar chart partitions total variance per attribute into four sources: Sample (product effect), Assessor (individual scale use), Assessor:Sample (interaction / disagreement), and Residual (unexplained error). A large Sample proportion relative to residual error indicates the panel is effectively differentiating between products.

knitr::include_graphics("figs/R/variance_components.png")

Consensus PCA

Principal Component Analysis (PCA) is performed on the consensus matrix — the grand mean of all assessor scores per sample and attribute, averaged across replicates. This provides a low-dimensional representation of sample and attribute relationships as perceived by the panel as a whole.

Biplot

The biplot overlays sample scores (points) and attribute loadings (arrows) in the space defined by the first two principal components. Samples close together are perceived as similar; attributes pointing in the same direction are positively correlated.

knitr::include_graphics("figs/R/pca_biplot.png")

Scree Plot

The scree plot shows the percentage of variance explained by each principal component, along with a cumulative variance line. Components to the left of the elbow are typically retained for interpretation.

knitr::include_graphics("figs/R/pca_scree.png")

Variable Loadings

Loading bars show the contribution of each sensory attribute to the first two principal components. Longer bars indicate attributes that drive the most variation in the consensus space.

knitr::include_graphics("figs/R/pca_loadings.png")

Sample Coordinates

The sample coordinate table reports the PCA scores (position on each component) for every sample. These values correspond to the point positions in the biplot.

tables[["pca_sample_coords"]] |>
  mutate(across(where(is.numeric), \(x) round(x, 2))) |>
  gt() |>
  tab_header(
    title    = "Table 15. PCA Sample Coordinates",
    subtitle = "Consensus matrix scores projected onto principal components"
  ) |>
  fmt_number(decimals = 2) |>
  tab_style(
    style = cell_text(weight = "bold"),
    locations = cells_column_labels()
  ) |>
  opt_row_striping() |>
  opt_table_font(font = google_font("Source Sans Pro")) |>
  tab_options(
    table.font.size = px(13),
    heading.align   = "left"
  )

Sample	x	y	Dim.3	Dim.4
Table 15. PCA Sample Coordinates
Consensus matrix scores projected onto principal components
Bread1	−4.64	0.63	0.19	0.03
Bread2	0.80	−2.74	0.52	0.47
Bread3	0.73	−1.20	−0.03	−0.76
Bread4	2.07	2.46	1.15	0.07
Bread5	1.03	0.85	−1.84	0.19

Variable Coordinates

The variable coordinate table reports the PCA loadings (contribution of each attribute to each component), corresponding to the arrow endpoints in the biplot.

tables[["pca_variable_coords"]] |>
  mutate(across(where(is.numeric), \(x) round(x, 2))) |>
  gt() |>
  tab_header(
    title    = "Table 16. PCA Variable Coordinates (Loadings)",
    subtitle = "Sensory attribute contributions to each principal component"
  ) |>
  fmt_number(decimals = 2) |>
  tab_style(
    style = cell_text(weight = "bold"),
    locations = cells_column_labels()
  ) |>
  opt_row_striping() |>
  opt_table_font(font = google_font("Source Sans Pro")) |>
  tab_options(
    table.font.size = px(13),
    heading.align   = "left"
  )

variable	Dim.1	Dim.2	x	y
Table 16. PCA Variable Coordinates (Loadings)
Sensory attribute contributions to each principal component
Yeast-t	0.26	−0.94	0.45	−1.67
Yeast-od	0.42	−0.90	0.73	−1.58
Bread-od	0.57	0.82	1.01	1.45
Salt-t	0.74	0.61	1.31	1.08
Tough	0.85	0.48	1.50	0.84
Other-t	−0.93	0.32	−1.65	0.56
Off-flav	−0.87	0.40	−1.53	0.70
Sweet-t	−0.98	0.03	−1.73	0.06
Moisture	0.97	−0.05	1.72	−0.08
Colour	0.51	0.01	0.90	0.02

Session Information

sessionInfo()

## R version 4.5.2 (2025-10-31)
## Platform: aarch64-apple-darwin20
## Running under: macOS Sequoia 15.3.1
## 
## Matrix products: default
## BLAS:   /System/Library/Frameworks/Accelerate.framework/Versions/A/Frameworks/vecLib.framework/Versions/A/libBLAS.dylib 
## LAPACK: /Library/Frameworks/R.framework/Versions/4.5-arm64/Resources/lib/libRlapack.dylib;  LAPACK version 3.12.1
## 
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
## 
## time zone: Australia/Brisbane
## tzcode source: internal
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
## [1] gt_1.3.0     DT_0.34.0    dplyr_1.2.0  purrr_1.2.1  readxl_1.4.5
## 
## loaded via a namespace (and not attached):
##  [1] jsonlite_2.0.0    compiler_4.5.2    tidyselect_1.2.1  xml2_1.5.2       
##  [5] jquerylib_0.1.4   yaml_2.3.12       fastmap_1.2.0     R6_2.6.1         
##  [9] generics_0.1.4    knitr_1.51        htmlwidgets_1.6.4 tibble_3.3.1     
## [13] bslib_0.10.0      pillar_1.11.1     rlang_1.1.7       cachem_1.1.0     
## [17] xfun_0.56         fs_1.6.6          sass_0.4.10       otel_0.2.0       
## [21] cli_3.6.5         withr_3.0.2       magrittr_2.0.4    crosstalk_1.2.2  
## [25] digest_0.6.39     rstudioapi_0.18.0 lifecycle_1.0.5   vctrs_0.7.1      
## [29] evaluate_1.0.5    glue_1.8.0        cellranger_1.1.0  rmarkdown_2.30   
## [33] tools_4.5.2       pkgconfig_2.0.3   htmltools_0.5.9

PanelCheck — R Analysis Report

Sensory Panel Performance Analysis · Data Bread Example Dataset

16 March 2026

Introduction

Descriptive Statistics

By Sample

Overall

Panel Performance

Summary Table

Performance Counts

Mean Score Plot

Assessor Discrimination

Discrimination Table

Discrimination Bars

Panel ANOVA

ANOVA F-Ratios

Panel ANOVA Detail

F-Value Heatmap

F-Value Dotplot

P-Value Heatmap

Panel ANOVA F-Values Plot

Repeatability & Agreement

Repeatability ANOVA

Assessor Agreement

Profile Plots

Assessor Profile (AS1)

All Assessors Overview

Spider Plot

Mixed Model ANOVA

Fixed Effects

Random Effects

Post-hoc Analysis — Tukey HSD

Estimated Marginal Means

Compact Letter Display

Pairwise Contrasts

Means & CLD Plot

Pairwise P-value Heatmap

Variance Components

Variance Breakdown Plot

Consensus PCA

Biplot

Scree Plot

Variable Loadings

Sample Coordinates

Variable Coordinates

Session Information