NutritionScore monitoring across WaszKrak schools

A simulated dataset of weekly NutritionScore measurements collected from 41 schools across three districts of WaszKrak megapolis (Districts 7, 12, and 23) over 26 weeks. The dataset is designed to illustrate nested (hierarchical) ANOVA with fixed effects, post-hoc comparisons, and the detection of a single outlier school.

NutritionScore is a composite index (0–100) derived from weekly AI health checks performed on students — measuring weight indicators, biochemical markers, and energy levels. It is updated every Friday by the SynBio TierCare diagnostic system.

The story

The dataset originates from a tip sent by Tomasz Bernat, a mathematics teacher at School 4 in District 12, who noticed that his students were unable to concentrate and were falling asleep by 10am. The school nutritionist reported that NutriFirst program scores were within normal range. Bernat did not believe the scores.

Beta and Bit obtained a leaked export of the school monitoring system covering all 41 schools. The nested ANOVA revealed that School 4 — the only school enrolled in the NutriFirst program (SynBio batch SB-2046-NF-07) — scored more than 20 points below every other school in District 12, and below the District 7 mean, despite District 12 being a substantially wealthier district.

A data entry error by a procurement clerk had assigned School 4 to a cartridge batch intended exclusively for districts with MedScore below 55. The batch had reduced protein bioavailability. The error was statistically visible. The students' fatigue was not a mystery. It was a data point.

Statistical design

Schools are nested within districts — School 4 in District 12 is a different entity from School 4 in District 7. Both district and school are treated as fixed effects (not random), because the analysis concerns these specific schools and districts, not schools and districts in general.

The nested model is:

NutritionScore ~ district + district:school

which in R notation is equivalent to aov(Score ~ district/school).

The key finding is a significant school(district) term, driven entirely by School 4 in District 12. Post-hoc Tukey comparisons confirm that School 4 differs significantly from every other District 12 school (all adjusted p < 0.001).

District means (approximate)

District	n schools	Mean Score	SD
D7	11	54.1	3.2
D12	19	66.8	9.1
D23	11	79.3	3.4

The anomalously large SD for District 12 is the first signal that something is wrong — it is more than twice the SD of either other district.

Usage

nutrition

Format

A data frame with 1,066 rows and 5 variables:

school: Character. School identifier, e.g. "D12_S4". Format: district prefix + underscore + S + school number within district. Schools are uniquely identified within districts — D7_S1 and D12_S1 are different schools.
week: Integer (1–26). Observation week within the 26-week monitoring period. Week 1 corresponds to the start of the academic term. NutritionScore is recorded once per week per school.
district: Factor with 3 levels: "D7", "D12", "D23". Ordered by socioeconomic status: D7 (lowest) < D12 (middle) < D23 (highest). District determines baseline NutritionScore through access to food infrastructure, healthcare, and algorithmic resource allocation.
nutrifirst: Logical. TRUE if the school is enrolled in SynBio's NutriFirst synthetic food programme (cartridge batch SB-2046-NF-07). Only one school in the dataset has nutrifirst = TRUE: School 4 in District 12 ("D12_S4"). This school was assigned to the batch by a data entry error — the clerk mistyped the district code. The batch is otherwise distributed exclusively to schools in districts with MedScore below 55.
Score: Numeric (0–100). Weekly NutritionScore for the school, averaged across all students in that school for that week. Derived from SynBio TierCare AI health checks. Higher values indicate better nutritional status. The true school mean is stable across weeks; within-school week-to-week variation reflects natural measurement noise (SD ≈ 4 points).

Source

Simulated dataset generated by data-raw/generate_nutrition.R. The data structure is based on the chapter "The Outlier" in Equations from District 7: A Practical Guide to Linear Models (BetaBit StatPunk universe). All values are fictional.

Examples

data(nutrition)

# District-level summary
aggregate(Score ~ district, data = nutrition, FUN = mean)
#> Error in eval(predvars, data, env): object 'Score' not found
aggregate(Score ~ district, data = nutrition, FUN = sd)
#> Error in eval(predvars, data, env): object 'Score' not found

# School-level means
school_means <- aggregate(Score ~ district + school + nutrifirst,
                          data = nutrition, FUN = mean)
#> Error in eval(predvars, data, env): object 'Score' not found
school_means[order(school_means$Score), ]
#> Error: object 'school_means' not found

# Identify the outlier school
school_means[school_means$nutrifirst == TRUE, ]
#> Error: object 'school_means' not found

# Nested ANOVA: schools nested within districts, both fixed effects
model <- aov(Score ~ district + district:school,
             data = school_means)
#> Error: object 'school_means' not found
summary(model)
#> Error: object 'model' not found

# Post-hoc comparisons within District 12
if (requireNamespace("emmeans", quietly = TRUE)) {
  library(emmeans)
  emm <- emmeans(model,
                 specs = ~ school,
                 data  = school_means[school_means$district == "D12", ])
  pairs(emm, adjust = "tukey")
}
#> Error: object 'model' not found

# Visualise: school means coloured by district and NutriFirst status
if (requireNamespace("ggplot2", quietly = TRUE)) {
  library(ggplot2)
  ggplot(school_means,
         aes(x = district, y = Score,
             colour = district, shape = nutrifirst)) +
    geom_jitter(width = 0.15, size = 3) +
    scale_shape_manual(values = c("FALSE" = 16, "TRUE" = 8)) +
    labs(title = "NutritionScore by district and school",
         subtitle = "Star = NutriFirst batch SB-2046-NF-07") +
    theme_minimal()
}
#> Error: object 'school_means' not found