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The Tale of the Strawberries — Measurement Non-Invariance

Source: Cremieux Date Published: November 13, 2025

Core Concept: Measurement Non-Invariance

The central thesis: trends are meaningless if you don't know what you're measuring. Two series can look identical on a chart while being driven by completely different underlying mechanisms — a phenomenon known as measurement non-invariance.

The Strawberry Analogy

The essay's namesake example: both the United States and the European Union show parallel growth in strawberry production over recent decades. On the surface, they look like the same trend. But the mechanisms are entirely different:

  • US: Bred superior strawberry cultivars that yielded 4,800% more strawberries per hectare
  • EU: Simply planted more acres of land

Same aggregate trend, completely different causal stories. Ignoring what's behind the numbers leads to bad policy and worse science.

Real-World Examples

PISA Score Declines

Headlines have warned of declining PISA scores in many Western nations. However, after controlling for demographic changes, the corrected trend is essentially flat. The apparent decline was an artifact of changing student populations, not falling educational quality.

Norwegian Sovereign Wealth

Norway claims massive national wealth figures. But this includes the Government Pension Fund Global — a sovereign wealth fund that is not directly accessible for ordinary government spending. The headline number gives a misleading picture of national prosperity.

LLM IQ Scores

When Large Language Models score IQ 120 on standardized tests, it sounds impressive. But the cognitive processes involved are fundamentally incomparable to human reasoning. An LLM does not "reason" in any human sense — it pattern-matches at enormous scale. The score is measurement-non-invariant across species.

The Key Quote

"You shouldn't assume that common trends mean common causes."

Takeaways

  • Always ask: what is this metric actually measuring?
  • Beware of aggregate trends that mask heterogeneous mechanisms
  • Measurement invariance must be established before comparing across groups, contexts, or time periods
  • In data science and statistics, the hardest question is often not what does the data say? but rather what is the data?