AI correlation audit: preserve pairs and check Pearson r

What question does this paired-data audit answer?

An AI correlation audit starts by preserving which two numbers belong to the same source identifier. Pearson’s correlation coefficient r describes the direction and strength of linear association in supplied pairs. It is not a probability, a model accuracy score or evidence that changing one variable causes another to change.

The English card contains five deliberately constructed pairs with a perfect negative linear pattern. x and y are abstract teaching measurements, not revenue, advertising spend or observed model performance. No random sample, intervention or real statistical experiment was performed. Perfect teaching inputs make the arithmetic easy to inspect; they do not represent typical business data.

Write the rule first: “Practice V1; B1–B5; preserve every ID’s x–y pair; include all supplied pairs; change no source values.” Sorting the x and y columns independently could create different pairs. Filling an unknown value or removing an inconvenient record would also create a different source rather than audit this one.

The artificial intelligence guide provides broader context. The output here is a saved row-product and squared-value ledger with column totals and a reproducible coefficient calculation. The familiar warning about correlation and causation is not the whole task: another reader must be able to reconstruct the number from the original paired source.

How do the five source pairs stay attached to their IDs?

Copy the three-column card below. B1 pairs x=1 with y=10, while B5 pairs x=5 with y=2. Do not store the columns as unrelated lists and later assume that their positions still match. Keep the identifier and both values on the same source row throughout the calculation.

As x increases across these constructed pairs, y decreases. That visual direction is an initial reasonableness check, not proof of causation or predictive reliability. A scatter plot would place each pair as a point; drawing one is optional for this manual ledger. No chart or software run transforms fictional inputs into measured observations.

If a new pair is added later, label it as a new source version and recompute the relevant totals. Do not attach the old coefficient to a changed list. An unknown member of a real pair requires a separate source decision; it must not be silently replaced by zero just to complete the table.

The mean and median audit inspects a single complete numeric variable and a sorted copy. This task uses two measurements per identifier. Correct marginal totals alone cannot establish correct pairing, because rearranging one column can change the cross-products without changing either column’s sum.

Which products and squares should be checked row by row?

Open a calculator. For each row, multiply x by y to obtain xy. Square x and y separately to obtain x² and y². For B3 the products are 3×6=18, 3×3=9 and 6×6=36. Squaring means multiplying a value by itself, not multiplying it by two.

After completing all rows, sum each of the five numeric columns separately. The totals are Σx=15, Σy=30, Σxy=70, Σx²=55 and Σy²=220. There are n=5 complete pairs. The symbol Σ means sum. Keep these labels beside the totals so they cannot be swapped during substitution.

In particular, Σxy is the sum of the row-by-row products. It is not the product of the two column totals: here those values are 70 and 15×30=450 respectively. The distinction is central to the correlation formula. A fluent answer that substitutes one for the other would not preserve the paired-data calculation.

Check at least one row directly against its source ID before accepting the totals. B4 must still pair 4 and 4, producing 16 in all three derived columns. The AI data analysis guide covers a wider reporting workflow; this exercise creates a specific paired arithmetic trail rather than a general explanation of trends or possible drivers.

How is the negative coefficient calculated from the totals?

Use the raw-sum formula r = [n×Σxy − Σx×Σy] / √([n×Σx² − (Σx)²] × [n×Σy² − (Σy)²]). The square-root sign applies to the product of the two bracketed factors. Keep the square of a sum distinct from the sum of squares: both appear in the same expression but mean different operations.

First calculate the numerator: 5×70−15×30=350−450=−100. The x factor is 5×55−15²=275−225=50. The y factor is 5×220−30²=1100−900=200. Their product is 10000 and its positive square root is 100. The coefficient is therefore −100/100=−1.

This describes perfect negative linear association among the five supplied pairs. The negative sign shows direction, not weakness. Both −1 and +1 have absolute value one and represent perfect linear relationships with opposite directions. r is unitless; −1 is not a negative success probability, and +1 would not mean 100% task success.

A constant variable can make the denominator zero, in which case Pearson r is undefined. Do not invent zero or perfect correlation for that situation. Our supplied denominator is positive and equals 100. The segment-rate audit instead checks subgroup and pooled proportions. No subgroup mixture, treatment winner or percentage pooling is calculated here.

How should the three interpretation claims be judged?

Claim one says: “A perfect coefficient proves that x causes y.” Mark it unsupported. A numerical relationship does not establish how the observations were generated. This card supplies no intervention, random assignment, causal design or information about other influences. The accepted finding is limited to the constructed five pairs and their descriptive r=−1.

Claim two says: “A negative coefficient always means weak association.” Reject it. The sign describes opposite direction, while magnitude describes linear strength. The absolute value of −1 is one. Do not use positive and negative as labels for good and bad performance; that is not what these signs mean.

Claim three says: “The perfect card guarantees that all future pairs will follow this line.” Mark it unsupported. No out-of-sample evaluation or population inference has been performed. We calculate neither a forecast nor a significance test, and the coefficient does not certify a model’s reliability. Any future-data claim requires separate evidence about collection and applicability.

OpenStax documents paired displays, the raw-sum coefficient, its sign and magnitude, and the distinction between association and causal evidence. The two linked pages belong to one textbook authority, not independent institutional studies. The chart audit checks axes and percentage claims rather than paired cross-products. General prompt advice also warns against causal overstatement; the concrete artifact here goes further by preserving every source pair and the calculation behind the reported coefficient.

What must your saved calculation record contain?

On Windows, open Start, type Notepad and launch the editor. Head the document “Paired correlation audit V1.” Add the boundary card and all five original identifier–x–y pairs. Follow them with the xy, x² and y² ledger, the five column totals, n and each formula stage.

Before saving, include all three claim decisions with their evidence. Write an unresolved question: “How were real pairs collected, and what separate design or evaluation would support a causal or future-data claim?” The fictional source does not answer it. A correct coefficient must not hide that limitation.

Press Ctrl+S, choose Documents and save as paired-correlation-audit-V1.txt. Close the editor and reopen the file from the folder. Verify B3’s pair 3 and 6, the product sum 70, the numerator −100 and the final −1 coefficient. Confirm that the note calls the result descriptive and unitless rather than a probability or a forecast.

For an optional second opinion, supply only this fictional card to an assistant you already use. Ask: “Preserve all source ID pairs; do not sort columns separately. Compute each xy, x² and y², show all totals and n, then calculate Pearson r through numerator, two factors and square root. Distinguish sign from strength and make no causal, prediction or model-quality claim.” If no comparison was performed, record it as not performed.

A suggested fifteen-minute allowance gives three minutes to source preservation, five to arithmetic, three to claims and four to saving and reopening. This is a cognitive planning allowance, not a measured participant result or speed promise. In earlier public writing about perfection and effectiveness, I described delaying projects while pursuing every detail. Here that principle means completing one reproducible calculation note, not claiming a personal statistical trial or a customer outcome.