Two continuous variables and the question of whether they move together. What r does and does not tell you, why Quanta hands you three coefficients instead of one, and how to report a correlation matrix in APA 7.
Pearson's r measures the strength and direction of the straight-line relationship between two continuous variables. It runs from −1 to +1. Zero means no linear relationship, which is not the same as no relationship at all.
That distinction is the one worth carrying. A perfect U-shaped relationship can produce an r near zero. Anxiety and performance, dose and response, practice and fatigue all bend, and a correlation coefficient reports almost nothing about them.
Square r and you get the proportion of variance the two variables share. An r of .30, which looks respectable in a table, is 9% shared variance. Reporting r² alongside r keeps a modest relationship from reading as a strong one.
Most packages make you choose a coefficient before you run, which means choosing before you know what the relationship looks like. Quanta reports Pearson r, Spearman rho, and Kendall tau-b together, each with its own p value and n.
That turns a guess into a comparison. Where all three agree, the choice never mattered and you can report the conventional one without hedging. Where Pearson is low and Spearman is high, the relationship is real but not linear, and that gap is the finding rather than a nuisance.
On the self-awareness items in a 250-case sample, Pearson comes to .536, Spearman to .540, and Kendall tau-b to .440. The first two agreeing closely says the relationship is essentially linear; tau reading lower is a property of its scale rather than a weaker result.
A Bayes factor accompanies the coefficients, applied to the Pearson r, with the prior stated as a JZS linear-model prior at r scale 0.35. On a null correlation this is the difference between evidence for no association and not enough data to say.
Both variables continuous. For a single ordinal item, read the Spearman value in the same table.
The relationship is linear. Quanta draws the scatter with a least-squares fit beside the coefficients, so this check takes seconds rather than requiring a separate plotting step. Look at it before you trust the number.
Outliers matter enormously. A single extreme point can create a correlation that does not exist in the rest of the data, or erase one that does. If removing one case changes your conclusion, that is the finding, and it belongs in the paper.
Restricted range shrinks r. Correlating admission test scores with graduate GPA among admitted students understates the true relationship, because everyone who scored poorly was never admitted. The correlation describes the range you observed.
A negative correlation among items that should agree usually means a scoring error. A reverse-worded item that was never rescored correlates negatively with everything else on its scale. See reverse-coded items.
Quanta builds a full matrix from a checkbox list of variables, badged as APA descriptives plus correlations. It carries n, M, and SD for each variable alongside the numbered lower-triangle matrix, with significance marked, which is the form journals ask for and the form that usually has to be assembled by hand.
Because the descriptives sit in the same table as the coefficients, a reader can see the scale of each variable while reading its correlations, and you are not maintaining two tables that have to agree.
Select variables deliberately rather than including everything. A matrix of twenty variables contains 190 coefficients, and at a .05 threshold roughly nine will reach significance by chance alone. If you are scanning a large matrix for significant cells, say so, and treat what you find as hypothesis-generating.
Bring in the data. Import from CSV, Excel, SPSS .sav, Stata .dta, or a ReliCheck survey package. Quanta reports rows, columns, and missing cells as the file lands.
Configure the two fields on the right and the coefficients, the Bayes factor, and the scatter appear together in the center panel.
For a matrix, tick the variables you want in the correlation matrix card and the APA table builds from that selection.
Use the action bar to add the result to a report, copy the table, or copy the APA text. Every result also carries the ReliCheck Intelligence card for a plain-language explanation computed on your Mac.
Report r with its degrees of freedom, p, and a confidence interval. Do not put a zero before the decimal point: correlations cannot exceed one.
Self-awareness items 1 and 2 were positively related, r(248) = .54, p < .001.
Degrees of freedom are n − 2, so a correlation on 250 cases reports r(248). This is one of the most visible errors in a results section.
State which coefficient you report. Since Quanta gives you three, saying nothing invites the question of whether you picked the largest.
Report r² or otherwise address practical size. Significance on a large sample says almost nothing about whether a relationship matters.
Every result carries a ReliCheck Intelligence card with one action: explain this result in plain language. It runs entirely on your Mac with Apple Intelligence. No upload, no API key, nothing to configure. The model only explains the result Quanta has already computed and validated. It never computes a statistic, and it never applies a decision on your behalf.
From the action bar you can add the result to a report, copy the table, or copy the APA text. Exported reports carry the APA table, its note, and a caution specific to that analysis beneath it.
Quanta's correlation and nonparametric procedures are validated against R's cor and against hand-computed closed-form values, matched exactly. Pearson r agrees with R 4.6 and Python 3 to ten decimal places on the published head-to-head. The engine is pure Swift with no R or Python at runtime. Full record on the validation page.
Correlation is part of every Quanta subscription, $9.99 a month or $79.99 a year after the 30-day trial. One price for everyone. See pricing.
The analysis, the report builder, and the on-device explanations all work with the network off. Your dataset is never uploaded.
Spearman for ranks, ordinal data, or curved relationships · Kendall's tau-b for small samples with many ties · Partial correlation holding a third variable constant · the complete list on the analyses page.