Interpretation – method notes #

The decisions behind the verdicts, bands and legends every module prints – which rule stands behind each part of a verdict and each threshold setting, and the source it rests on. Sections follow the manual pages’.

Verdicts and bands #

A verdict is composed from clauses, not written whole. Decision, direction, band or band across the interval, and an assumption check’s consequence are each a phrase of their own, joined in a fixed order, rather than one sentence per combination – Correlation alone carried 54 such sentences before. One phrase then reads the same on every card and in every language, a combination nobody wrote out cannot be missing, and a table that has no interval or no direction simply leaves that clause out.

The band reads the interval when one is on screen. A point’s band says how large the estimate is and nothing about how sure it is; the interval says both, so when the graded statistic’s interval is shown the verdict names the bands of the smallest and the largest magnitude it contains, and an interval containing the null value – 0 for a difference, 0.5 for a probability of superiority, 1 for a ratio, folded so that OR and 1/OR read alike – has a negligible end. The point’s band stands in three cases: the row has no interval; an adjusted p decides, since the interval on screen is the unadjusted one and would pair a family-wise decision with a per-comparison range; and the graded statistic has no interval of its own, as η²G has none even where η²p’s is printed. A few grades are read on one limit by their sources’ rule – Mokken’s H on its lower limit, SEM’s factor correlations on the limit farther from zero – and their modules’ notes name them.

An equivalence margin hands the verdict to the TOST. “Negligible effect across the CI” describes an interval at the confidence level; it is not an equivalence test, which needs a margin chosen before the data and a (1 − 2α) interval. When the user sets a margin, the verdict is the four-way reading of the two-sided test and the TOST (Lakens 2017), and the band clause never claims equivalence on its own.

“The test and the CI disagree” rather than a silent choice. The decision reads the test and the band reads the interval on screen, and where the two rest on different quantities – a Welch t beside a pooled-SD d, a Woolf or Fisher interval for an odds ratio beside a χ² p, a bootstrap interval beside a Wald p – they can legitimately point different ways. The verdict then says so instead of letting one overrule the other. A different confidence level and a one-sided test also produce such pairs, but predictably, so each gets a note rather than the clause: the always-shown note that an upper-tail F or χ² test beside a two-sided interval lets a significant row’s lower limit reach 0 when α/2 < p ≤ α – reworded for interval methods whose lower limit is not 0 exactly there (bootstrap, ω², ε²) – and, with interpretation on, the note naming which level the decision and which the interval read.

A non-rejection never reads as an assumption met. A check that does not reject has failed to find a violation, not shown there is none – absence of evidence is not evidence of absence (Altman & Bland 1995) – and a pre-test’s non-rejection does not license the test that rests on the assumption (Rochon, Gondan & Kieser 2012). So a check reads “No evidence of …”, “… not rejected” or “No significant …”, and never “met”, “holds”, “assumed”, “confirmed” or “appears normal”.

Caution for a rejection the run does not treat as a violation. Some rejections leave the analysis that ran untouched – non-normality in a group the central limit theorem covers, or no more rejections across many variables than chance alone produces. Reading them Fail would point the user to a switch the recommendations under the table do not make, so they read Caution, a caveat, and the status and the recommendation list draw the line from one split.

A verdict an interval decides is worded as its finding. An indirect effect, a bootstrap row or an AUC against chance is decided by whether its interval at the confidence level set excludes the null, and its verdict reads “Significant indirect effect”, not “CI excludes 0”. A mediation is typed on Zhao, Lynch and Chen’s (2010) five outcomes – complementary, competitive, indirect-only, direct-only, no effect – never “full” or “partial”, labels that follow the sample size (Rucker, Preacher, Tormala & Petty 2011, pp. 364–365).

The best model by an information criterion is “preferred”. AIC ranks models by expected Kullback–Leibler loss, not by fit, so a ranking calls its top model preferred, never better fitting, and each table grades by the criterion it ranks on. ΔAICc up to 7 is plausible, up to 14 equivocal and beyond 14 implausible, read on the continuum of Burnham, Anderson and Huyvaert (2011, p. 25, Fig. 2), who draw it without boundaries: its plausible region ends at “perhaps four to seven” and its implausible one starts at “about 14”, so 7 – the top of their range – and 14 are the app’s placement, an exact 7 or 14 staying in the better grade, and the same cuts grade ΔAIC and ΔQAIC; ΔBIC takes Raftery’s (1995, p. 139) grades as evidence against the row’s model – weak up to 2, positive up to 6, strong up to 10, very strong beyond – an exact 2, 6 or 10 staying in the weaker grade, as his printed ranges 0–2, 2–6 and 6–10 place it.

No observed power. Power computed from the effect a study observed is a one-to-one function of its p-value and “adds nothing to the interpretation of results” (Hoenig & Heisey 2001, p. 20), so no card prints it.

No probability on a magnitude. A band describes an interval, not a probability that the effect is small or large: “likely beneficial” and “possibly small” are magnitude-based inference, which does not control its error rates (Sainani 2018; Sainani, Lohse, Jones & Vickers 2019), and no verdict uses them.

No band without a source. A band reaches the screen only with a published source, cited on the card where it renders; a band nobody could source was dropped or replaced by a sourced rule, and its number stays printed. The grading pass that set this rule dropped, among others, the .85 rung of CFI and TLI, SRMR’s .05 and .10, the correlation bands’ .70 and .90, the correlation ratio’s .005 and .25, and the strength bands of Cramér’s V, the information measures and Chatterjee’s ξ, which Correlation now prints without a word or grades through a sourced conversion. An unsourced threshold is kept only where the user wants one, labelled as the app’s convention – the assumption advisory thresholds.

One statistic, one scale. A measure that is a fixed conversion of d or r under a stated model is graded on the other’s published benchmarks through the conversion, so one effect reads one word whichever measure prints it: Cliff’s δ and the rank-biserial r on Vargha and Delaney’s (2000) A, through $A=(1+\delta )/2$; an odds ratio on Cohen’s d through $d=\ln (\text{OR})\sqrt{3}/\pi$ (Hasselblad & Hedges 1995; Chinn 2000); Kendall’s τ on r through $r=\sin (\pi \tau /2)$; distance correlation on r through the distance correlation of a bivariate normal (Székely, Rizzo & Bakirov 2007), which the app’s own simulation found within .004 of the map it inverts. The rule stores the source’s printed cuts and the conversion – never cuts computed onto the other scale – so a legend quotes the numbers a reader will find in the paper and names the scale they are printed on.

Cohen’s dz and Hedges’ gz print without a band. Their denominator is the spread of the within-pair changes, which shrinks as the two conditions correlate, while Cohen’s benchmarks were written for a d on the spread of the values; graded on them the same change would read a band or two higher in a well-correlated design. The paired measures on the values’ scale, d_av and g_av, carry the bands.

A statistic graded in two modules reads one rule. Each shared rule – the fit cutoffs, the RMSEA interval’s span, skewness and kurtosis, ω_h and coefficient H, AVE, KMO, R², loadings, ΔAIC and ΔBIC, the effect-size families – is one object that every module reading the statistic calls, so the same number cannot earn two words on two cards. A module that wants a different rule records its reason beside it.

Boundaries follow the source’s printed table. Whether a value exactly on a cut belongs to the band above or below is the source’s choice, and each rule reproduces it: a fit index at its cut stays in the better band, Raftery’s 2, 6 and 10 in the weaker grade, a VIF of exactly 5 or 10 below the cut James et al. say it must exceed, an ω_h or ω_hs of exactly .50 in the weak band, since Reise, Bonifay and Haviland (2013) ask for a value “greater than .50”, and a coefficient H of exactly .80 in the adequate one, since Rodriguez, Reise and Haviland (2016) write the top band “(>.80)”. Where a source prints no table or no exact bound, the side is the app’s choice: Burnham, Anderson and Huyvaert’s 7 and 14 stay in the better grade, and ω_h’s .75 opens the strong band, from a source that calls values “closer to .75” much preferred without drawing a line.

No combined fit verdict. Model fit gets one badge per index. Hu and Bentler’s two-index combination rule is the sourced form of a joint verdict, but its cutoffs generalise no further than the simulation conditions that set them (Fan & Sivo 2005; Marsh, Hau & Wen 2004), and a worst-of-four reading has no source at all.

Statistical thresholds #

Two cuts for CFI and TLI, one for SRMR. The default 0.95 for CFI and TLI is Hu and Bentler’s (1999), and 0.90 the older convention for both (Bentler & Bonett 1980); the 0.85 rung below them had no source and went, leaving three bands. For SRMR, 0.08 is Hu and Bentler’s; no source was found for 0.05 or 0.10, so SRMR has one cut and two bands. RMSEA keeps four – 0.05 and 0.08 from Browne and Cudeck (1993), and 0.10, past which they would not employ a model (p. 144) – with Mediocre fit naming the band between the last two. Every fit badge uses the settings’ own words, Excellent, Acceptable and Poor. A saved or imported cutoff set in an earlier shape loads as the default rather than field by field, which would have read old cuts into new bands.

Correlation presets are field norms. The default bands are Cohen’s (1988) 0.10, 0.30 and 0.50 for r; the 0.70 and 0.90 rungs above them had no source and went. Cohen meant his values for fields without norms of their own, and the presets are norms several fields have since measured on the correlations they report: Gignac and Szodorai (2016) for individual differences, Lovakov and Agadullina (2021) for social psychology, Gómez Penedo and Flückiger (2026) for psychotherapy process–outcome research, each with three cuts, and Bosco et al. (2015) for applied psychology and Li (2026) for criminology, with two. The two-cut sources call everything below their first cut small, so their weak band starts at 0 and nothing reads negligible. A preset moves the cuts for coefficients on r’s own scale only; a coefficient graded through a conversion – τ, β, distance correlation and Hoeffding’s D on Cohen’s r cuts, the point-biserial r on McGrath and Meyer’s (2006) 0.10, 0.24 and 0.37, Cramér’s V on Cohen’s w – keeps its source’s bands, and the legend says so. The correlation ratio’s bands are Cohen’s η² benchmarks, 0.01, 0.06 and 0.14.