Researchers routinely compute correlations between variables, but the “right” correlation method depends on what kinds of variables are being compared. Pearson correlation is the default in most software, yet it is only optimal for continuous-continuous pairs. When variables are binary, ordinal, or categorical, specialised methods (point-biserial, phi, polychoric, polyserial, Cramer’s V, Kendall’s tau, and others) are more appropriate.
The scale of the problem is visible in published research. For the accompanying paper (Harshvardhan and Ranjan, 2026), we traced correlation usage through the replication supplements of published economics articles: across 197 papers issuing at least one correlation command, 92.3% of the calls were Pearson, and 88% of the papers used Pearson and nothing else, whatever the variable types involved. Recomputing 3,322 variable pairs from those supplements shows when that default is harmless and when it is not: the type-appropriate method diverges from the authors’ choice in 8.1% of pairs where no variable is ordinal, but in every single one of the 732 pairs involving an ordinal variable. Where the methods diverge the median change in the coefficient is small (\(|\Delta r| \approx 0.017\)), but the distribution has a long tail (reaching \(0.47\)), and in 36 pairs the divergence moves the result across the conventional \(p < 0.05\) threshold.
smartcor automates this process: it detects variable types, selects the best method, and explains its reasoning.
The main function is smart_cor(). Pass two vectors and
it will figure out the rest:
# continuous + continuous → Pearson
smart_cor(mtcars$mpg, mtcars$wt)
#>
#> ── Variable types ──
#>
#> ℹ Detected as continuous (numeric with 25 unique values).
#> mtcars$mpg: "continuous"
#> ℹ Detected as continuous (numeric with 29 unique values).
#> mtcars$wt: "continuous"
#>
#> ── Method selection ──
#>
#> ✔ Selected: Pearson Correlation
#>
#> ── Smart Correlation ───────────────────────────────────────────────────────────
#> Estimate: -0.8677
#> Method: Pearson Correlation
#> Variables: mtcars$mpg ("continuous") × mtcars$wt ("continuous")
#> N: 32
#> p-value: < 0.001
#> Test: t-test on r (cor.test)
#> H0: rho = 0
#> Small p-values (e.g., p < 0.05) indicate evidence against H0.
#> 95% CI: [-0.9338, -0.7441]
#> Source: Fisher z (cor.test)
#>
#> Both variables are continuous; Pearson correlation selected.
#>
#> ℹ Alternatives: "spearman" and "kendall" (pass `method = "..."` to use)# continuous + binary → point-biserial (= Pearson)
smart_cor(mtcars$mpg, mtcars$vs)
#>
#> ── Variable types ──
#>
#> ℹ Detected as continuous (numeric with 25 unique values).
#> mtcars$mpg: "continuous"
#> ℹ Detected as binary (numeric with 2 unique values: 0, 1).
#> mtcars$vs: "binary"
#>
#> ── Method selection ──
#>
#> ✔ Selected: Point-Biserial Correlation (= Pearson)
#>
#> ── Smart Correlation ───────────────────────────────────────────────────────────
#> Estimate: 0.6640
#> Method: Point-Biserial Correlation (= Pearson)
#> Variables: mtcars$mpg ("continuous") × mtcars$vs ("binary")
#> N: 32
#> p-value: < 0.001
#> Test: t-test on r (cor.test)
#> H0: rho_pb = 0
#> Small p-values (e.g., p < 0.05) indicate evidence against H0.
#> 95% CI: [0.4104, 0.8223]
#> Source: Fisher z (cor.test); = Pearson
#>
#> One variable is continuous and the other is binary. Point-biserial correlation
#> is mathematically identical to Pearson when the binary variable is coded 0/1.When both variables have a small number of unique values, smartcor detects them as ordinal:
# numeric variables with ≤10 unique values are treated as ordinal by default;
# assume_latent_normal controls whether polychoric or Kendall is used
smart_cor(mtcars$gear, mtcars$carb, assume_latent_normal = FALSE)
#>
#> ── Variable types ──
#>
#> ℹ Detected as ordinal (numeric with 3 unique values, at or below threshold of 10).
#> mtcars$gear: "ordinal"
#> ℹ Detected as ordinal (numeric with 6 unique values, at or below threshold of 10).
#> mtcars$carb: "ordinal"
#>
#> ── Method selection ──
#>
#> ✔ Selected: Kendall's Tau-b
#>
#> ── Smart Correlation ───────────────────────────────────────────────────────────
#> Estimate: 0.0980
#> Method: Kendall's Tau-b
#> Variables: mtcars$gear ("ordinal") × mtcars$carb ("ordinal")
#> N: 32
#> p-value: 0.5302
#> Test: asymptotic normal (cor.test, exact = FALSE)
#> H0: tau = 0
#> Small p-values (e.g., p < 0.05) indicate evidence against H0.
#> 95% CI: [-0.1455, 0.3303]
#> Source: Fieller, Hartley, and Pearson (1957)
#>
#> Both variables are ordinal. Kendall's tau selected (no latent normality
#> assumption; stable bias across distributions).
#>
#> ℹ Alternatives: "polychoric", "spearman", and "gamma" (pass `method = "..."` to use)# some categorical data
colour = factor(sample(c("red", "blue", "green"), 100, replace = TRUE))
shape = factor(sample(c("circle", "square", "triangle"), 100, replace = TRUE))
smart_cor(colour, shape)
#>
#> ── Variable types ──
#>
#> ℹ Detected as categorical (factor/character with 3 levels).
#> colour: "categorical"
#> ℹ Detected as categorical (factor/character with 3 levels).
#> shape: "categorical"
#>
#> ── Method selection ──
#>
#> ✔ Selected: Cramer's V
#>
#> ── Smart Correlation ───────────────────────────────────────────────────────────
#> Estimate: 0.1748
#> Method: Cramer's V
#> Variables: colour ("categorical") × shape ("categorical")
#> N: 100
#> p-value: 0.1912
#> Test: Pearson chi-square test of independence
#> H0: variables are independent
#> Small p-values indicate evidence that the variables are not independent.
#> 95% CI: [0.0000, 0.2790]
#> Source: Noncentral chi-square pivot
#>
#> Both variables are categorical. Cramer's V selected as the standard symmetric
#> measure of nominal association.
#>
#> ℹ Alternatives: "theils_u" and "tschuprows_t" (pass `method = "..."` to use)If the automatic detection gets it wrong, you can override:
# force cyl to be treated as continuous
smart_cor(mtcars$mpg, mtcars$cyl, y_type = "continuous")
#>
#> ── Variable types ──
#>
#> ℹ Detected as continuous (numeric with 25 unique values).
#> mtcars$mpg: "continuous"
#> mtcars$cyl: "continuous" (user-specified)
#>
#> ── Method selection ──
#>
#> ✔ Selected: Pearson Correlation
#>
#> ── Smart Correlation ───────────────────────────────────────────────────────────
#> Estimate: -0.8522
#> Method: Pearson Correlation
#> Variables: mtcars$mpg ("continuous") × mtcars$cyl ("continuous")
#> N: 32
#> p-value: < 0.001
#> Test: t-test on r (cor.test)
#> H0: rho = 0
#> Small p-values (e.g., p < 0.05) indicate evidence against H0.
#> 95% CI: [-0.9258, -0.7163]
#> Source: Fisher z (cor.test)
#>
#> Both variables are continuous; Pearson correlation selected.
#>
#> ℹ Alternatives: "spearman" and "kendall" (pass `method = "..."` to use)smart_cor(mtcars$mpg, mtcars$wt, method = "spearman")
#>
#> ── Variable types ──
#>
#> ℹ Detected as continuous (numeric with 25 unique values).
#> mtcars$mpg: "continuous"
#> ℹ Detected as continuous (numeric with 29 unique values).
#> mtcars$wt: "continuous"
#>
#> ── Method ──
#>
#> ℹ User specified method: "spearman"
#>
#> ── Smart Correlation ───────────────────────────────────────────────────────────
#> Estimate: -0.8864
#> Method: Spearman Rank Correlation
#> Variables: mtcars$mpg ("continuous") × mtcars$wt ("continuous")
#> N: 32
#> p-value: < 0.001
#> Test: t approximation (cor.test, exact = FALSE)
#> H0: rho_S = 0
#> Small p-values (e.g., p < 0.05) indicate evidence against H0.
#> 95% CI: [-0.9503, -0.7511]
#> Source: Bonett and Wright (2000)
#>
#> Method selected by user: spearmansmart_cormat() computes all pairwise correlations for a
data frame, using the best method for each pair:
mat = smart_cormat(
mtcars[, c("mpg", "cyl", "vs", "gear")],
assume_latent_normal = FALSE
)
#>
#> ── Smart Correlation Matrix (4 variables) ──────────────────────────────────────
#>
#> ── Detected variable types ──
#>
#> mpg: "continuous"
#> cyl: "ordinal"
#> vs: "binary"
#> gear: "ordinal"
#>
#> ── Computing correlations ──
#>
#> ℹ Processing 6 variable pairs...
#> ✔ Done. 6 pairs computed.
mat
#>
#> ── Smart Correlation Matrix ────────────────────────────────────────────────────
#>
#> ── Variable types ──
#>
#> mpg: "continuous"
#> cyl: "ordinal"
#> vs: "binary"
#> gear: "ordinal"
#>
#> ── Correlations ──
#>
#> mpg cyl vs gear
#> mpg 1.00 -0.91 0.66 0.54
#> cyl -0.91 1.00 -0.88 -0.51
#> vs 0.66 -0.88 1.00 0.30
#> gear 0.54 -0.51 0.30 1.00
#> ── Methods used ──
#> mpg cyl vs gear
#> mpg Pr Sp PB Sp
#> cyl Sp Kn RB Kn
#> vs PB RB Ph RB
#> gear Sp Kn RB Kn
#>
#> ℹ Legend:
#> "Pr" = Pearson Correlation
#> "Sp" = Spearman Rank Correlation
#> "PB" = Point-Biserial Correlation (= Pearson)
#> "Kn" = Kendall's Tau-b
#> "RB" = Rank-Biserial Correlation
#> "Ph" = Phi Coefficient (= Pearson for 0/1)Both smart_cor() and smart_cormat() support
tidy() for integration with the tidyverse:
res = smart_cor(mtcars$mpg, mtcars$wt, verbose = FALSE)
tidy(res)
#> # A tibble: 1 × 20
#> var_x var_y x_type y_type estimate method method_label rationale statistic
#> <chr> <chr> <chr> <chr> <dbl> <chr> <chr> <chr> <dbl>
#> 1 mtcars$m… mtca… conti… conti… -0.868 pears… Pearson Cor… Both var… -9.56
#> # ℹ 11 more variables: p.value <dbl>, p_method <chr>, null_hypothesis <chr>,
#> # p_interpretation <chr>, ci_lower <dbl>, ci_upper <dbl>, conf_level <dbl>,
#> # ci_method <chr>, ci_source <chr>, n <int>, n_complete <int>tidy(mat)
#> # A tibble: 6 × 20
#> var_x var_y x_type y_type estimate method method_label rationale statistic
#> <chr> <chr> <chr> <chr> <dbl> <chr> <chr> <chr> <dbl>
#> 1 mpg cyl continuous ordin… -0.911 spear… Spearman Ra… One vari… 10425.
#> 2 mpg vs continuous binary 0.664 point… Point-Biser… One vari… 4.86
#> 3 mpg gear continuous ordin… 0.543 spear… Spearman Ra… One vari… 2495.
#> 4 cyl vs ordinal binary -0.881 rank_… Rank-Biseri… One vari… -3.91
#> 5 cyl gear ordinal ordin… -0.513 kenda… Kendall's T… Both var… -3.16
#> 6 vs gear binary ordin… 0.302 rank_… Rank-Biseri… One vari… 1.43
#> # ℹ 11 more variables: p.value <dbl>, p_method <chr>, null_hypothesis <chr>,
#> # p_interpretation <chr>, ci_lower <dbl>, ci_upper <dbl>, conf_level <dbl>,
#> # ci_method <chr>, ci_source <chr>, n <int>, n_complete <int>Use available_methods() to see what methods are
available for a given variable-type pair:
available_methods("ordinal", "ordinal")
#> # A tibble: 4 × 2
#> method label
#> <chr> <chr>
#> 1 polychoric Polychoric Correlation
#> 2 kendall Kendall's Tau-b
#> 3 spearman Spearman Rank Correlation
#> 4 gamma Goodman-Kruskal's Gamma
available_methods("continuous", "binary")
#> # A tibble: 2 × 2
#> method label
#> <chr> <chr>
#> 1 pearson Pearson Correlation
#> 2 point_biserial Point-Biserial Correlation (= Pearson)
available_methods("categorical", "categorical")
#> # A tibble: 3 × 2
#> method label
#> <chr> <chr>
#> 1 cramers_v Cramer's V
#> 2 theils_u Theil's U (Uncertainty Coefficient)
#> 3 tschuprows_t Tschuprow's TThe method selection is based on the following decision matrix, drawn from simulation studies comparing correlation methods (Harshvardhan and Ranjan, 2026):
| Variable types | Default method | Alternative |
|---|---|---|
| Correlation methods (signed, from -1 to +1) | ||
| Continuous + continuous | Pearson | Spearman (suggested, especially if nonlinear) |
| Continuous + binary | Pearson = point-biserial | — |
| Binary + binary | Pearson = phi | Tetrachoric (preferred, if latent normality holds) |
| Continuous + ordinal | Spearman/Kendall | Polyserial (preferred, if latent normality holds) |
| Ordinal + ordinal | Kendall’s tau | Polychoric (preferred, if latent normality holds) |
| Binary + ordinal | Rank-biserial | Spearman |
| Association measures (unsigned, from 0 to 1) | ||
| Continuous + categorical | Cramer’s V (binned) | — |
| Binary + categorical | Cramer’s V | — |
| Ordinal + categorical | Cramer’s V | — |
| Categorical + categorical | Cramer’s V | Theil’s U, Tschuprow’s T |
Count variables are treated as numeric continuous variables, so each count combination follows the corresponding continuous row.
Key findings from the simulation studies:
When the decision matters (ordinal or binary variables), the default
assume_latent_normal = "auto" runs a likelihood-ratio
chi-square test on the pair via test_bivariate_normality()
and lets the data decide:
A binary-binary pair is the exception: its 2 x 2 table is saturated
(df = 0), the test cannot run, so smartcor uses phi and leaves
tetrachoric to an explicit assume_latent_normal = TRUE or
method = "tetrachoric". Set
assume_latent_normal = TRUE or FALSE to skip
the test, or NULL to be asked interactively
(non-interactive sessions then default to TRUE).
The latent-variable methods rely on polycor
(polychoric, polyserial, and tetrachoric estimates, with their standard
errors). It is listed under Imports, so it installs with
smartcor.
When a latent-variable estimator fails numerically on a particular
dataset, such as a singular Hessian or a sparse contingency table,
smartcor does not simply error. For the polyserial correlation it first
retries the fit from a safe starting value, since polycor’s default
start for the correlation can land outside \((-1, 1)\) on strongly correlated pairs and
abort the optimiser before it takes a step; this rescues most failures.
Only if no fit can be obtained does smartcor fall back to Kendall’s tau
(for polychoric) or Spearman (for polyserial); the returned
method, method_label, and
rationale then name the method actually used, so the
substitution is visible in the output.