Correlation Test: rel interface

The rel implementation performs a correlation test between exactly one independent variable and one response variable.

Use rel() as the variable mapper <var_id> to select this implementation.

Arguments

The following arguments are passed via ... in CORTEST():

.alt

String. One of "two.sided", "greater", or "less". Default "two.sided".

.ci

Numeric. Confidence level. Default 0.95. Not applicable to Spearman and Kendall variants.

.rho

Numeric. Hypothesized population correlation coefficient under H\(_0\). Default 0. Only applicable to the base (Pearson) variant. When 0, delegates to stats::cor.test(). When non-zero, uses a Fisher-z test against the specified null value.

Variants

"spearman"

Spearman's \(\rho\). Uses stats::cor.test() with method = "spearman". No confidence interval is returned. Does not support state_null().

"kendall"

Kendall's \(\tau\). Uses stats::cor.test() with method = "kendall". No confidence interval is returned. Does not support state_null().

Correlation test default class

By default, it returns a class_corr_two object inheriting from class_stat_infer. All variants that also return class_ttest_two inherit auto_tidy() and print() automatically. Otherwise, to process outputs:

• print(): Write it down through print from variant().

• tidy(): Use making_tidy() to register a tidy method if needed.

For the base variant, df, lower_ci, and upper_ci are always populated. For spearman and kendall, those slots are numeric(0) and are omitted from the printed output.

Hypothesis claims

Supports RHO() via state_null(). Only available on the base (Pearson) variant. The claim is parsed as follows:

• The operator maps to .alt: == and != become "two.sided", >= and > become "less", <= and < become "greater".

• The scalar maps to .rho: RHO(x, y) == 0.9, not 0.9 == RHO(x, y), is handled correctly via claim_scalar().

References

Fisher, R. A. (1915). Frequency distribution of the values of the correlation coefficient in samples from an indefinitely large population. Biometrika, 10(4), 507–521. doi:10.2307/2331838

Fisher, R. A. (1921). On the "probable error" of a coefficient of correlation deduced from a small sample. Metron, 1, 3–32.

Zar, J. H. (2010). Biostatistical Analysis (5th ed.). Pearson. Section 19.3.

See also

Other cortest-implementations: cortest-formula

Examples

# base (Pearson)
cars |>
    define_model(rel(speed, dist)) |>
    prepare_test(CORTEST) |>
    conclude()
#> 
#> == Model ======================================================================= 
#> 
#> Variable Mapper : rel 
#> Args : speed ; dist 
#>     x_vars : 1 
#>     resp_vars : 1 
#> 
#> == Correlation Test ============================================================ 
#> 
#> -- Summary ---------------------------------------------------------------------
#> 
#> ─────────────────────────────────────────────────
#>       pair      estimate  statistic  df  p_val   
#> ─────────────────────────────────────────────────
#>   dist ~ speed   0.807      9.464    48  <0.001  
#> ─────────────────────────────────────────────────
#> 
#> 
#> -- Confidence Interval ---------------------------------------------------------
#> 
#> ────────────────────────────────────
#>       pair      lower_95  upper_95  
#> ────────────────────────────────────
#>   dist ~ speed   0.682     0.886    
#> ────────────────────────────────────
#> 
#> 

# Spearman
suppressWarnings({
    cars |>
        define_model(rel(speed, dist)) |>
        prepare_test(CORTEST) |>
        via("spearman") |>
        conclude()
})
#> 
#> == Model ======================================================================= 
#> 
#> Variable Mapper : rel 
#> Args : speed ; dist 
#>     x_vars : 1 
#>     resp_vars : 1 
#> 
#> == Correlation Test · spearman ================================================= 
#> 
#> -- Summary ---------------------------------------------------------------------
#> 
#> ─────────────────────────────────────────────
#>       pair      estimate  statistic  p_val   
#> ─────────────────────────────────────────────
#>   dist ~ speed   0.830    3532.819   <0.001  
#> ─────────────────────────────────────────────
#> 
#> 

# Kendall
suppressWarnings({
    cars |>
        define_model(rel(speed, dist)) |>
        prepare_test(CORTEST) |>
        via("kendall") |>
        conclude()
})
#> 
#> == Model ======================================================================= 
#> 
#> Variable Mapper : rel 
#> Args : speed ; dist 
#>     x_vars : 1 
#>     resp_vars : 1 
#> 
#> == Correlation Test · kendall ================================================== 
#> 
#> -- Summary ---------------------------------------------------------------------
#> 
#> ─────────────────────────────────────────────
#>       pair      estimate  statistic  p_val   
#> ─────────────────────────────────────────────
#>   dist ~ speed   0.669      6.665    <0.001  
#> ─────────────────────────────────────────────
#> 
#> 

# hypothesis claim: two-sided against zero
cars |>
    define_model(rel(speed, dist)) |>
    prepare_test(CORTEST) |>
    state_null(RHO(speed, dist) == 0) |>
    conclude()
#> 
#> == Model ======================================================================= 
#> 
#> Variable Mapper : rel 
#> Args : speed ; dist 
#>     x_vars : 1 
#>     resp_vars : 1 
#> 
#> == Correlation Test ============================================================ 
#> 
#> -- Summary ---------------------------------------------------------------------
#> 
#> ─────────────────────────────────────────────────
#>       pair      estimate  statistic  df  p_val   
#> ─────────────────────────────────────────────────
#>   dist ~ speed   0.807      9.464    48  <0.001  
#> ─────────────────────────────────────────────────
#> 
#> 
#> -- Confidence Interval ---------------------------------------------------------
#> 
#> ────────────────────────────────────
#>       pair      lower_95  upper_95  
#> ────────────────────────────────────
#>   dist ~ speed   0.682     0.886    
#> ────────────────────────────────────
#> 
#> 

# hypothesis claim: non-zero null, one-sided
cars |>
    define_model(rel(speed, dist)) |>
    prepare_test(CORTEST) |>
    state_null(RHO(speed, dist) >= 0.8) |>
    conclude()
#> 
#> == Model ======================================================================= 
#> 
#> Variable Mapper : rel 
#> Args : speed ; dist 
#>     x_vars : 1 
#>     resp_vars : 1 
#> 
#> == Correlation Test ============================================================ 
#> 
#> -- Summary ---------------------------------------------------------------------
#> 
#> ────────────────────────────────────────────
#>       pair      estimate  statistic  p_val  
#> ────────────────────────────────────────────
#>   dist ~ speed   0.807      0.133    0.553  
#> ────────────────────────────────────────────
#> 
#> 
#> -- Confidence Interval ---------------------------------------------------------
#> 
#> ────────────────────────────────────
#>       pair      lower_95  upper_95  
#> ────────────────────────────────────
#>   dist ~ speed     -1      0.876    
#> ────────────────────────────────────
#> 
#>