T-Test: Two-Sample (x_by) — ttest-xby • statim

The x_by implementation performs an independent or paired two-sample t-test. It accepts one or more grouping variables via x_by().

Arguments

The following arguments are passed via ... in TTEST() or via():

.paired: Logical. Whether to perform a paired t-test. Default FALSE.
.mu: Numeric. Hypothesized mean difference. Default 0.
.alt: Direction: "two.sided", "greater", or "less". Default "two.sided".
.ci: Confidence level. Default 0.95.
.first_group: Only if uses state_null(). Considers first term as the first order. Default is NULL.

Variants

"boot": Bootstrap CI. Accepts n (reps) and seed.
"permute": Permutation test. Accepts n and seed.
"contrast": Welch-Satterthwaite linear contrast test. Accepts .w, .mu, .ci, .op.
"multi": Accepts multiple selected group variables

Two-sample t-test default class

By default, returns a class_ttest_two object. 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.

Hypothesis claims

Supports MU() via state_null(). The contrast variant performs Welch-Satterthwaite linear contrast test and additionally accepts contrast coefficients via .w.

Claim order is respected: writing MU(x, g == "a") - MU(x, g == "b") versus MU(x, g == "b") - MU(x, g == "a") flips the sign of estimate and t_stat, since the group with coefficient +1 in the parsed claim becomes x in stats::t.test(). This is implemented via an internal .first_group argument resolved from the claim — it is not meant to be set directly by users. If you call via("base", .first_group = ...) or use update() to override it manually, note that it accepts a single group label (one of the two levels of the grouping variable) and silently falls back to the data's natural level order (unique() on the grouping variable) if NULL, unset, or not found among the levels.

References

Welch, B. L. (1947). The generalization of "Student's" problem when several different population variances are involved. Biometrika, 34(1-2), 28-35. https://doi.org/10.1093/biomet/34.1-2.28

Satterthwaite, F. E. (1946). An approximate distribution of estimates of variance components. Biometrics Bulletin, 2(6), 110-114. https://doi.org/10.2307/3002019

Kutner, M. H., Nachtsheim, C. J., Neter, J., & Li, W. (2004). Applied Linear Statistical Models (5th ed.). McGraw-Hill/Irwin.

Examples

sleep |>
    define_model(x_by(extra, group)) |>
    prepare_test(TTEST) |>
    conclude()
#> 
#> == Model ======================================================================= 
#> 
#> Variable Mapper : x_by 
#> Args : extra | group 
#>     x_vars : 1 
#>     by_vars : 1 
#> 
#> == T-Test ====================================================================== 
#> 
#> -- Summary ---------------------------------------------------------------------
#> 
#> ──────────────────────────────────────────
#>   group  estimate  t_stat    df    p_val  
#> ──────────────────────────────────────────
#>   group   -1.580   -1.861  17.780  0.079  
#> ──────────────────────────────────────────
#> 
#> 
#> -- Confidence Interval ---------------------------------------------------------
#> 
#> ─────────────────────────────
#>   group  lower_95  upper_95  
#> ─────────────────────────────
#>   group   -3.365    0.206    
#> ─────────────────────────────
#> 
#> 

sleep |>
    define_model(x_by(extra, group)) |>
    prepare_test(TTEST) |>
    via("boot", n = 2000) |>
    conclude()
#> 
#> == Model ======================================================================= 
#> 
#> Variable Mapper : x_by 
#> Args : extra | group 
#>     x_vars : 1 
#>     by_vars : 1 
#> 
#> == T-Test · boot =============================================================== 
#> 
#> ============================== Bootstrapped T-test =============================
#> 
#> 
#> -- Summary ---------------------------------------------------------------------
#> 
#> Warning: running command 'tput cols' had status 2
#> -------------------------------
#>   CI     :   [-3.11, -0.0798]
#>   n_reps :               2000
#> -------------------------------
#> 
#> 

# contrast t-test, which allows `state_null()` to have weights
# Around population parameter function `MU()` notation
# Also `%by%` is just the infixed form of `x_by()`
sleep |>
    define_model(extra %by% group) |>
    prepare_test(TTEST) |>
    state_null(
        2 * MU(extra, group == "1") - MU(extra, group == "2") <= 0
    ) |>
    via("contrast") |>
    conclude()
#> 
#> == Model ======================================================================= 
#> 
#> Variable Mapper : x_by 
#> Args : extra | group 
#>     x_vars : 1 
#>     by_vars : 1 
#> 
#> == T-Test · contrast =========================================================== 
#> 
#> -- Summary ---------------------------------------------------------------------
#> 
#> ──────────────────────────────────────────
#>   group  estimate  t_stat    df    p_val  
#> ──────────────────────────────────────────
#>   group   -0.830   -0.640  14.130  0.734  
#> ──────────────────────────────────────────
#> 
#> 
#> -- Confidence Interval ---------------------------------------------------------
#> 
#> ─────────────────────────────
#>   group  lower_95  upper_95  
#> ─────────────────────────────
#>   group   -3.112     Inf     
#> ─────────────────────────────
#> 
#>

T-Test: Two-Sample (`x_by`)