TOSTtwo: TOST function for an independent t-test (Cohen's d)

In Lakens/TOSTER: Two One-Sided Tests (TOST) Equivalence Testing

TOST function for an independent t-test (Cohen's d)

Description

Development on TOSTtwo is complete, and for new code we recommend switching to tsum_TOST, which is easier to use, more featureful, and still under active development.

Usage

TOSTtwo(
  m1,
  m2,
  sd1,
  sd2,
  n1,
  n2,
  low_eqbound_d,
  high_eqbound_d,
  alpha,
  var.equal,
  plot = TRUE,
  verbose = TRUE
)

TOSTtwo.raw(
  m1,
  m2,
  sd1,
  sd2,
  n1,
  n2,
  low_eqbound,
  high_eqbound,
  alpha,
  var.equal,
  plot = TRUE,
  verbose = TRUE
)

Arguments

m1	mean of group 1
m2	mean of group 2
sd1	standard deviation of group 1
sd2	standard deviation of group 2
n1	sample size in group 1
n2	sample size in group 2
low_eqbound_d	lower equivalence bounds (e.g., -0.5) expressed in standardized mean difference (Cohen's d)
high_eqbound_d	upper equivalence bounds (e.g., 0.5) expressed in standardized mean difference (Cohen's d)
alpha	alpha level (default = 0.05)
var.equal	logical variable indicating whether equal variances assumption is assumed to be TRUE or FALSE. Defaults to FALSE.
plot	set whether results should be plotted (plot = TRUE) or not (plot = FALSE) - defaults to TRUE
verbose	logical variable indicating whether text output should be generated (verbose = TRUE) or not (verbose = FALSE) - default to TRUE
low_eqbound	lower equivalence bounds (e.g., -0.5) expressed in raw scale units (e.g., scalepoints)
high_eqbound	upper equivalence bounds (e.g., 0.5) expressed in raw scale units (e.g., scalepoints)

Value

Returns TOST t-value 1, TOST p-value 1, TOST t-value 2, TOST p-value 2, degrees of freedom, low equivalence bound, high equivalence bound, low equivalence bound in Cohen's d, high equivalence bound in Cohen's d, Lower limit confidence interval TOST, Upper limit confidence interval TOST

References

Berger, R. L., & Hsu, J. C. (1996). Bioequivalence Trials, Intersection-Union Tests and Equivalence Confidence Sets. Statistical Science, 11(4), 283-302.

Gruman, J. A., Cribbie, R. A., & Arpin-Cribbie, C. A. (2007). The effects of heteroscedasticity on tests of equivalence. Journal of Modern Applied Statistical Methods, 6(1), 133-140, formula for Welch's t-test on page 135

Examples

## Eskine (2013) showed that participants who had been exposed to organic
## food were substantially harsher in their moral judgments relative to
## those exposed to control (d = 0.81, 95% CI: [0.19, 1.45]). A
## replication by Moery & Calin-Jageman (2016, Study 2) did not observe
## a significant effect (Control: n = 95, M = 5.25, SD = 0.95, Organic
## Food: n = 89, M = 5.22, SD = 0.83). Following Simonsohn's (2015)
## recommendation the equivalence bound was set to the effect size the
## original study had 33% power to detect (with n = 21 in each condition,
## this means the equivalence bound is d = 0.48, which equals a
## difference of 0.384 on a 7-point scale given the sample sizes and a
## pooled standard deviation of 0.894). Using a TOST equivalence test
## with default alpha = 0.05, not assuming equal variances, and equivalence
## bounds of d = -0.43 and d = 0.43 is significant, t(182) = -2.69,
## p = 0.004. We can reject effects larger than d = 0.43.

TOSTtwo(m1=5.25,m2=5.22,sd1=0.95,sd2=0.83,n1=95,n2=89,low_eqbound_d=-0.43,high_eqbound_d=0.43)

Lakens/TOSTER documentation built on April 17, 2024, 6:42 p.m.