Eq_Testing: Bayesian Equivalence Testing for Cohen's d in t-test Designs
In rnorouzian/BayesianforL2: Introduction to Bayesian Thinking for L2 Researchers

Description Usage Arguments Details Value Author(s) Examples

Provides complete results of Bayesian Equivalence Testing with an "additional function" showing the result of changing the equivalence bounds to any different sizes.

1	Eq_Testing(t, N1, N2, wid = "wi", dL = -.1, dU = .1)

`t`	The observed t-value.
`N1`	Group 1 sample size.
`N2`	Group 2 sample size (if a two-sample design).
`wid`	Width or Scale of a Cauchy prior.
`dL`	Lower limit of equivalence bound for d.
`dU`	Upper limit of equivalence bound for d.

Equivalnce Testing simply presents another alternative to absolute hypotheis testing (i.e., testing whether an effect is excatly 0). Specifically, we allow a bound of values which in our view are practically equivalent to zero to be our null hypothesis (i.e., a composite Null). However, most Bayeian point decisions are better decided upon using a "Decision-Theoritic" approch (see, Berger, 1985).

Provides complete results of Bayesian Equivalence Testing using High Desity Region (HDI) with an "additional function" showing the result of changing the equivalence bounds to any different sizes.

Reza Norouzian <rnorouzian@gmail.com>

# Suppose a researcher obtains a t-value of 1, from 2 groups each with 20 participants.
# The researcher picks a "wi", wide, Cauchy prior. The researcher uses
# dL of -0.1 and dU of 0.1 to see the result of equivalene testing:


 Eq_Testing(t = 1, N1 = 20, N2 = 20, dL = -.1, dU = .1 )