# pingouin.tost

pingouin.tost(x, y, bound=1, paired=False, correction=False)[source]

Two One-Sided Test (TOST) for equivalence.

Parameters
x, yarray_like

First and second set of observations. x and y should have the same units. If y is a single value (e.g. 0), a one-sample test is performed.

boundfloat

Magnitude of region of similarity (a.k.a epsilon). Note that this should be expressed in the same unit as x and y.

pairedboolean

Specify whether the two observations are related (i.e. repeated measures) or independent.

correctionauto or boolean

Specify whether or not to correct for unequal variances using Welch separate variances T-test. This only applies if paired is False.

Returns
statspandas.DataFrame
• 'bound': bound (= epsilon, or equivalence margin)

• 'dof': degrees of freedom

• 'pval': TOST p-value

References

1

Schuirmann, D.L. 1981. On hypothesis testing to determine if the mean of a normal distribution is contained in a known interval. Biometrics 37 617.

2

https://cran.r-project.org/web/packages/equivalence/equivalence.pdf

Examples

1. Independent two-sample TOST with a region of similarity of 1 (default)

>>> import pingouin as pg
>>> a = [4, 7, 8, 6, 3, 2]
>>> b = [6, 8, 7, 10, 11, 9]
>>> pg.tost(a, b)
bound  dof      pval
TOST      1   10  0.965097

1. Paired TOST with a different region of similarity

>>> pg.tost(a, b, bound=0.5, paired=True)
bound  dof      pval
TOST    0.5    5  0.954854

1. One sample TOST

>>> pg.tost(a, y=0, bound=4)
bound  dof      pval
TOST      4    5  0.825967