# Interpretation of EQUIVNONINF (gofind_t) test

Does anyone know how we can interpret the result of:

EQUIVNONINF:gofind_t(alpha,r,s,eps,xv)


I run the following code on this contingency table to find whether these two categorical samples are equivalence?

    T1   T2   T3   T4
G1  57   79   43   41
G2  65   87   44   24

xv<-c(57,79,43,41,65,87,44,24)
EQUIVNONINF::gofind_t(0.05,2,4,0.05,xv)


I obtained the following results:

 n = 440   alpha = 0.05   eps = 0.05   r = 2   s = 4   X(r,s) : 57 79 43 41
65 87 44 24   DSQ_OBS = 0.001079545   VN = 0.01972656   CRIT = 0.0009531352
REJ = 0


When I changed the eps value from 0.05 to 0.06 or higher the results have ben changed as follows:

 n = 440   alpha = 0.05   eps = 0.06   r = 2   s = 4   X(r,s) : 57 79 43 41
65 87 44 24   DSQ_OBS = 0.001079545   VN = 0.01972656   CRIT = 0.002053135
REJ = 1


I was wondering what is the hypothesis here in this case. I think in equivalency test, the null hypothesis (H0) is "these two samples are not equivalence", so we should find enough evidence to reject the null hypothesis (H0) and conclude that these two samples are equivalent, or the difference is minor, right? if it is, how we can determine the right $eps$ value and what these $VN$, $CRIT$, $eps$ and $DSQ_OBS$ exactly show?