In: Math
The test statistic for a sign test is the smaller of the number of positive or negative signs. True False
The given statement is incorrect.
The signs test is an example of non-parametric test which is
used to test if the population median is equal to some particular
value, say . Let
denote the number of observations that are greater than
denote
the number of observations that are lesser than
Logically, if the null hypothesis is assumed to be true, then,
the number of observations which are greater than must be
equal to number of observations smaller than
, thus,
implying that both
and
follow
the Binomial distribution with parameters,
and
.
The test statistic for the signs test, is:
Now the p-value (that is the probability of obtaining a
value greater than or equal to ) will be
computed using the Binomial distribution and compared with the
level of significance,
, to
make a decision regarding the acceptance (if p-value >
) or
the rejection (if p-value <
) of
the null hypothesis.