1. The Mc Nemar ,
Cox and Stuart Test for Significance of
Changes and trend
CREATED BY :
ZUHDHA BASOFI N (A410090204)
NIKEN DWI A. (A410090076)
APRILIA ARISTIYANI (A410090258)

2. DATA
• The data consist of observations on n’
independent bivariate random variables
(Xi,Yi), i= 1,2,…,n’.
a ( the number of pairs
where Xi=0 and Yi=0 )
b ( the number of pairs
where Xi=0 and Yi=1 )
c ( the number of pairs
where Xi=1 and Yi=0 )
d ( the number of pairs
where Xi=1 and Yi=1 )

3. HYPOTHESES
• H0 : P(Xi = 0, Yi=1 ) = P(Xi = 1, Yi=0 )
for all i
• Hi : P(Xi = 0, Yi=1 ) ≠ P(Xi = 1, Yi=0 )
for all i

4. TEST STATISTICS
The test statistics for the McNemar test is
usually written as
T1=
However, for b+c ≤ 20, the following test statistic is
preferred
T2=b
That neither T1 nor T2 depends on a or d. This is
because a and d represent the number of “ties”
and ties are discarded in this analysis.

5. DECISION RULE
Let n equal b+c. If n≤20, use table A3. If α
is the desired level of significance, enter
table A3 with n=b+c and p=1/2 to find the
table entry approximately equal to α/2.
Reject H0 if T2≤t or if T2≥n-t , at a level of
significance of 2α1.

6. COX AND STUART TEST FOR
TREND

7. DATA
• The data consist of observation on
sequence of random variable X1, X1,…, Xn
arranged in particular order, such as the
order in which the random variables are
observed. It’s desired to see if a trend
exist in the sequences.

8. • Group the random variables into pairs
(X1, X1+c), (X2, X2+c)…… (Xn’-c, Xn’),
• where c = n’/2 if n’ is even, and c =
(n’+1)/2 if n’ is odd.
• (note : that the middle random variable is
eliminated using this scheme if n’ is odd.
Replace each pair (Xi, Xi+c) with a “+” if Xi<
Xi+c, or a “-“ if Xi> Xi+c eliminating ties. The
number of untied pairs is called n.