Biostatystyka i Biometria- Wzory- Kolokwium nr 2
Ć Ć "waż
p1 - p2 U - źU 1 1+ r ś# k zi
(x1 - x2) - (ź1 - ź2)
Ć
p - p0 z = Z =
z = ln�# z =
ś# ź#
z =
z =
SED �U
2 2 2 r
�#1- #
- 3)
Ć Ć
p(1- p) p "(ni
�1 �
2
+ k
n
n1 n2
x - ź
(x1 - x2) - (ź1 - ź2)
t =
(x1 - x2) - (ź1 - ź1)
(x1 - x2) - (ź1 - ź2)
t =
t = t =
s / n
2 2
2 2
2
s1 s2
�# -1)s1 + (n2 -1)s2 ź#ś# n1 + n2 ź#
ś#�# ś# s1 + s2
(n1 2
+
ś#
ś# ź#ś#
n n1 n2
n1 + n2 - 2 n1n2 ź#
�# #�# #
2 2
s1 s2
tą[� ] + tą[� ]
1 2
n - 2
n1 n2
z1 - z2
tS = r tS = z n - 3
(x1 - x2) - (ź1 - ź2)
t'ą =
ts =
2 2
t'=
1- r2
s1 s2
2 2
1 1
s1 + s2
+
+
n1 n2
n1 - 3 n2 - 3
n
W - n(n +1) / 4
T =
n(n +1)(2n +1) / 24
(n -1)s2
Ą# ń#
'2 Ą# ń#
ż2 = =
1 1 1
ż2 = -1)Ą# ln s2 - -1) ln si2 C =1+
ó# Ą#
"żi
2 "(ni "(ni
ó#
-
"
�
ó#
n Ł# a Ś# a
3(a -1) (ni -1) -1)Ą#
a "(ni
ó# Ą#
Ł# a Ś#
2
2
N
ś#
N�#| f11 f22 - f12 f21 | - ź# (fij - fĆij)
ś#
Ć
(ni - ni ) 2
2 �# #
ż2 = ż2 = - 3)(zi - z)2
ż2 = żC = "" "(ni
"
Ć
ni C1C2R1R2 fĆij
k
a
n
n1(n1 +1)
W = Ik U = n1n2 + - R1 U '= n1n2 -U
"Rk
2
k =1
2 2
~ ~ ~ ~
s
s1 s2
Ć Ć p1(1- p1) p2(1- p2)
p(1- p)
SEx =
SEx -x2 = + ~ +
SEp = SED =
1
n n1 n2 Ć n n1 + z2 n2 + z2
2
n
1- r2 1 (xi - x) 1
2
�# ś#
1 1
SEr = sw
= sr + sr = - y)
Ć Ć ś# ź#
SED = p(1- p)ś# + "(yi
n
i
p
n
n1 n2 ź# n 2 n - 2
i=1
�# #
- x)
"(xi
i=1
k
z2 n
RiC
1 1
ż + j
'
~ 2 fĆij = ą = ś# ź#
"�# ś# �U = n1n2(N +1) żi = żi - ź
p =
N 2 2n j=0 �# #
n + z2 j 12 �
1
2
q1 / p1 1 1 1 1 (lnOR - ln ORst )2
�# ś#
OR = slnOR = + + +
ś# ź#
q2 / p2 a b c d s2
lnOR
�# #
n n
k l
( (
- x)(yi - y) - x)(yi - y)
"(xi "(xi (xi - x)(y - y)
""nij j
1
i=1 i=1
i=1 j=1
r = =
n n
n -1 sX sY r = k l
2 2
( 2 ( 2
- x) - y)
(xi - x) (y - y)
"(xi "(yi
"ni" "n" j j
i=1 i=1
i=1 j=1
n n
n n
- y)(xi - x) yi - nxy
2 2
"(yi "xi
Sy i=1
S = - y) = -ą - �xi ) a = y - bx
i=1
"(yi "(yi
b = r = =
n
i=1 i=1
Sx n 2 2
- x) - nx2
"(xi "xi
i=1 i=1
ż#
(n
�# -1)s2 2 (n -1)s2 �#
�#
P�# d" � d" = 1-ą
Ź#
�(ą / 2),[n-1]2 �(1-(ą / 2)),[n-1]2 �#
�# �#
�#
~
P{w
i - t[*n-2]sw
< yi < w
i + t[*n-2]sw
}= 1-ą
i i