-
LECTUREL-
Population
·
:
(constant
"
mean =
M :
m
·
standard deviation =
a
X X2
500 , 7112
Sample
·
:
100 , 3250 10065 105625, mean = - =
100 , 14224
mean = X
gg ggb2 ,
gggg , 240014
e
*425607-5
42 ,
.
100 , lue
>
standard deviation =
S
100 , 0123 10002 , 460151
>
-
must be random
924668 0211297)
=
100 2543
, 10050 , 0,
SD
100 , 1234 10024
695228 5
145367
= =
·
, 0 ,
Data types :
Sum [500 ,
7112 50142 , 425687 S12 = 0 ,
072 + round to 2 decimals + 1 because nlo
1. Nominal scale only classification
...
=
-
blood
groups ,
colour
.
2 Ordinal scale =
classification + rank order
stage
-
exam scores ,
of cancer
.
3 Interval Scale =
Measurement with fixed unit + no null point
temperature time
-
,
4
. ratio scale =
fixed unit + fixed null point
concentration
-
speed ,
· SD
Rounding a
>
calculate o and divide by 2
S
% rounding to decimals
0
07
:
-
=
. a
unto first non-zero
number
O
:
whole number
-
=
1 . 12
T
>
if n < 10 >
- add 1 decimal
~
if 5 >
- round to an even number
-
·
1 .
45 - 1 4 .
·
-
1 .
35 1 4
.
·
Standard deviation :
SD
·
accurate =
How far are the measurements from the true value ?
~
in the middle
How close
·
precise =
are the measurements from each other ?
>
close/not close · not accurattiener
accurate
not precise -
-
.
not accurate
accurate
Presise
de precise
, -
LECTUREL-
·
Pr(AMB) =
intersection
probability that both events
together occur
(notcured)
50
a n= -0 . 10
0
go
= =
.
.
·
Pr(AUB) =
union
OKT
n
-
X
·
probability that A or B occurs
50-0 . 10
10 = 0 . 005
·
Addition rule :
Pr(AuB) =
Pr(A) + Pr(B) -
Pr(AnB)
p(A) + P(B)
P(AUB) =
)
t
Pr(x(5) (Pr(o) + Pr()
exclusive
=
1 -
Pr(x(5) =
1 -
. ...
·
A and B are independent :
=> mutual
6161
1 0 0
3839
= -
=
Product Pr/An B) Pr(A) Pr(B)
.
1
.
=
rule :
ne
.
.
b IT = 0 .
05 same as a.
·
A and B
E
mutual not exclusive
are not independent
PCAuBP
:
Pr(AB)
Condobrobaility
is of A onaan
the probability i
·
Pr(AnB) =
Pr(A) ·
Pr(BIA) =
Pr(B) ·
Pr(AIB)
positivest sich
T
·
sensitivity = correct identified with disease = P(P/s)
·
identified with P(NIH)
specificity correct no disease
= =
healthy
L
negative
·
Uniform
~
probability
distribution
is equal
=
↓
categorical
for each
data
outcome
with
>
-
more
dice
categories
Pr(
at
+
sensitivity
/dis) =
-
Predis)
b
=
=
sensitivity
0 .
70 -
100 :
g
000St
'Pi =
P(X =
X i ) =
n
b =
0 01 .
-
0 . 0078 = 0 . 0022
·
Dinomial distribution =
Categorical data with 2
Categories
-
Yes/no
# Prl-In) = =
specificity
proportion probability it to have A probability (1) to have
= =
or
P(x) = mx .- c + d =
1 -
0 01 .
=
0 .
99
= (* ) (1 - )"
-
Y
d =
0 .
98
·
0 .
gg
= 0 .
9702
Example :
c= 0 .
gg
-
0 .
9702
=
0
098
.
P(x(2) =
P(x (1) =
P(0) + P(1) =....
·
Poisson
P(x) 1
distribution
) =
1 -
P(xX 1 )
=
=
random
1 -....
events
occuring incidentally in fixed time
Space
o
Preve va postgo
'M number of time or
9 diseased/total += 28 3 %
average events per space
= .
P(x) M
mota-go
· =
total
·
Expected value =
p(x) ·
N
↑
↳
LECTUREL-
Population
·
:
(constant
"
mean =
M :
m
·
standard deviation =
a
X X2
500 , 7112
Sample
·
:
100 , 3250 10065 105625, mean = - =
100 , 14224
mean = X
gg ggb2 ,
gggg , 240014
e
*425607-5
42 ,
.
100 , lue
>
standard deviation =
S
100 , 0123 10002 , 460151
>
-
must be random
924668 0211297)
=
100 2543
, 10050 , 0,
SD
100 , 1234 10024
695228 5
145367
= =
·
, 0 ,
Data types :
Sum [500 ,
7112 50142 , 425687 S12 = 0 ,
072 + round to 2 decimals + 1 because nlo
1. Nominal scale only classification
...
=
-
blood
groups ,
colour
.
2 Ordinal scale =
classification + rank order
stage
-
exam scores ,
of cancer
.
3 Interval Scale =
Measurement with fixed unit + no null point
temperature time
-
,
4
. ratio scale =
fixed unit + fixed null point
concentration
-
speed ,
· SD
Rounding a
>
calculate o and divide by 2
S
% rounding to decimals
0
07
:
-
=
. a
unto first non-zero
number
O
:
whole number
-
=
1 . 12
T
>
if n < 10 >
- add 1 decimal
~
if 5 >
- round to an even number
-
·
1 .
45 - 1 4 .
·
-
1 .
35 1 4
.
·
Standard deviation :
SD
·
accurate =
How far are the measurements from the true value ?
~
in the middle
How close
·
precise =
are the measurements from each other ?
>
close/not close · not accurattiener
accurate
not precise -
-
.
not accurate
accurate
Presise
de precise
, -
LECTUREL-
·
Pr(AMB) =
intersection
probability that both events
together occur
(notcured)
50
a n= -0 . 10
0
go
= =
.
.
·
Pr(AUB) =
union
OKT
n
-
X
·
probability that A or B occurs
50-0 . 10
10 = 0 . 005
·
Addition rule :
Pr(AuB) =
Pr(A) + Pr(B) -
Pr(AnB)
p(A) + P(B)
P(AUB) =
)
t
Pr(x(5) (Pr(o) + Pr()
exclusive
=
1 -
Pr(x(5) =
1 -
. ...
·
A and B are independent :
=> mutual
6161
1 0 0
3839
= -
=
Product Pr/An B) Pr(A) Pr(B)
.
1
.
=
rule :
ne
.
.
b IT = 0 .
05 same as a.
·
A and B
E
mutual not exclusive
are not independent
PCAuBP
:
Pr(AB)
Condobrobaility
is of A onaan
the probability i
·
Pr(AnB) =
Pr(A) ·
Pr(BIA) =
Pr(B) ·
Pr(AIB)
positivest sich
T
·
sensitivity = correct identified with disease = P(P/s)
·
identified with P(NIH)
specificity correct no disease
= =
healthy
L
negative
·
Uniform
~
probability
distribution
is equal
=
↓
categorical
for each
data
outcome
with
>
-
more
dice
categories
Pr(
at
+
sensitivity
/dis) =
-
Predis)
b
=
=
sensitivity
0 .
70 -
100 :
g
000St
'Pi =
P(X =
X i ) =
n
b =
0 01 .
-
0 . 0078 = 0 . 0022
·
Dinomial distribution =
Categorical data with 2
Categories
-
Yes/no
# Prl-In) = =
specificity
proportion probability it to have A probability (1) to have
= =
or
P(x) = mx .- c + d =
1 -
0 01 .
=
0 .
99
= (* ) (1 - )"
-
Y
d =
0 .
98
·
0 .
gg
= 0 .
9702
Example :
c= 0 .
gg
-
0 .
9702
=
0
098
.
P(x(2) =
P(x (1) =
P(0) + P(1) =....
·
Poisson
P(x) 1
distribution
) =
1 -
P(xX 1 )
=
=
random
1 -....
events
occuring incidentally in fixed time
Space
o
Preve va postgo
'M number of time or
9 diseased/total += 28 3 %
average events per space
= .
P(x) M
mota-go
· =
total
·
Expected value =
p(x) ·
N
↑
↳
