Download PRT3202 STATISTICAL TABLE AND FORMULA SHEET 1. BASIC

PRT3202
STATISTICAL TABLE AND FORMULA SHEET
1.
BASIC STATS
 xi
Mean:
x
Variance:
  xi  x 
s2 
Standard deviation (SD):
s  s2
Range:
xmax  xmin
2.
n
2
n 1
PROBABILITIES
Law of complement:
P( A)  1  P( A)
Addition law:
P( AUB)  P( A)  P( B)  P( AB)
Conditional probability:
P( AB)  P( B) P( A | B)
Total rule of probability:
P( A)  P( A | B) P( B)  P( A | B) P( B)
Bayes Theorem:
P( B | A) 
3.
P( A | B) P( B)
P( A | B) P( B)  P( A | B) P( B)
COMBINATIONS
Total no. of combinations (choose r from N):
N
N!
N  ( N  1)  ...  ( N  r  1)

 
r  (r  1)  ...  2 1
 r  r !( N  r )!
1
4.
NORMAL DISTRIBUTION
x = sample mean;  = pop. mean;  = pop. SD; n = sample size
4.1.
One-sample
Mean of sampling distibution: x  

SD of sampling distribution:
x 
Confidence interval (CI):
CI  x  z x (Read Table Z for the z value)
Hypothesis testing:
z
4.2.
n
x
x
Two-sample (independent)
xi = sample i mean; i = pop. i mean; i = pop. i SD; ni = sample size i
12  22
SD of sampling distribution:
 x x 
Confidence interval (CI):
CI  x1  x2  z x  x
Hypothesis testing:
z
1
2
n1


n2
1
2
(Read Table Z for the z value)
 x1  x2    1  2 
 x x
1
5.

2
t DISTRIBUTION
x = sample mean;  = pop. mean; s = sample SD; n = sample size
2
5.1.
One-sample
s
n
SD of sampling distribution:
sx 
Degrees of freedom:
df = n – 1
Confidence interval (CI):
CI  x  ts x (Read Table t for the t value)
Hypothesis testing:
t
5.2.
x
sx
Two-sample (independent)
xi = sample i mean; i = pop. i mean; i = pop. i SD; si = sample i SD; ni = sample size i
SD of sampling distribution:
sx  x
1
2

1 1

s p
n1 n2


 s12 s22
 n n
1
2

both pop. variance unknown but equal
both pop. variance unknown and unequal
 n1  1 s12   n2  1 s22
sp 
n1  n2  2
Degrees of freedom:
 n1  n2  2

2
  s12 s22 
   
n1 n2 

df   
2
2
  s2 
 s22 
1
 
  
  n1 
 n2 
 n 1  n 1
 1
2
Confidence interval (CI):
CI  x1  x2  ts x  x


1
3
2
both pop. variance unknown but equal
both pop. variance unknown and unequal
(Read Table t for the t value)
Hypothesis testing:
t
 x1  x2    1  2 
sx  x
1
5.3.
2
Two-sample (dependent/paired)
 d = mean of the paired differences for the population; n = no. of paired samples
d
Mean of paired differences for the sample:
d
SD of paired differences for the sample:
sd 
n
sd
n
d
sd 
2
 d 

n 1
2
n
Degrees of freedom:
df = n – 1
Confidence interval (CI):
CI  d  tsd (Read Table t for the t value)
Hypothesis testing:
t
6.
d  d
sd
CORRELATION AND LINEAR REGRESSION
Correlation coefficient:
r
S xy
S xx S yy
4



   x2   n 

 y
S xx   x  x
S yy   y  y
Simple linear regression equation:
Coefficient of determination:
Residual sum of squares:
x
2
2
2
S xy
S xx
b0  y  b1 x
;
R2 = r 2
SSE  S yy 
5
2
S xy
S xx
n
2
 y

y = b0 + b1x
b1 
  x   y 

S xy   x  x y  y   xy 
n
2