Download Inference Guidelines

Inference Guidelines
Confidence Interval = estimate ± (critical value)(standard deviation of estimate)
 
2
 obs  exp 
estimate  parameter
standard dev. of estimate
2
exp
Name of Test
When to Use
1 sample ztest
for a mean
Does a single mean =
A hypothesized value?
Hypotheses
H 0 :   0
H a :   0
H a :   0
H a :   0
1 sample t-test
for a mean
Test Statistic =
Does a single mean =
A hypothesized value?
H0 :   0
Ha :   0
 0
 0
Estimate
deg. freed.
x , the
sample
mean
NA
x , the
sample
mean
Parameter
 0 , the
hypothesiz
ed
mean
 0 , the
hypothesiz
ed
mean
Standard
Deviation
of estimate

n
P-Value
Assumptions
For each Alt.
Hyp.
P(Z < z)
P(Z > z)
SRS from pop of interest.
Sigma known
Pop approx Normal
(draw plot to check)
2  P(Z < - z )
For each Alt.
Hyp.
P(T < t)
P(T > t)
s
n
2  P(T < - t )
n-1
1 proportion
z test
Does a single
proportion
=A hypothesized value?
H 0 : p  p0
For C.I.,
H a : p  p0
p̂
p  p0
pˆ 1  pˆ 
p0
n
For test,
p  p0
NA
po 1  p0 
n
For each Alt:
P( Z  z )
SRS from pop of interest.
Pop approx Normal
(draw plot to check)
If symm, no outliers: n <15
If no major skew, no outliers,
n<40
If lots of skew, or outlier,
n>40
SRS from pop of int.
Normal Approx:
ˆ , n(1  pˆ )  10
CI: np
P( Z  z )
2  P( Z   z )
Test:
np0 , n(1  p0 )  10
Name of
test
2 sample t
for diff. in
means
2 prop z
test
When to use
Hypotheses
To compare 2 pop’s,
groups, treatments
that
are independent
H 0 : 1   2  0
Compare 2
proportions
Estimate
H a : 1   2  0 x1  x2
1   2  0
1   2  0
Parameter
2
p1  p2  0
P-Value
P(T < t)
P(T > t)
2
s1 s2

n1 n2
0
smaller n
minus 1
H 0 : p1  p2  0
H a : p1  p2  0
St. Dev. Of est.
2  P(T < - t )
CI:
pˆ1  pˆ 2
0
pˆ1 (1  pˆ )1 pˆ 2 (1  pˆ )2

n1
n2
P( Z  z )
2  P( Z   z )
Test:
p1  p2  0
P( Z  z )
1 1
pˆ 1  pˆ    
 n1 n2 
Linear
Regression
t-test
2 samples paired by
some characteristic.
Compare 2 groups
Not independent
Test for slope of
Reg. Line.
Test for assoc of 2
Quant. Var.
H 0 : d  0
H a : d  0
d  0
d  0
H0 :   0
Ha :   0
 0
 0
xd
0
n
  y  yˆ 
slope of
LSRL
n-2
i
0
n1 pˆ1 , n1 (1  pˆ1 ),
n2 pˆ 2 , n2 (1  pˆ 2 ),  5
n1 pˆ , n1 1  pˆ  ,
Same as 1-sample
T-test, but n refers
To number of pairs
2  P(T < - t )
pairs - 1
b
Ind SRS’s
Normal:
CI:
n2 pˆ , n2 (1  pˆ 2 )  5
P(T < t)
P(T > t)
sd
Ind. SRS’s
Both pop’s Normal:
Check
n1  n2 instead of n.
(draw both boxplots)
Test:
NA
Matched
Pairs t
Assumptions
i
n2
  xi  x 
2
2
P(T < t)
P(T > t)
2  P(T < - t )
Lin shape in scatter
variation of y-values
the same (resid plot)
resids normal
(boxplot)
Name of test
Chi-Square
Good-Fit
Chi-Square
for ind. or
homogeneity
When to use
pop dist of props
= hypothesized
distribution
test assoc of
categorical variables
Hypotheses
H 0 : p1  p10 ,..., pn  pn0
H a :Null incorrect
Null: No association
Alt: Association
P-Value
P(  2   2 )
P(    )
2
2
Assumptions
SRS
All exp counts at least 1
no more than 20% are less than 5
SRS or entire population
All exp counts at least 1
no more than 20% are less than 5,
unless 2x2-> all at least 5.
degrees of freedom
# of categories minus 1
(rows-1)(columns-1)