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STATS CHEAT SHEET
Eeeeeep! How do I decide which test to use?!
What type of data do I have?
Continuous Data Only
Nominal (Frequency) Data
Categorical/Nominal data and Continuous data
Do I know the population  and ?
Run a Chi Square
Do I have Independent Samples/Conditions?
Yes
No
Yes
Run a Paired Samples
T-Test
Run a Z - Test
Do I know the population ?
Yes
Do I have 2 conditions
or More conditions?
- aka Matched, Dependent,
Test-Retest
No
Run a Single
Sample T-test
- Use Sample
St. Dev. to predict 
No
Run Correlation
and/or Regression
analysis
2 Conditons
3 or more Conditions
Run an Independent Samples T-Test
Run an ANOVA
- Look for experimental groups
- Clues: Unequal N’s or Random
Assignment to one or other group
- Look for experimental groups
- Clues: Unequal N’s or Random
Assignment to one or other group
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Z-TESTS
In order to run a Z-Test you must be provided with
- Population 
- Population 
Equation:
Z  X 
/ N
Critical Z-Test values:
α = .05
α = .01
EXAMPLE:
1-Tailed
1.64
2.33
2-Tailed
1.96/-1.96
2.58/-2.58
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SINGLE SAMPLE T-TEST
In order to run a Single Sample T-test you must:
- Be provided with Population 
- Use the sample Standard Deviation to predict Population 
Equations:
t  X 
SX / N
EXAMPLE:
df = N – 1
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PAIRED SAMPLES T-TEST
Paired Samples T-Tests:
- Are also known as Dependent or Matched T-Tests
- Do not utilize population parameters, rather are a comparison of scores from a single
sample measured across time
- Look for key words such as “Test-retest”; “Pre-Post”; “Same individuals tested”
- =0
Equations:
t  D
SD 
SD / N


Confidence Intervals: D  t crit  S D / N
EXAMPLE:

2
 D   D  / N
N 1

2

df = N - 1
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INDEPENDENT SAMPLES T-TEST
(N’s Equal)
Independent Samples T-Tests:
- Are used to compare 2 Independent groups
- Have experimental groups / conditions
- May have unequal N’s
- Look for key words such as “Experiment”; “Conditions”; “Random Assignment to
one condition or another”
Equations:
t  (X1  X 2 )
S
S 



n

n
1
2


2
1
2
2

Confidence Intervals: X 1  X 2
EXAMPLE:

S 2   x 2   x  / N
2

N 1


 S 2 S 2 

 t crit   1  2 
 n1 n 2 



N = n1 + n2
df = N - 2
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INDEPENDENT SAMPLES T-TEST
(N’s Unequal)
Equations:
t  (X1  X 2 )
1
1 
S P2   
 n1 n 2 
S
2
P
 (n1  1) S12  (n 2  1) S 22
n1  n 2  2

 1 1 
Confidence Intervals: X 1  X 2  t crit  S P2    

 n1 n 2  

EXAMPLE:

df = N – 2
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ANOVA
ANalysis Of VArience:
- Are virtually the same thing as an Independent T-Test except that there are more than
2 conditions
- Accounts for possible inflation of the  level by dividing the  level between all
possible comparisons (i.e. 3 conditions = /3 .:  of 0.017 per comparison)
Equations:
Sums of Squares
(SS)
Source
  X i 2    X tot 2 


Between =  
n1  
N

i 1 

 
df
Mean Square Error
(MS)
k
Within
SSTot - SSBtwn
Total
  X tot 2    X tot 2 

=

N


 



k-1
N-k =
=
SS Btwn
df Btwn
SSW ithin
OR
dfW ithin
F
=
MS Btwn
MSW ithin
 ni  S i2 
 N 


N-1
Estimating the Magnitude of Experimental Effect:
SS
 SSW ITHIN
SS
 k  1  MSWITHIN 
(eta) =  2  TOT
(omega) =  2  BTW N
SS TOT
SS TOT  MSWITHIN
EXAMPLE:
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CHI SQUARE
Chi Square:
 Is used when you have ordinal data
 You are using the obtained data to make a prediction about what the relationship
would have been if there were no difference between the groups
Equations:
2  
(O  E ) 2
E
Likelihood Ratio:
Eij 
 (2R1)(C 1)
Ri C j
N
 Oij 
 2 Oij ln  
E 
 ij 
Measures of Association:
 Used to test the strength of the relationship
Phi: (2 by 2)

2
N
C 
Cramér’s Phi: (X by X)
Odd’s Ratio: (2 by 2) P 
EXAMPLE:
Ri
Cj
2
N (k  1)
df  ( R  1)(C  1)
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CORRELATION AND REGRESSION
Correlation:
- Does not imply causation
- Determine if two sets of continuous data co vary / can one predict the other?
Regression:
- Is a way of predicting the score of the dependent (criterion) variable based on the level of the
independent (predictor) variable
Correlation Equation:
r
(X
 X Y
 XY  N
( X )
( Y )
)
  (Y ) 
N
N
2
2
2
2
Regression Equations:
Y’= bX + a
b
N ( XY )  ( X   Y )
N ( X )  ( X )
2
a  Y  bX
2
Standard Error of the Estimate:
 est  S Y'  S Y  X  S Y (1  r 2 )
SY’ 2 = Sy2(1-r2)
Confidence Limits on Y:
CI (Y )  Y '(t / 2 )( s'Y  X )
s 'Y  X  sY  X


2
1  Xi  X 

1  
N  ( N  1) s X2 


Note: for (t/2), if your  = 0.05, you would use the critical t value for  = 0.025.
Hypothesis Testing:
Testing r
r ( N  2)
t
(1  r 2 )
df = N - 2
EXAMPLE:
Testing b
t
(b)  ( s x )  ( N  1)
sY  X
df = N - 2
Testing Independent b’s
b  b2
t 1
sb21  sb22
df = N - 4
sY  X
sb 
sX  N 1
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POWER
Power Calculations:
 What is the probability of correctly rejecting a false H0?
 Power is a function of:
o  level
o H1
o Sample size
o Test statistic used
 Where n is unknown, used the power table to estimate  on a given  level.
Power for 1 sample
Effect Size
  0
d 1

Noncentrality parameter Estimating Required Sample Size
 d n
 
n 
d 
2
Power for 2 samples (N’s Equal)
Effect Size
  0
d 1

Noncentrality parameter Estimating Required Sample Size
n
 d
2
 
n  2 
d 
2
Power for 2 samples (N’s Unequal)
Effect Size
*Where  is pooled
d
1   0

Harmonic N
nh 
2n1n2
n1  n2
Noncentrality parameter Estimating Required Sample Size
 
n  2 
d 
nh
 d
2
2
Power when  is known
Effect Size Noncentrality parameter Estimating Required Sample Size
2
d  1
EXAMPLE:
  1  N  1
 
n     1
 1 