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# Statistics Flowchart

Know what statistical test should be used
by

## Scott Crawford

on 22 October 2013

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#### Transcript of Statistics Flowchart

What am I testing?
Numerical Data
Means
Categorical Data
Proportions
How many?
1
2
How many?
lots
Numerical
x Categorical
A moving mean
Numerical
x Numerical
Categorical
x Categorical
1
2
lots
Is it normal?
Is it normal?
Is it normal?
Is it normal?
Yes, it says
it's normal
No but
n>30
No and
n is small
By the Central Limit Theorem
You are stuck.
for a bootstrapping
technique
Do you know the population standard deviation: sigma?
Or was the standard deviation given as part of a sample: s?
The standard deviation
was known before the
sample was taken
The standard deviation
was calculated after a
sample was chosen
Sigma
S
One sample z-test for a mean
One sample t-test for a mean
No and
n is small
You are stuck.
for a resampling
technique
Yes, it says
it's normal
No but n1>30
and n2>30
By the Central Limit Theorem
Are the samples independent
Or is this matched pairs?
Matched Pairs
Matched Pairs test for a difference of means
Does each group have the
same standard deviation?
It doesn't say so
Yes, sigma1 = sigma2
Two sample independent t-test for a difference in means
Two sample pooled t-test for a difference in means
No,
np<15 or
n(1-p)<15
Yes,
np>15 and
n(1-p)>15
One sample z-test for a proportion
By the Central Limit Theorem
You are stuck.
for Fisher's Exact Test
Yes,
n1p1>15 and n1(1-p1)>15
and
n2p2>15 and n2(1-p2)>15
Two sample z-test for a difference in proportions
By the Central Limit Theorem
No,
np<15 or n(1-p)<15
for at least one of the samples
You are stuck.
for Fisher's Exact Test
Do you expect at least
5 observations
in every category?
No, the sample
is not that large
You are stuck.
Try consolidating categories
Or as a statistician for a
cluster analysis
Do you know the proportions
you expect to get?
Yes, at least
Yes
No, I am testing for
Independence
Chi-squared Goodness of Fit test
Chi-squared test of Independence
Can you tell from the residuals
1) Linear
2) Normal
3) Constant Variance
4) Independent
5) Residuals average 0
I do not see any pattern
in the residuals
You are stuck.
for a generalized
non-linear model
I not see a pattern
in the residuals
Regression test of the slope
Is it normal?
No, and my sample
size is small
You are stuck
a Bayesian model
Yes it says it
is normal
No, but n>30 for
every group
Are the standard
deviations equal?
No, it does
not say so
You are stuck.
Levene's Test or
ANCOVA
Yes, it says so
MSE
MSG
DFE
SSE
DFG
SSG
MSG/MSE
SSE/DFE
SSG/DFG
N-1
N-k
k-1
SST
ANOVA
ANalysis Of VAriance
SSR/σ2
SSR
N-1
N-2
1
Using ANOVA
Using ANOVA
SSE
Full transcript