Transcript Conceptual outline. Pearson linear correlation

What does researcher want of
statistics?
What does researcher want of
statistics?
“I had a fun and get it in
addition to my cool
microscope images!”
“I have done a statistical
analysis of my results and
now give me my PhD,
pleeeease!..”
1. How variable it is?
2. Does “my pet thing” work?
3. Why do the things differ?
4. Why does it fail from time to
time?
5. Why patients have different
fate and where is the hope
for them?
6. What would the outcome of
a perturbation?
Generally speaking, all the statistics is about finding
relations between variables
Basic concepts to understand
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Variability
Variable
Relation
Signal vs. noise
Factor vs. response (outcome), independent vs.
dependent variables
Statistical test
Null hypothesis
Power
Experimental design
Distribution
Deterministic
vs.
stochastic
data
Two graph concepts:
Histograms:
show quantities of objects of particular qualities
as variable-height columns
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No of obs
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Distance in chromosome, b.p.
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14000
Two graph concepts:
Scatterplots:
show objects arranged by 2 particular qualities
as coordinates
Scatterplot (Irisdat 5v*150c)
SEPALWID = 3.4189-0.0619*x
4.6
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SEPALWID
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SEPALLEN
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Two graph concepts:
Histograms vs. scatterplots
Matrix Plot (Irisdat 5v*150c)
SEPALLEN
SEPALWID
PETALLEN
PETALWID
Normal distribution
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No of obs
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0
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SEPALWID
––––––
+++–––
+-+–+–
……………
---+++
++++++
Not a normal distribution
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No of obs
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Distance in chromosome, b.p.
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• Variance:
Var = Sum(deviation from mean)2
• Standard deviation:
SD = Square root from Var
• Skewness:
deviation of the distribution from symmetry
• Kurtosis:
“peakedness” of the distribution
• Standard error:
e.g. SE = SD / square root from N
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Kurtosis: positive
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No of obs
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0
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SEPALWID
3.4
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Kurtosis: negative
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No of obs
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SEPALWID
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Skewness
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No of obs
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SEPALWID
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4.0
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4.4
Analysis of correlations
• Simple linear correlation (Pearson r):
r = Mean(CoVar) / (StDev(X) x StDev(Y))
CoVar = (Deviation Xi from mean X) x (Deviation
Yi from mean Y)
• How to interpret the values of correlations
– Positive: the higher X, the higher Y
– Negative: the higher X, the lower Y
– ~0: no relation
Confidence:
– |r| > 0.7: strong
– 0.25 < |r| < 0.7: medium
– |r| < 0.25: weak
• Outliers
• Correlations in non-homogeneous groups
• Nonlinear relations between variables
• Measuring nonlinear relations
• Spurious correlations
• Multiple comparisons and Bonferroni
correction
• Coefficient of determination: r2
• How to determine whether two correlation
coefficients are significant
• Other correlation coefficients
When it should not work?
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5.0
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ASSETS
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INCOME
•Graphs
•2D graphs
•Scatterplots w/Histograms
Exploratory examination of correlation matrices
Matrix Plot (Irisdat 5v*150c)
SEPALLEN
SEPALWID
PETALLEN
PETALWID
When it should not work?
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Var2
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NewVar
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30000 0
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Normalize it!
20000
E.g. NewX = log(X)
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NewVar2
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NewVar1
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Causality
There is no way to establish from a correlation
which variable affects which.
It is just about a relation.
• Casewise vs. pairwise deletion of missing
data
• How to identify biases caused by the bias
due to pairwise deletion of missing data
• Pairwise deletion of missing data vs. mean
substitution
Statsoft’s Statistica
• A perfect, almost universal tool for the
researchers in the range for “very beginner” to
”advanced professional”.
• An old software with intrinsic development
history
• Most of the methods can be found in >1 module
• Most of the modules contain >1 method
• No method is perfect
• No module is complete
• Most of the special modules are unavailable in
the basic “budget” license