Transcript Chapter 3-Statisicsx

Statistics (Chapter 3)
Statistics
Forensic science is based in experiment, measurement, and
analysis.
Whenever measurements are made, however, there is an
inherent variability and uncertainty in the measurement…
CHE 113 2
Uncertainty in Measurement
• Precision vs. Accuracy
– Precision - how closely individual
measurements agree
– Accuracy- how closely the measurements
agree with the true value
• Significant Figures
– All measurements are inaccurate
intrinsically
– measured quantities are reported such
that the last figure is uncertain
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Measurement
Measurement and Significant Digits
• You can only be as precise
as the instrument used to
make the measurement
• Significant figures give the
reader an idea of how well
you could actually
measure/report your data
Sig Figs
• 12.34500 kg of drugs
– 7 significant figures
What if scale only reads measures to 12.345 kg?
http://chemsite.lsrhs.net/measurement/sig_fig
.html
http://chemsite.lsrhs.net/measurement/sig_fig
.html
Statistics vs. Probability
•Statistics is focused upon the collection, handling, validation,
and interpretation of data.
•learn about the properties of a larger population from
studying a small subset or sample of the population
•Probability deals with representing the likelihood that a
particular event or set of events will occur given a set of
reference data.
•learn about a particular sample given knowledge about the
larger population.
CHE 113 9
Statistics and Probability
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Statistical Terms to Know
• Average or Arithmetic Mean:
– The average or mean is the sum of the
values of each of the individual data points
divided by the total number of data points in the
set.
• Mode:
– The mode is that value that occurs most
frequently in a data set.
Statistical Terms to Know
• Range:
– The difference between the lowest and highest
value in a set of data is the range.
• Standard Deviation (σ or SD):
– How spread out numbers are in a set of data
Statistical Terms to Know
• Variance :
– The square of the standard deviation relates the
total variance found in the data set…
You and your friends have just measured the heights of your
dogs (in millimeters):
Height in mm
The heights (at the shoulders) are: 600mm, 470mm, 170mm, 430mm and 300mm.
Find out the Mean, the Variance, and the Standard Deviation.
Your first step is to find the Mean:
Answer:
Mean =
600 + 470
+ 170 +
430 + 300
5
=
1970
5
http://www.mathsisfun.com/data/standard-deviation.html
= 394mm
so the mean (average) height is 394 mm. Let's plot
this on the chart:
Height in mm
Now, we calculate each dogs difference from the
Mean:
http://www.mathsisfun.com/data/standard-deviation.html
To calculate the Variance, take each difference, square it, and
then average the result:
So, the Variance is 21,704.
And the Standard Deviation is just the square root of Variance, so:
Standard Deviation: σ = √21,704 = 147.32... = 147 (to the nearest mm)
And the good thing about the Standard Deviation is that it is useful. Now
we can show which heights are within one Standard Deviation (147mm) of
the Mean:
So, using the Standard Deviation we have a
"standard" way of knowing what is normal,
and what is extra large or extra small.
Rottweilers are tall dogs. And Dachshunds are
a bit short ... but don't tell them!
Statistics in Forensics
Relate alcohol in small blood sample to that believed in whole body
Probability
Probability is the chance that something will
happen. It can be shown on a line
Experimental Probability
Of the last 18 trains to arrive at Danville
Station, 15 were on time. What is the
experimental probability that the next
train to arrive will be on time?
Answer: on time/total= 15/18= 5/6
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Theoretical Probability
If we toss a fair coin, what is the
probability that a tail will show up?
1/2
What about Head, Head, Head and Tail?
CHE 113 21
Jury Vote
Likelihood ratio =
Probability of Prosecution Hypothesis/Probability
of Defense Hypothesis
Table 3.2.2. Evidential values based upon
=
Likelihood Ratios (LR)
P[P]/P[D]
Likelihood Ratio Value of Evidence in
Support of Hypothesis
<1 Does not support
1 No support or refute
1 to 10 Weak support
10 to 100 Limited support
100 to 1,000 Strong support
>1,000 Very strong support
Probability that this hair came from
someone else than suspect?
Hair from a
crime scene
Suspect
Need to examine a SAMPLE and compare it to a POPULATION