1. Statistics (Chapter 3)

2. CHE 113 2 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…

3. CHE 113 3 Uncertainty in Measurement Precision vs. Accuracy Precision vs. Accuracy – Precision - how closely individual measurements agree – Accuracy- how closely the measurements agree with the true value Significant Figures Significant Figures – All measurements are inaccurate intrinsically – measured quantities are reported such that the last figure is uncertain

4. Measurement

5. 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

6. Sig Figs 12.34500 kg of drugs – 7 significant figures What if scale only reads measures to 12.345 kg?

7. http://chemsite.lsrhs.net/measurement/sig_fig.html

9. CHE 113 9 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.

10. CHE 113 10 Statistics and Probability

11. 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 dataset.

12. 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

13. Statistical Terms to Know Variance : – The square of the standard deviation relates the total variance found in the data set…

14. You and your friends have just measured the heights of your dogs (in millimeters): Height in mm Mean = 600 + 470 + 170 + 430 + 300 = 1970 = 394mm 55 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: http://www.mathsisfun.com/data/standard-deviation.html

15. Height in mm so the mean (average) height is 394 mm. Let's plot this on the chart: Now, we calculate each dogs difference from the Mean: http://www.mathsisfun.com/data/standard-deviation.html

16. 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)

17. 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!

18. Statistics in Forensics Relate alcohol in small blood sample to that believed in whole body

19. Probability Probability is the chance that something will happen. It can be shown on a line

20. CHE 113 20 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

21. CHE 113 21 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?

22. Likelihood ratio = Probability of Prosecution Hypothesis/Probability of Defense Hypothesis = P[P]/P[D] Jury Vote Table 3.2.2. Evidential values based upon Likelihood Ratios (LR) 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

23. Probability that this hair came from someone else than suspect? Suspect Hair from a crime scene Need to examine a SAMPLE and compare it to a POPULATION