1. Introduction
Osborn

2. “Legal” Science Daubert is a benchmark!!!:
Daubert (1993)- Judges are the “gatekeepers” of scientific evidence.
Must determine if the science is reliable
Has empirical testing been done?
Falsifiability
Has the science been subject to peer review?
Are there known error rates?
Is there general acceptance?
Frye Standard (1928) essentially
Federal Government and 26(-ish) States are “Daubert States”

3. Measurement and Randomness
Any time an observation is made, one is making a “measurement”
Experimental error is inherent in every measurement
Refers to variation in observations between repetitions of the same experiment.
It is unavoidable and many sources contribute
Error in a statistical context is a technical termBHH

4. Measurement and Randomness
Experimental error is a form of randomness
Randomness: inherent unpredictability in a process
The the outcomes of the process follow a probability distribution
Statistical tools are used to both:
Describe the randomness
Make inferences taking into account the randomness
Careful!:
Bad data, assumptions and models lead to garbage (GIGO)

5. Probability
Frequency: ratio of the number of observations of interest (ni) to the total number of observations (N)
Probability (frequentist): frequency of observation i in the limit of a very large number of observations
We will almost always use this definition
It is EMPIRICAL!

6. Frequency
Roll a “fair” die 20 times (N = 20). What is the frequency of obtaining 2 (n2 = ?)?
Let’s do this with simulation (Monte Carlo):
In R:
Result:
n2 = 2
freq2 = 2/20 = 0.1

7. What is Statistics?? Study of relationships in data
Descriptive Statistics – techniques to summarize data
E.g. mean, median, mode, range, standard deviation, stem and leaf plots, histograms, box and whiskers plots, etc.
Inferential Statistics – techniques to draw conclusions from a given data set taking into account inherent randomness
E.g. confidence intervals, hypothesis testing, Bayes’ theorem, forecasting, etc.

8. Data
Random variables - All measurements have an associated “randomness” component
Randomness –patternless, unstructured, typical, total ignoranceChaitin, Claude
Any experiment/observation recorded is a random variate

9. T.I.C. of Gasoline

10. Observations from the T.I.C.
GC-MS instrument output for a gasoline :

11. Population and Sample
Almost all of statistics is based on a sample drawn from a population.
Population: The totality of observations that might occur as a result of repeatedly performing an experiment
Why not measure the whole population?
Usually impossible
Likely wasteful
Population should be relevant.
Part logic
Part guess
Part philosophy….

12. Data and Sampling Sample Representations: Representative Sample
Population
Biased Samples
Population
Population
Sample
Sample

13. Parameters and Statistics
Parameter: any function of the population
Statistic: any function of a sample from the population
Statistics are used to estimate population parameters
Statistics can be biased or unbiased
Sample average is an unbiased estimator for population mean
We may construct distributions for statistics
Populations have distributions for observations
Samples have distributions for observations and statistics

14. What is ? R : A powerful Platform for Statistical Analysis
Why bother learning R ?
Basic Graphing
Basic Data Summary and Analysis Tools
Basic Statistical Inference Tools
We will learn R and Rstudio
Getting Help
Basic input/output and calculating
Visualizing with Graphing

15. Finding our way around R/RStudio
Script Window
Command Line

16. Handy Commands: x <- 4 x <- “text goes in quotes”
Basic Input and Output
Numeric input
x <- 4
variables:
store
information
:Assignment operator
x <- “text goes in quotes”
Text (character) input

17. Get help on an R command:
Handy Commands:
Get help on an R command:
If you know the name: ?command name
?plot brings up html on plot command
If you don’t know the name:
Use Google (my favorite)
??key word

18. R is driven by functions:
Handy Commands:
R is driven by functions:
func(arguement1, argument2)
input to function goes in parenthesis
function name
function returns something; gets dumped into x
x <- func(arg1, arg2)

19. Handy Commands: Matrices: X User defined functions syntax:
X[,1] returns column 1 of matrix X
X[3,] returns row 3 of matrix X
Handy functions for data frames and matrices:
dim, nrow, ncol, rbind, cbind
User defined functions syntax:
func.name <- function(arguements) {
do something
return(output) }
To use it: func.name(values)

20. R commands not to forget for today
<- (assignment or “gets”)
? (to get help with a command)
: (range operator)
c (“collect”)
sample
seq (generate a sequence)
plot
library
install.packages (to install libraries you don’t have)
For matrices and vectors: x[,3] vs. x[3,] vs. x[,] vs. x[3,3] vs. x[] vs. x[1:3] etc…