Introduction to data analysis

background [prelab assignment (20 points) due at the begining of lab]

1. using algebra / calculus show:

a. linear regression analysis: formula for slope in the equation: y = mx + b [need only algebra]

b. propagation of errors: find SDz, where z = x + a y [need both algebra & calculus]

c. describe Nyquist frequency in the digitization of a signal

2. describe the central limit theorem and its implication in regards to the use of various statistical tests

using the below resources; include appropriate citation - bibilography and in-text citation.

purpose

lab data analysis concepts

mean & standard deviation; normal probability distribution

basis of linear regression analysis (using calculus)

basis of propagation of errors (using calculus)

illustrate (qualitatively) the central limit theoreom

signal processing - intro to analog to digital (data) conversion

numeric differentiation - estimate the value of a derivative

develop your inter-group cooperation / organization skills (not content for your lab report): different students do different aspects of the lab; use / share work

materials

"dry" lab: internet resource

Excel simulations: Central limit theorem (enable VBA macro) & uncertainty

methods / data analysis

student design

content of lab report [50 points; up to 2 weeks to work on lab report]

uncertainty simulation: include appropriate screenshot of simulation output and written description addressing ___ [35 points]

effect of the value of the mean and SD in the probability density distribution (pdf) of the normal distribution

effect of sample size on the estimate of the mean, SD, and SEM

effect of the value of the mean and SD in the histogram of the normal distribution; compare to preceding pdf

propagation of errors: compare theory vs. experiment (simulation)

propagation of errors: for z(x,y) [where z as a function of x & y], relate SD(z), SD(x), and SD(y)

regression: y = mx; graph of R vs m

regression: y = mx + b; 3D graph of R vs m & b

central limit theoreom simulation [10 points]

histogram: distribution of a sample of means of various sample sizes

describe the shape of the histogram and the effect of sample size on the histogram; refer to histogram to support your claim(s)

numeric differentiation [5 points]

resources

me: intro stats - article; suppl (calculus (not published); algebra (published)); linear regression

me: propagation of errors: intro; appln

central limit theoreom; implication

basis of analog to digital (data) conversion

Fourier thereom

Fourier series: cdf; phet (requires java; first default panel only); falstad

Nyquist theoreom: cdf (ignore bottom panel)

relate: (i) sampling rate to sampling period and (ii) sampling rate to number of samples collected

numeric differentiation: defn; algorithm (1; 2)