How do you know something?

• tenacity
• authority
• intution
• science

Scientific Method - observe, develop a theory to explain, test - use new data to cross-check

Variables

1. Random (stochastic, non-deterministic) - value not known at start
2. Non-random (non-stochastic, deterministic) - value is known

Probability - the chance that a random variable will take a certain value
                 - (distribution must add to 100%)
  Probalilty Distribution - set of all possible values of a random variables with the probabilities for each

Dependent, independent, discrete, continuous and limited in a range or not

Distribution

Continuous distribution (points on a continuous scale)
vs.
Discrete distribution (clumps, not all values are possible)

Subjective Distribution - have someidea of probalities of outcomes
Objective Distribution - based on # of times an outcome occurs divided by the total number of outcomes

Correlation- when two+ variables show a systematic patrern of movement
Causation - when 1 variable actually causes the other variable to change

* Correlation DOES NOT imply causation.
* Canusaion implies correlation.

Regression vs. Causaiton -  a significant sign on a regression coefficient DOES NOT imply causation.

3 Types of Data

1. Time Series Data - same set of variables in different time periods
2. Cross Sectional Data - same set of variables at a point of time over different cross-sections
3. Pooled Data - cross-section dataset over different time periods

Some Sample Statistics

Mean - add all, divide by total #

Median - sum average/middle value of mean and mode

Mode - max probality, most frequent value of variable

Standard deviation - average deviation from the mean

CV (coefficient of variation) - in relation tp mean it ttells how signigicant/how much variance)

Measure of Associaion - relationship between variables

 1. positive, negative, none

 2. covariance (cov) and correlation (p) - makes relative to variance
*Sometimes it is heapful to figure the prooduct of deviations and the sum of squared deviations

Regression - process of finding line or curve that "best" fits a given set of data points (F. Galton, 1886)

OLS linear regression - smalles sumof sqaure error for all points from the line/curve

   - good for estimating what comes next
   - good at average

Multivariate - plane of best fit (rather than a line)

  1. structural or reduced forms
  2. robustness or specification tests
  3. intuition or hedonics

Two books mentioned in class concerning how we know:

1. On being certain: believing you are right even when you're not by Robert Burton
BD171 .B87 2009 

Covering: the feeling of knowing, how do we know what we know?, classification of mental states and neural networks, when does a thought begin?, genes, perceptual and sensational thoughts, reason and objectivity, faith, etc.

2. Thinking Fast and Slow by Daniel Kahneman
BF441 .K238 2011  

The author, a recipient of the Nobel Prize in Economic Sciences for his seminal work in psychology that challenged the rational model of judgment and decision making, has brought together many years of research and thinking. He explains two systems that drive the way we think. System 1 is fast, intuitive, and emotional; System 2 is slower, more deliberative, and more logical.