ECON2300 lecture 1 intro notes

LECTURE 1: INTRODUCTION & REVIEW USING DATA TO MEASURE CASUAL EFFECTS:  Ideally, we would like an experiment - What would be an experiment to estimate the effect of class size on standardized test scores?  almost always, we only have observational (nonexperimental) data - returns to education - cigarette prices - monetary policy  Most of the course deals with difficulties arising from using observational to estimate causal effects - confounding effects (omitted factors)  not all relevant variables are observed  omitted factors cause bias to arise - simultaneous causality - correlation does not imply causation  although correlation is closely related to causation 1.2 EXAMPLE: THE CALIFORNIA TEST SCORE DATA SET  Empirical problem: class size & educational output  2 main variables of interest  Policy question: what is the effect on test scores of reducing class size by one student per class? Important question for decision makers as they have to allocate resources & money to improve education  We use data from California school districts (n=420)  We observe 5 th grade test scores (district average) & student-teacher ratio (STR) 1.INITIAL LOOK AT THE DATA - this table doesn't tell us anything about relationship b/w test scores & STR 2. DRAW SCATTER PLOT OF 2 VARIABLES  Do districts with smaller classes have higher test scores? What does this figure show? - Some data distribution, but relationship b/w test score & STR is unclear

3. GETTING NUMERICAL EVIDENCE ON WHETHER DISTRICTS W/ LOW STRS HAVE HIGHER TEST SCORES: 1. Estimation: - compare average test scores in districts w/ low STRs to those w/ high STRs 2. Hypothesis testing: - test the "null" hypothesis that the mean test scores in the 2 types of districts are the same, against the "alternative" hypothesis that they differ  statistical inference 3. Confidence interval: - estimate an interval for the difference in the mean test scores, high vs low STR districts INITIAL DATA ANALYSIS:  To do estimation, hypothesis testing & confidence intervals  classify districts by class size  Compare districts with "small" (STR < 20) and "large" (STR ≥ 20) class sizes:  We will do the following: 1. Estimation of ∆ = difference between group means 2. Test the hypothesis that ∆ (difference) = 0 3. Construct a confidence interval for ∆ (difference) 1.3. 1. ESTIMATION: Is this difference large in a real-world sense?  Standard deviation of all test scores across districts = 19.1  difference is not that large  not even 1 SD  statistical observation  Difference b/w the 60 th & 75 th percentiles of test score distribution is 666.7-659.4=7.3  similar to mean difference  statistical observation  It's hard to know if this difference is large in a real-world sense  more info. needed on whether the difference is large or not "small" class size: STR < 20 "large" class size: STR ≥ 20

2. HYPOTHESIS TESTING:  Difference-in-means test: compute the t-statistic: COMPUTE THE T-STATISTIC: 3. CONFIDENCE INTERVAL:  A 95% confidence interval for the difference between the means is:  confidence intervals are closely related for hypothesis testing CONCEPTS REVIEW: RANDOM VARIABLE:  informally, a random variable gives you a number that's determined by outcomes of underlying experiments  concept of random variable is closely related to experiments & experimental outcomes  in stats, the term experiment is used more broadly - e.g the experiment here may include some complicated underlying process that determines the gender, weight, size etc. of a newborn baby - e.g some unknown process that determines a graduates first salary & its difference for the salary of a high school graduate  referred to as an experiment