Goals of Statistics 8/27

How are you today? A - excited to learn some statistics B - willing to learn some statistics C - wish they didn't make us take statistics D - hung over E - present F - up all night finishing grant proposal

Overview Types of scientific studies Independent and dependent variables Populations and samples Parameters vs. statistics Descriptive vs. inferential statistics

Scientific Studies Experiment Non-experiment Involves some sort of intervention Researcher sets some variable(s) and assesses effect on other variable(s) Vary number of items in a memory list Allows inference of causation Non-experiment Purely observational Measure naturally occurring variables and examine relationships Row of classroom, exam grade Can't be sure about causality

Non-experiments Measure variables without influencing Correlation Row of classroom, exam grade Time spent outside, depression Bicycles currently owned, lifetime head injuries (6, 4) Apples per week, colds per year Correlation Reverse causation High scores reduce pressure Motivation Third variable problem Health-consciousness Selection Math GREs by major Quasi-independent variables Height by sex Row Score Attitude Colds Apples

Experiments X Independent variable Dependent variable Manipulated by researcher Drug/placebo, training time, priming Importance of control Dependent variable Measured by researcher Recovery rate, proficiency, reaction time Intervention assures causality Random assignment Values of IV chosen at random for each subject Only way to assure causal relationship 3rd variable again Outright cheating Time of semester Attitude Colds Apples X Ability Performance Condition

Populations and Samples Set of subjects, items, or events we want to learn about Generally very large or infinite All people, all men/women, all pigeons, concrete & abstract nouns, experimental trials (repetitions) Sample Subset of population assessed in a given study Much smaller Randomly selected Noisy, not perfectly representative of population (sampling error) Importance of random selection Every member of population must have equal chance of inclusion Otherwise sample is biased Selection variables may interact with outcome Undergrads Racial distribution

Parameters Characteristics of the population Usually theoretically meaningful Mean, variance, proportion, rate, correlation What's the average IQ of college students? How many attempts does it take a normal rat to learn this maze? How many attempts if we cut out its hippocampus? What fraction of words can a subject remember? What's the correlation between height and extraversion? …

Statistics Mathematical functions to be computed from data Usually serves one of three functions: Summarizes some aspect of the data (descriptive statistic) Mean, median, maximum, quartiles, standard deviation, etc. Estimates some parameter of the population (estimator) Mean, standard deviation, etc. (almost always descriptive stat too) Aids testing of some hypothesis about the population (inferential statistic) Numerical value generally has no physical meaning t, F, r, p, c2 Sample Size Effect Size Variability Effect Size * Sample Size Variability  “t” t > 2  difference probably real; t<2  probably chance