Review Measure testosterone level in rats; test whether it predicts aggressive behavior. What would make this an experiment? Randomly choose which rats to measure Force some rats to get into fights Manipulate testosterone levels Make sure nothing differs across rats except testosterone

Review Measure testosterone level in rats; test whether it predicts aggressive behavior. Perhaps getting in fights increases testosterone. What kind of problem is this? Reverse causation Confound Self-selection Third-variable problem

Review Test people’s memory for lists of nouns or verbs, to see if one is easier to recall. Word type (noun/verb) is a(n) Confound Independent variable Dependent variable Data

Goals of Statistics 9/3

Overview Populations and samples Parameters vs. statistics Types of statistics

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, all concrete or abstract nouns Sample Subset of population assessed in a given study Much smaller Randomly selected Not perfectly representative of population (sampling variability) Sometimes population is hypothetical Experimental trials (repetitions) Your reaction time to a red square Imagine we could repeat infinite times Sample is finite times we actually do it

Random Selection Every member of population must have equal chance of inclusion Property of data-gathering process Study design must take random selection into account Otherwise sample is biased Only testing students at library Selection variables may interact with outcome People/events in sample may differ from rest of population Undergrads Racial distribution

Parameter Characteristic 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? …

Statistic Mathematical function to be computed from data Difference between statistic and its value E.g., mean is a statistic (arithmetic average) Value for any dataset will be some number Usually serves one of three functions Descriptive statistic: Summarizes some aspect of the sample data Estimator: Estimates some parameter of the population Inferential statistic: Aids testing of some hypothesis about the population

Descriptive Statistic Summarizes some aspect of the data Mean, median, maximum, quartiles, standard deviation, etc. Used only for describing sample data Not for making inferences about population Can be first step of data analysis Also useful if sample is all you’re interested in E.g. average age of students in class

Estimator Estimates some parameter of the population Mathematical function applied to sample that usually gives close to correct answer for population Usually also a descriptive statistic Sample mean is estimator for population mean Difference is just in what you use it for Sampling error Value of estimator almost never exactly correct Different samples give different results

Inferential Statistic Aids testing of some hypothesis about the population Indicates how reliable an effect in the sample is Value generally has no physical meaning Not like inches, time, or even psychological variables Examples: t, F, c2, p Sample Size Effect Size Variability Effect Size * Sample Size Variability  “t” t > 2  difference probably real t < 2  probably chance

Review Which qualifies as random selection? Measure 200 people, then randomly choose 100 to base your analysis on Randomly select what variables to measure Randomly choose members of the population to be in your study For every subject, randomly decide which experimental group they are in

Review Which of these is NOT a population? All women in Lithuania All English prepositions Your mom’s reaction times to a blue circle, if we showed it to her an infinite number of times All subjects in an experiment

Review You want to know whether men or women can hold their breath longer. You measure 10 of each and get averages of 116 seconds for the mean and 107 seconds for the women. Then you compute a number that tells you whether that difference is reliable. This number is a(n) Descriptive statistic Estimator Inferential statistic Parameter