“I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it” Lord William Thomson, 1st Baron Kelvin

Statistics = “getting meaning from data” (Michael Starbird)

descriptive statistics “inferential” statistics measures of central values, measures of variation, visualization beating chance!

“inferential” statistics beating chance!

“inferential” statistics beating chance! Sample Population inference PARAMETERS ESTIMATES

But what’s the value of inferential statistics in our field?? 1. More explicit theories 2. More constraints on theory 3. (Limited) generalizability

H 0 = there is no difference, or there is no correlation H a = there is a difference; there is a correlation The (twisted) logic of hypothesis testing

Type I error = behind bars… … but not guilty Type II error = guilty… … but not behind bars The (twisted) logic of hypothesis testing

p < 0.05 What does it really mean?

p < 0.05 = Given that H 0 is true, this data would be fairly unlikely

One- sample t-test Unpaired t-test ANOVA ANCOVA Regression MANOVA χ 2 test Discrimant Function Analysis Paired t-test

One- sample t-test Unpaired t-test ANOVA ANCOVA Regression MANOVA χ 2 test Discrimant Function Analysis Paired t-test

Linear Model

General Linear Model General Linear Model

General Linear Model General Linear Model Generalized Linear Model Generalized Linear Model Generalized Linear Mixed Model

General Linear Model General Linear Model Generalized Linear Model Generalized Linear Model Generalized Linear Mixed Model

what you measure what you manipulate “response” “predictor” RT ~ Noise

best fitting line (least squares estimate)

the intercept the slope

Same intercept, different slopes

Positive vs. negative slope

Same slope, different intercepts

Different slopes and intercepts

The Linear Model response ~ intercept + slope * predictor

The Linear Model Y ~ b 0 + b 1 *X 1 coefficients

The Linear Model Y ~ b 0 + b 1 *X 1 slopeintercept

The Linear Model Y ~ *X 1 slopeintercept

With Y ~ *x, what is the response time for a noise level of x = 10? *10 = 390

Deviation from regression line = residual “fitted values”

The Linear Model Y ~ b 0 + b 1 *X 1 + error

The Linear Model Y ~ b 0 + b 1 *X 1 + error

is continuous is continuous, too!

RT ~ Noise men women

men women RT ~ Noise + Gender

The Linear Model Y ~ b 0 + b 1 *X 1 + b 2 *X 2 coefficients of slopes coefficient of intercept noise (continuous) gender (categorical)

The Linear Model “Response” ~ Predictor(s) Has to be one thing Can be one thing or many things “multiple regression”

The Linear Model “Response” ~ Predictor(s) (we’ll relax that constraint later) Can be of any data type (continuous or categorical) Has to be continuous

The Linear Model RT ~ noise + gender examples pitch ~ polite vs. informal Word Length ~ Word Frequency

Edwards & Lambert (2007); Bohrnstedt & Carter (1971); Duncan (1975); Heise (1969); in Edwards & Lambert (2007) Correlation is (still) not causation

“Response” ~ Predictor(s) Assumed direction of causality Correlation is (still) not causation