“I often say that when you can measure what you are speaking about, and express it in numbers, you...

“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)

descriptivestatistics

“inferential”statistics

measures of central values,measures of variation,

visualization

beatingchance!

“inferential”statistics

beatingchance!

“inferential”statistics

beatingchance!

SamplePopulation

inference

PARAMETERS

ESTIMATES

But what’s the valueof inferential statisticsin our field??1. More explicit theories

2. More constraints on theory

3. (Limited) generalizability

H0 = there is no difference, or there is no correlation

Ha = 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 < 0.05What does

it really mean?

p < 0.05= Given that H0 is true,

this data would befairly unlikely

One-sample t-test

Unpairedt-test ANOVA

ANCOVA Regression

MANOVAχ2

test

Discrimant

Function Analysis

Pairedt-test

One-sample t-test

Unpairedt-test ANOVA

ANCOVA Regression

MANOVAχ2

test

Discrimant

Function Analysis

Pairedt-test

Linear Model

GeneralLinear Model

GeneralLinear Model

GeneralizedLinear Model

GeneralizedLinearMixed Model

GeneralLinear Model

GeneralizedLinear Model

GeneralizedLinearMixed 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 ~ b0 + b1*X1

coefficients

The Linear Model

Y ~ b0 + b1*X1

slopeintercept

The Linear Model

Y ~ 300 + 9*X1

slopeintercept

With Y ~ 300 + 9 *x,what is the response time for a

noise level of x = 10?

30010

300 + 9*10 = 390

Deviation from regression line

= residual

“fitted values”

The Linear Model

Y ~ b0 + b1*X1 + error

The Linear Model

Y ~ b0 + b1*X1 + error

is continuous

is continuous,too!

RT ~ Noise

men

women

men

women

RT ~ Noise + Gender

The Linear Model

Y ~ b0 + b1*X1 + b2*X2

coefficientsof slopes

coefficient ofintercept

noise(continuous)

gender(categorical)

The Linear Model

“Response” ~ Predictor(s)

Has to be onething

Can be one thingor many things

“multiple regression”

The Linear Model

“Response” ~ Predictor(s)

(we’ll relaxthat constraint

later)

Can be of any data type

(continuous or categorical)

Has to becontinuous

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 directionof causality

Correlation is (still) not causation