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“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
