Lord William Thomson, 1st Baron Kelvin
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Transcript of Lord William Thomson, 1st Baron Kelvin
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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
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Statistics =“getting meaning
from data”(Michael Starbird)
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descriptivestatistics
“inferential”statistics
measures of central values,measures of variation,
visualization
beatingchance!
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“inferential”statistics
beatingchance!
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“inferential”statistics
beatingchance!
SamplePopulation
inference
PARAMETERS
ESTIMATES
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But what’s the valueof inferential statisticsin our field??1. More explicit theories
2. More constraints on theory
3. (Limited) generalizability
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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
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Type I error =behind bars…… but not guilty
Type II error =guilty…… but not
behind bars
The (twisted) logic of hypothesis testing
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p < 0.05What does
it really mean?
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p < 0.05= Given that H0 is true,
this data would befairly unlikely
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One-sample t-test
Unpairedt-test ANOVA
ANCOVA Regression
MANOVAχ2
test
Discrimant
Function Analysis
Pairedt-test
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One-sample t-test
Unpairedt-test ANOVA
ANCOVA Regression
MANOVAχ2
test
Discrimant
Function Analysis
Pairedt-test
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Linear Model
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GeneralLinear Model
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GeneralLinear Model
GeneralizedLinear Model
GeneralizedLinearMixed Model
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GeneralLinear Model
GeneralizedLinear Model
GeneralizedLinearMixed Model
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what you measure
what you manipulate
“response”
“predictor”
RT ~ Noise
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best fitting line(least squares estimate)
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the intercept
the slope
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Same intercept, different slopes
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Positive vs. negative slope
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Same slope, different intercepts
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Different slopes and intercepts
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The Linear Model response ~ intercept + slope * predictor
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The Linear ModelY ~ b0 + b1*X1
coefficients
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The Linear ModelY ~ b0 + b1*X1
slopeintercept
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The Linear ModelY ~ 300 + 9*X1
slopeintercept
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With Y ~ 300 + 9 *x,what is the response time for a
noise level of x = 10?
30010
300 + 9*10 = 390
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Deviation from regression line
= residual
“fitted values”
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The Linear ModelY ~ b0 + b1*X1 + error
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The Linear ModelY ~ b0 + b1*X1 + error
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is continuous
is continuous,too!
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RT ~ Noise
men
women
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men
women
RT ~ Noise + Gender
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The Linear ModelY ~ b0 + b1*X1 + b2*X2
coefficientsof slopes
coefficient ofintercept
noise(continuous)
gender(categorical)
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The Linear Model
“Response” ~ Predictor(s)
Has to be onething
Can be one thingor many things
“multiple regression”
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The Linear Model
“Response” ~ Predictor(s)
(we’ll relaxthat constraint
later)
Can be of any data type
(continuous or categorical)
Has to becontinuous
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The Linear Model
RT ~ noise + gender
examples
pitch ~ polite vs. informal
Word Length ~ Word Frequency
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Edwards & Lambert (2007); Bohrnstedt & Carter (1971); Duncan (1975); Heise (1969); in Edwards & Lambert (2007)
Correlation is (still) not causation
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“Response” ~ Predictor(s)
Assumed directionof causality
Correlation is (still) not causation
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