Transcript History of the English Language - uni

Hypothesis testing
Hypothesis testing
•
Null hypothesis
•
Alternative (experimental) hypothesis
Example
Der Mann, der dich gesehen hat.
Der Mann, den du gesehen hast.
Der Film, der dir gefallen hat.
Der Film, den du gesehen hast.
21
6
12
17
Null hypothesis:
There is no relationship between the animacy of the
head noun and the syntactic role of the relative
pronoun.
Alternative hypothesis:
There is a relationship between the animacy of the
head noun and the syntactic role of the relative
pronoun.
Population
Sample
Animate
Inanimate
Subject
50
50
Object
50
50
Animate
Inanimate
Subject
21
12
Object
6
17
Statistical tests determines the probability that the
relationship we observe has arisen from sample
error.
If that probability is very low (i.e. > 5%), we can
reject the null hypothesis, i.e. the hypothesis that
there is no relationship between variables.
Statistical hypothesis testing does not prove that
the (explanation for the) alternative hypothesis.
p-value
The p-value is a conditional probability.
The p-value indicates that, given that there is no
relationship between x and y, what is the probability
that we obtain the distribution in our sample.
If there is no relationship (correlation) between X and Y
in the true population, then there is a less than 5%
chance (i.e. 1 out of 20 chance) that there is a correlation
in the sample.
p-value
P = 0.05. What does that mean?
The probability of the null hypothesis
to be true is 5%.
False
The probability of the alternative
hypothesis to be true is 95%.
False
Given that the null hypothesis is true,
there is a 5% chance of obtaining the
distribution in the given sample.
Correct
Type 1 and type 2 errors
•
Type 1 error: The p-value is significant (p < .05) and
you reject the null hypothesis although there is no
correlation between X and Y.
•
Type 2 error: The p-value is not significant (p >
.05) and you accept the null hypothesis although
there is a difference between X and Y.
Type 1 and type 2 errors
The p-value indicates the probability of making a type
1 error. It does not say anything about the probability
of a type 2 error occurring.
While a type 2 error is as fatal as a type 1 error, in
practice it is less dramatic. Why?
If p > 0.05 and you accept the null-hypothesis, it is not
automatically assumed that there is no correlation (or
difference) between conditions. Why?
Because sample error is only one possible source for
the non-significant p-value. Other sources:
experimental design.
One-tailed and two-tailed tests
A researcher wants to find out if sex influences
language development during childhood. He has
collected MLU values from a group of 3 year-old boys
and 3 year-old girls. – State the hypotheses.
•
Sex does not influence development (i.e. MLU).
•
Sex influences development (i.e. MLU)
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Girls have a higher MLU.
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Boys have a higher MLU.
One-tailed and two-tailed tests
Statistical measures
•
p-value
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Confidence intervals
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Effect size