What does statistical significance mean?
result of a statistical test
if a sample deviates strongly enough from an assumption made beforehand (the Null hypothesis), so that this assumption can be rejected according to a rule also defined beforehand
What is a significance level?
The significance level alpha (probability of error) is mostly defined beforehand and states the probability that H0 is rejected by mistake.
Explain the terms standard deviation, t-test and p-value.
standard deviation states the intensity of the spread of observations around their mean
t-test is a statistical test used to compare the means of two groups and determine if the differences between them are statistically significant
p-value is consistent with the lowest significance level, with which H0 can be rejected. If we were too low, the probability of error alpha any lower we could not reject H0 any longer
What is economic relevance in this context?
Compare the effect of the variable with the mean of the variable and ask whether the effect is large or small?
Interpret the marginal effect of the continuous variable x and the binary variable z in the following models:
y= β0 + β1· x+ β2· z+ ϵ
Level-level: A one unit increase of x results on average in a ß1 unit change in y c.p. when z changes from 0 to 1, y changes on average by ß2 c.p.
log(y) = β0 + β1· x+ β2· z+ ϵ
log-level: A one unit increase of x results on average in a 100xß1% change in y c.p. When z changes from 0 to 1, y changes on average by 100xß2% c.p.
y= β0 + β1· log(x) + β2· log(z) + ϵ
level-log: When x increases by 1%, y changes on average by ß1/100 units c.p. It is not possible to dummy variables, as log(0) is not defined. The model can not be estimated.
log(y) = β0 + β1· log(x) + β2· log(z) + ϵ
log-log: When x increases by 1%, y changes on average by ß1% c.p. Again log(0) is not defined.
y= β0 + β1· x+ β2· x2 + β3· z2 + ϵ
For a one unit increase in x, y increases by ß1 + 2ß2x c.p.
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