Uncertainty and Hypothesis Testing Flashcards
Lecture 3 (18 cards)
estimand
unobserved quantity we are trying to learn about
estimator
the procedure we apply to data to generate a numerical result
estimate
the numerical result arising from the application of our estimator
estimator error
estimate - truth
estimate = estimand + bias + noise
bias is difference between estimate and estimand that arise for systematic reasons. Noise is the differences that arise due to idiosynchratic facts about the sample
sampling distribution
the imaginary distribution of estimates if we repeated sampling and estimation process many times
two ways to quantify precision
standard error and confidence interval
standard error
standard deviation of the sampling distribution
confidence interval
an interval so that 95% of all values that we obtain from repeated sampling yield contains the population B1 value - thus under repeated sampling, the true B1 will lie within the confidence interval
what does the confidence interval mean
If we draw many samples from the same population, we would expect approximately 95% of
the samples to produce confidence intervals that correctly contain the population mean.
p-value
the probability that we would observe a value at least as extreme
as the one we observed if H0 is true
test statistic
function of observed data that can be used to test the null hypothesis.
reference distribution
probability distribution of the test statistics under the null
test stat
the test statistic is a function of our data whose sampling distribution under the
null is known
z stat
This z-statistic tells us how
many standard deviations away our estimate of βˆ
1 is from the true β1 (if we assume the
hypothesized value is true β1).
Z
statistically signficant
when it is not likely to be 0
substantively signficant
when its size is large enough to be consequential
