Download Standard error of estimate & Confidence interval

Survey
yes no Was this document useful for you?
   Thank you for your participation!

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Document related concepts

German tank problem wikipedia, lookup

Law of large numbers wikipedia, lookup

History of statistics wikipedia, lookup

Taylor's law wikipedia, lookup

Bootstrapping (statistics) wikipedia, lookup

Misuse of statistics wikipedia, lookup

Transcript
Standard error of estimate
&
Confidence interval
Two results of probability theory
 Central limit theorem

Sum of random variables tends to be normally
distributed as the number of variables
increases
 Law of large numbers

Larger sample size -> the relative frequency in
the sample approaches that of a population
-> the sample average is closer to population
mean
Calculating expected values and
variances
x: random variable
k: constant
E(x)=expected value of x
V(x)=variance of x
E(x+x)=E(x)+E(x)
V(x+x)=V(x)+V(x) (if independent)
E(k*x)=k*E(x)
V(k*x)=k2 V(x)
V(x/k)=V(x)/ k2
Standard error of an estimator
 Before knowing the value:
“Standard deviation of the estimates in repeated
sampling IF the true value of the parameter was
known”
 After knowing the observed value:
“Standard deviation of the estimates in repeated
sampling IF the true value of the parameter is the
observed one”
 Not a statement of uncertainty about the parameter,
but a statement of uncertainty about the hypothetical
values of the estimator
Confidence interval
 95% CI:
Intervals calculated like this one include the
true value of the parameter in 95% of the
cases within infinitely repeated sampling
 Interval is random, it depends on the
randomly sampled data
 Wrong interpretation:
“The true value of the parameter lies in this
interval with probability 0.95”
95% Confidence interval for the mean
 Interval that contains the true mean in 95% of
the cases in infinitely repeated sampling
 Sample averages are approximately normally
distributed
 Assume known standard deviation of the
population:

 

, x  1.96
 x  1.96

n
n
