Standard errors Flashcards
what does the standard error of the mean represent?
uncertainty around the mean, and with more data we are more certain about the value
what is the idea behind standard error?
since our sample was random, we could have gotten different data. With different data, we’d get a different mean and sd.
definition of standard error
The standard deciation of the sampling distribution
how to calculate standard error
standard diviation from the sample/ root of sample size
how does standard error relate to P-values
as we increase the sample size deceraseing the standard error we get a decrease in the p-value making it more likley to reject the null hypo
relationship between power and the standard error
Power depends on the distance between u and u0 relative to the standard error ( increasing sample size decreases standard error and gives more power)(ability to reject the null)
type II error and its relationship to standard error
Type II error is a false negative ( not rejecting when null is false) this may be due to low power(ability to reject the null) which is due to a high standard error, this may be solved by increaseing the samples size
how does standard error relate to the test statictic?
the test statisitc is used to detemrine the likelyhood of observing our data under the null hypothesis. The test statistic is derboed from the sample data and the preamaters of the popultion and thus may have variability if repeated. The standard error of the test statistic quantidies how much variability we would expected within the test statistic if we were to have repeated the sampling process many times
how does standard error relate to the p-value
p-values indicate the probability of observing the test statistic or one more extream under the assumption that the null hypo is true. the standard error quantifies the varibaility we would observe if we were to have rerun the sampling process randomly multiple times. (how much the p-value varryies to chance alone
