Week 5 day 2 Flashcards
Is Central Limit Theorem one of the most important results in statistics?
Yes.
What is the sampling distribution of the mean?
The sampling distribution of the mean is a theoretical idea that captures what you would expect the means of lots of samples from a population to look like.
What is the Central Limit Theorem?
Central Limit Theorem says that the sampling distribution of the mean will always be normal, regardless of the shape of the underlying distribution.
What does a confidence interval mean for a sampling distribution of the mean?
A 95% confidence interval gives the range that reflects where a sample’s mean would fall 95% of the time.
The larger the range of our confidence interval, the less confident we are about estimating the true mean of a population.
The sampling distribution of the mean is built from two key pieces of data: our sample mean and standard error of the mean, which is determined from sample standard deviation and sample size.
Is it true that any statistical claim you make when doing null hypothesis significance testing is about the nulll hypothesis and NOT the alternative hypothesis?
Yes.
What is a type I error?
A type I error is a false positive - we accept the alternative when the hull hypothesis is actually correct.
It occurs when we reject the null hypothesis when it is actually correct.
Type I error rate is denoted as alpha.
Alpha is called the significance level.
What is a type II error?
A type II error is a false negative. - we accept the null when it is actually false.
It occurs when we accept the hull hypothesis when the alternative is actually correct and we should have accepted the altnerative.
Type II error rate is denoted as beta.
Beta is called the power.
In general, which is worse?/Which do we want to avoid the most out of type I and II errors?
Type I errors are the ones we really want to avoid, but we also want to avoid type ii errors as well.
Is NHST based around avoiding type I errors?
Yes.
In an ideal world both alpha and beta would be zero. However, this is not the case and when all else is equal lower alpha means higher beta.
True?
True.
As alpha increase, what happens to beta?
Beta decreases.
What is a test statistic?
Could be mean or standard deviation or anything you can calculate from your data.
It has to be one number and it is chosen based on what we think will differentiate the alternative from the null.
What is a p-value?
p-value is the probability of observing the value from our data given the null was true.
If our alpha is 0.05, then we would only reject null hypothesis if p is <0.05
p-value is the probability that the alternative hypothesis is true.
True or false?
False!
p-value is the probability of obersving a certain value GIVEN the NULL hypothesis is TRUE.
Can you say that p is probability that the null hypothesis is true?
No!
This is “so badness”.
p is only referring to the probability that we see the observed data if the null hypothesis is tue.
