Hypothesis testing Flashcards
What is the Central Limit Theorem?
If you repeatedly take samples form the same population at any given sample size, and calculate sample means and plot these means both these means are normally distributed
Population mean distribution = Population mean
What is the standard error of the mean?
Measure of how much the sample means would on average differ from the population mean
Measure of just how variable the estimate of the mean is
What are confidence limits?
Limits between which estimated parameters have a defined likelihood of occurring e.g. 95% or 99%
How do you calculate a 95% confidence limit?
Need to know 3 things:
1) Sample mean
2) Estimated SE
3) The number of ±SE away from the estimate of the population mean within which the real population mean (μ) will be found 95 times out of 100 (found using the t-distribution)
Estimate of the population mean within which the real population mean will be found 95 times out of 100
What is the formula for estimating standard error?
What is the formula for 95% CI?
LEARN IT ITS IN THE BOOK
SE is smaller than s (sample standard deviation) and gets smaller still as n increases
Have to use the t-distribution: Similar to normal distribution but accounts for the fact that we have to be more cautious because we have ESTIMATED our standard error
Increase sample size= Better confidence level
How do you carry out a null hypothesis test?
1) Formulate a null hypothesis
2) Calculate the test statistic- Measuring the size of any effect relative to the amount of variability there is in the sample
3) Calculate the significance probability. The probability of getting the effect measured just by chance, if the null hypothesis were true
4) If the test statistic is consistent with the null (95%)= Retain the null
What is a null hypothesis (H0)?
A statement about the value of a population parameter. Your data may allow you to reject this hypothesis
What is the alternative hypothesis (H1)?
A statement that describes the value of the population parameter if H0 is rejected
What is a hypothesis test?
A statistical test that tests the claim made about a parameter by H0 against that made by H1. Tests whether H0 should be rejected or not, based on evidence from sample data
What is a test statistic?
A statistic calculated from sample data that is used to decide whether or not to reject H0
What does a One-sample t test test for?
Test whether the sample mean from a single population is different from an expected value (E)
Calculates how many standard errors the sampling mean is away from the expected value
The further away the mean is from E, the larger the value of t and the less probable it is that the real population mean could be the expected value= significant
If |t| > critical value, the difference is significant= Reject the null hypothesis
What is the critical value?
Boundary between something that is rare and not rare
What does the t-test strictly assumes?
When do you use this test?
The subjects come from a normal distribution
1540 and the data is roughly normal OR n>40 even if data is not normal as Central limit theorem= a big enough the sample size, the sample means tends to be normally distributed anyway even if the underlying data is not
What are different types of errors?
Type I error (α): probability of rejecting the null hypothesis when it is true
Type II error (β): probability of failing to reject the null hypothesis when it is false
What are independent samples?
Knowing a value form one sample gives no information about a value in the other sample
