The t-distribution, CI and hypothesis Tests for means Flashcards
What is the t-distribution?
a symmetric probability distribution that depends for its exact shape on a parameter known as degrees of freedom (df)
What do degrees of freedom represent?
the information content of a sample of information, allowing for the fact that we need to estimate a standard deviation before carrying out any formal inference
When is student’s t test used?
to adjust confidence interval for use with small samples (<30) as can’t measure the variability of the sample mean very precisely
What happens to the critical value as sample size decreases?
it increases
What is the formula for confidence intervals in small sample sizes?
sample mean +/- (t(5%, n-1) x SE(mean) Where t(5%, n-1) is the critical value for the t distribution with n-1 df
What are the assumptions required for calculating the CI using t -test?
the observations are normally distributed
the observations are independent
What is a common use for the 1-sample confidence interval?
the situation where ether are 2 measurements on each individual in the study (paired data)
The difference in each measurement in each subject can be used as the quantity of interest and a ci for the derived value can be used
How do you calculate the CI for the difference between two population means?
(sample mean1- sample mean 2) +/- t(5%,n1 +n2 - 2) X SE(mean1-mean2)
when SE for (mean1-mean2 ) is square root of Sp2(1/n1+1/n2)
What assumptions are required when using CI for the difference between two population means?
both sets are Normally distributed
the population variability is the same in each group
the observations are independent
What is Sp?
square root of ((n1-1)s1squared +(n2-1)s2squared/n1+n2-2)
What does a hypothesis test do?
attempts to measure the strength of the evidence supporting statements about population parameters relating to a measurement of interest, and report this in a brief, numerical summary
What does the P value tell you?
The probability that we could have obtained the observed data (or data that were more unusual or extreme) assuming that the Null hypothesis is truw
What would we do if the p value was very small?
reject the Ho
What would we do if the p value was very large?
Fail to reject the null hypothesis
What is the general procedure for hypothesis testing?
Define Ho
Calculate the relevant test statistic
Compare the observed value of the Test statistic to it reference distribution, assuming that Ho is true, obtain the p value
inspect the p value to decide whether or not to reject Ho
