Flashcards in The t-distribution, CI and hypothesis Tests for means Deck (15)

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1

## What is the t-distribution?

### a symmetric probability distribution that depends for its exact shape on a parameter known as degrees of freedom (df)

2

## 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

3

## 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

4

## What happens to the critical value as sample size decreases?

### it increases

5

## 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

6

## What are the assumptions required for calculating the CI using t -test?

###
the observations are normally distributed

the observations are independent

7

## 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

8

## 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)

9

## 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

10

## What is Sp?

### square root of ((n1-1)s1squared +(n2-1)s2squared/n1+n2-2)

11

## 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

12

## 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

13

## What would we do if the p value was very small?

### reject the Ho

14

## What would we do if the p value was very large?

### Fail to reject the null hypothesis

15