estimation and confidence intervals 5/11

Question 1

The spread of the sample mean can be obtained from…

Answer 1

… taking repeated samples (of the same size) from a population.

Question 2

sample means can be plotted…

Answer 2

on …
dot plot
or
histogram.

Question 3

In the distribution of sample means, the mean of all the sample means will be the same as…

Answer 3

the population mean

Question 4

Define Standard error

Answer 4

a measure of the precision of a sample estimate

The standard deviation of the spread of mean SD of sample means (spread of means of repeated samples collected from the population) provides a measure of how far from the true value the sample estimate is likely to be.

Question 5

Equation: SE of the mean

Answer 5

SD/√n

Question 6

Equation: SE of a proportion

Answer 6

√(p(1−p)/n)

Question 7

Equation: SE of the difference between sample means

Answer 7

SE(x ̅_1−x ̅_2 )=√((s_1^2)/n_1 +(s_2^2)/n_2 )

Question 8

Equation: SE of the difference between sample proportions

Answer 8

SE(p ̅_1−p ̅_2 )=√(√(p(1−p)/n) +√(p2(1−p2)/n) )

Question 9

3 Properties of Standard Errors

Answer 9

A large SE indicates that the estimate is imprecise.
A small SE indicates that the estimate is precise.
The SE is reduced (we obtain a more precise estimate) if the size of the sample is increased.

Question 10

SE is used to construct CI

Equation: 95%CI (mean)

Answer 10

x ̅±[1.96× SE (of the mean)]

Question 11

SE is used to construct CI

Equation:95% CI (proportion)

Answer 11

p±[1.96 x SE(proportion)]

Question 12

Equation: 95% CI of the difference in two means

Answer 12

Difference in two means

(x ̅_1 − x ̅_2 ) ± [1.96 x SE(of the difference in the two means)]

Question 13

Equation: 95% CI of the difference in two means (proportion)

Answer 13

Difference in two proportions

(p_1 − p_2 ) ± [1.96 x SE(of the difference in the two means)]

Question 14

Define CI

Answer 14

A range of values that is likely to cover the true but unknown population mean value, μ.

Question 15

define 95% CI

Answer 15

the range of values within which we are 95% confident that the true population mean lies (our best estimate is the mean

Question 16

What does the width of the CI show?

Answer 16

The precision of the estimate. The width of the CI is determined by the size of the SE (depends on the sample size). When considering a numerical variable, the variability of the data. Therefore, small studies on variable data give wider CI than larger studies on less variable data.

Question 17

What clinical implications can be drawn from a confidence interval?

Answer 17

The upper and lower limits of the interval provide a means of judging whether the results are clinically or practically important

Question 18

Define: Random sample

Answer 18

All members of the population are equally likely to be picked, and each independently of each other.

this is done to pick a sample which is representative of the population

Question 19

Define: Stratified random sample

Answer 19

Stratified random sample - Population divided into groups beforehand, e.g. males and females before random sampling conducted.

Question 20

Define: Cluster sampling

Answer 20

Cluster sampling - e.g. GP practices randomised not individual GP’s.

Question 21

Define: Quota sample

Answer 21

Quota sample - As used by opinion polls etc, supposedly more ‘representative’ of population.

Question 22

Define: ‘Convenience’ sample

Answer 22

‘Convenience’ sample e.g. Those patients who turn up at an outpatient clinic. May nor be reflective of population