Estimation & Confidence Intervals

Question 1

what is SE

Answer 1

The standard deviation of all the sample means (not individual values!) is known as the STANDARD ERROR.

The standard error (SE) is an estimate of the precision of the population parameter estimate that does not require lots of repeated samples.
It provides an measure of how far from the true value the sample estimate is likely to be

Question 2

how do you work of the SE of the mean

Answer 2

SD/square root of the number of people/sample size

Question 3

how do you work of the SE of the proportion

Answer 3

proportionx(1-P)/n

Suqareroot the answer

Question 4

how do you work of the SE of the difference between two sample means

Answer 4

means of sample 1/number in sample 1
+
Mean of S2/N2

SQroot the number form this addition to get the SE

Question 5

Standard Error (of the difference between two proportions

Answer 5

p1X(1-P1)/n1+ p2x(1-p2)/n2- SQroot

Question 6

Properties of Standard Errors

Answer 6

a measure of the precision of a sample estimate

A large standard error indicates that the estimate is imprecise.

A small standard error indicates that the estimate is precise.

The standard error is reduced, that is, we obtain a more precise estimate, if the size of the sample is increased

Question 7

what is A CI

Answer 7

a range of values in which we are confident the true population mean/proportion will lie

Question 8

what is the formula for CI fot the mean

Answer 8

mean -+ [1.96xSE(f the mean)

Question 9

what is the formula for CI for a proportion

Answer 9

p+-[1.96xSE of the p]

Question 10

what is the formula for CI for diffrences between 2 means

Answer 10

Diffrence (x1-x2) -+ (1.96 x SE of the dif)

Question 11

what is the formula for CI for diffrences between 2proportions

Answer 11

(p1-p2)-+ [1.96xSE of dif P]

Question 12

if we repate a study 100 time how many will contain the true population value

Answer 12

of the 100 resulting 95% confidence intervals, we would expect 95 of these to include the population parameter, μ.

Question 13

what does a 95% CI tell us

Answer 13

that their is a 95% liklyhood of the range containing the true pop value

Question 14

example
The mean systolic blood pressure in our sample of 16 middle aged men is = 141.13 mmHg with a standard deviation of s = 13.62 mmHg. The standard error (of the mean) is 3.41mmHg.
what is the CI

Answer 14

141.13 - (1.96 x 3.41) to 141.13 + (1.96 x 3.41) = 134.4 mmHg to 147.8 mmHg

Question 15

example

Out of 263 patients giving their views on the use of personal computers in general practice, 81 thought that the privacy of their medical file had been reduced
find the CI

Answer 15

Proportion- 81/263- 0.31
SE- (0.31X(1-0.31)/263- SQROOT- 0.028

CI
0.31-+(1.96x0.028)- 2.25 to 0.36

Question 16

example
Blood pressure levels were measured in 100 diabetic and 100 non-diabetic men aged 40-49 years. The mean systolic blood pressures were 146.4 mmHg (SD 18.5) among the diabetics and 140.4 mmHg (SD16.8) among the non-diabetics.

Answer 16

mean 1- mean 2
146.4-140.4-6
SE- 18.5Z(2)/100 + 16.82(2)/100- SQroot= 2.50

6-+(1.96x2.50)= 1.1 to 10.9

Question 17

How wide is the Ci

Answer 17

A wide interval shows that the estimate is imprecise; a narrow interval shows a more precise estimate. The width of the confidence interval is determined by the size of the standard error, which in turn depends on the sample size and, when considering a numerical variable, the variability of the data. Therefore, small studies on variable data give wider confidence intervals than larger studies on less variable data

Question 18

where can Clinical implication be drawn from the interval

Answer 18

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