Estimation & Confidence Intervals Flashcards
what is SE
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
how do you work of the SE of the mean
SD/square root of the number of people/sample size
how do you work of the SE of the proportion
proportionx(1-P)/n
Suqareroot the answer
how do you work of the SE of the difference between two sample means
means of sample 1/number in sample 1
+
Mean of S2/N2
SQroot the number form this addition to get the SE
Standard Error (of the difference between two proportions
p1X(1-P1)/n1+ p2x(1-p2)/n2- SQroot
Properties of Standard Errors
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
what is A CI
a range of values in which we are confident the true population mean/proportion will lie
what is the formula for CI fot the mean
mean -+ [1.96xSE(f the mean)
what is the formula for CI for a proportion
p+-[1.96xSE of the p]
what is the formula for CI for diffrences between 2 means
Diffrence (x1-x2) -+ (1.96 x SE of the dif)
what is the formula for CI for diffrences between 2proportions
(p1-p2)-+ [1.96xSE of dif P]
if we repate a study 100 time how many will contain the true population value
of the 100 resulting 95% confidence intervals, we would expect 95 of these to include the population parameter, μ.
what does a 95% CI tell us
that their is a 95% liklyhood of the range containing the true pop value
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
141.13 - (1.96 x 3.41) to 141.13 + (1.96 x 3.41) = 134.4 mmHg to 147.8 mmHg
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
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
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.
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
How wide is the Ci
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
where can Clinical implication be drawn from the interval
The upper and lower limits of the interval provide a means of judging whether the results are clinically or practically important.
