Confidence Intervals and Standard Error of the Mean

Question 1

What is the simple definition of a confidence interval?

Answer 1

A range of values within which the true effect of intervention is likely to lie.

Question 2

What determines the true effect lying within the confidence intervals?

Answer 2

The determined confidence level.

(e.g. Confidence level of 95% means the true effect will lie within the confidence interval 95% of the time)

Question 3

What is the standard error of the mean?

Answer 3

A measure of the spread expected for the mean of the observations (i.e. how ‘accurate’ the calculated sample mean is from the true population)

Question 4

How do you calculate the SEM?

Answer 4

SEM=SD/ Square root of n

n=sample size.

Question 5

If the sample size gets bigger, what happens to the SEM?

Answer 5

It gets smaller

(Because it more accurately represents the mean)

Question 6

If you have a 95% confidence interval, what are the upper and lower confidence limits?

Answer 6

Lower limit= mean - (1.96 x SEM)

Upper limit = mean - (1.96 x SEM)

NOTE: 1.96 comes from the Student’s T critical value look-up table to replace 1.96 with a different value depending on what confidence interval you want.

Question 7

Sometimes a mean value is given along with confidence intervals. Solve this:

Mean height in a sample is 183cm.

The standard error of the mean is 2cm.

What is your 95% confidence interval limits?

Answer 7

Limts = 183 +/- (1.96 x 2) = ~4

therefore 183 +/- 4 = 187 and 179.

Question 8

A follow-up study is performed looking at the height of 100 adults who were given steroids during childhood. The average height of the adults is 169cm, with a standard deviation of 16cm. What is the standard error of the mean?

Answer 8

Standard error of the mean =

standard deviation / square root (number of patients)

16/10 = 1.6cm