CONFIDENCE INTERVALS

Question 1

336 adults with osteoarthritis of the knee were included to test New Consultation vs Usual Consultation. At 4 months, New group showed greater weight loss than Usual group (mean 1.11 kg (95% CI 0.70 to 1.52) v 0.37 kg (0.02 to 0.72); P=0.007). Authors concluded that, compared with Usual, the New Consultation resulted in significantly greater short term weight loss

How would you best describe the info provided by 95% confidence interval for mean weight loss at 4 months for the New Consultation group?

Answer 1

There is a probability of 0.95 that the population mean weight loss at 4 months with the New Consultation would be between 0.70 kg and 1.52 kg

Question 2

At 4 months, the New Consultation group showed mean weight loss of 1.11 kg. Mean weight loss is the sample estimate of the population parameter, sometimes referred to as what?

Answer 2

Point estimate

Question 3

What is the ‘population parameter’ in this context?

Answer 3

The mean weight loss that would be seen in the population if all members received the New Consultation

Question 4

What would the ‘population’ be in this context?

Answer 4

Those adults with osteoarthritis of knee who fulfilled trial’s inclusion criteria

Question 5

Why is a sample is taken from the population to estimate the population parameter?

Answer 5

The population parameter is in effect constant but unknown and therefore needs to be tested

Question 6

Because not all of the population was studied, sampling error may have been introduced - what does this mean for the sample estimate?

Answer 6

Sample estimate may not equal population parameter exactly

Question 7

Why is it essential that some indication of the precision of the sample estimate is derived?

Answer 7

Sample estimate may not equal population parameter exactly because not all of the population was studied

Question 8

What gives an indication of the prescision of the sample estimate?

Answer 8

Confidence interval

Question 9

What does a confidence interval represent?

Answer 9

The uncertainty of the sample in estimating the population parameter as a result of potential sampling error

Question 10

In this context, does the confidence interval represent uncertainty in the sample mean of weight loss?

Answer 10

No, the SAMPLE estimate of mean weight loss is a single value that is known exactly. CI relates to estimating the POPULATION parameter

Question 11

Describe what is meant by a mean weight loss of 0.70-1.52 kg in New Consultation group with 95% confidence interval when applying to the population

Answer 11

Probability of 0.95 the population mean weight loss after New Consultation could be as small as 0.70 kg or as great as 1.52 kg

Question 12

How is the confidence interval derived?

Answer 12

From standard error of mean weight loss for New Consultation group. Standard error represents the precision of the sample estimate of the population parameter and is derived from sample data. CI extends either side of sample mean of weight loss by a multiple of the standard error

Question 13

Why is deriving a confidence interval that contains the population parameter with a fixed probability often described as estimating uncertainty?

Answer 13

Because the population parameter is unknown

Question 14

Why would a 99% confidence interval for the population mean difference in weight loss would be wider than the 95% confidence interval?

Answer 14

It would reflect increased certainty about the possible values of population parameter. A 90% confidence interval would be narrower, reflecting reduced certainty.

Question 15

Why is a 95% CI often chosen?

Answer 15

Trade off - a smaller probability would not provide an interval estimate with enough certainty, whereas a greater probability would present an interval estimate that was too wide to be of practical benefit

Question 16

The 95% confidence intervals for the population mean weight loss for standardised consultation and usual care overlapped. Can it be inferred that the mean weight loss between treatments was not significant at the 5% level?

Answer 16

No. It is a common misinterpretation that overlapping 95% confidence intervals between groups imply a lack of significance at the 5% level

Question 17

When comparing two interventions in mean weight loss, it would have been good practice and more informative to present a CI for what rather than for mean weight loss in each group?

Answer 17

For the difference in mean weight loss between treatment groups (i.e. 1.11kg - 0.37kg = 0.74kg)

Question 18

What does standard deviation show?

Answer 18

Quantifies how much data is spread out

Question 19

What is standard error?

Answer 19

The SD of the mean of multiple means of the same experiment done with different samples. Can be estimated from a single set of measurements.

Question 20

What does the standard error tell you?

Answer 20

Describes the precision of the sample mean as an estimate of the population mean