Estimation

Question 1

Central limit theorem

Answer 1

If we were to take repeat samples and calculate the mean each time…
Those sample means will be Normally distributed around the true population mean
…even if the population itself is not Normally distributed

Question 2

Distribution of sample means

Answer 2

Normal distribution

Question 3

Standard error

Answer 3

Standard deviation of the sampling distribution

indicates how different a sample mean is likely to be from the population mean

It tells us the precision of estimation

Question 4

Standard deviation is for

Answer 4

Describing

Question 5

Standard error is used for

Answer 5

Estimating

Question 6

Smaller standard error of the mean

Answer 6

More precise the estimate of our mean- closer it is likely to be to the true population mean

Question 7

Standard error of the mean equation

Answer 7

Standard deviation/ square root of sample size

Question 8

precision is affected by these two things

Answer 8

how variable our data are (the SD) and how large our sample is (n)

The other thing being held constant…
The bigger the SD -the bigger the standard error
The bigger the sample size -the smaller the standard error

Question 9

Confidence interval

Answer 9

We wish to estimate a population mean…
We have our observed estimate: the sample mean
We have our estimate of its precision: the standard error of the mean
We can use these two things and properties of the Normal distribution to calculate a range of values we can be confident includes the true mean

Question 10

95% confidence interval for the mean

Answer 10

Mean + 1.96 * standard error

95% of the time our confidence interval will encapsulate the true (unknown) population value we are trying to estimate
Range of values within which the true mean lies 95% of the time- statistically significant if it doesn’t include 0 or 1

Question 11

Factors affecting that confidence interval width:

Answer 11

Variability in the sample (SD)
Sample size (n)
The desired level of confidence
- typically we use 95% but it could be 90%, 99%, etc.

Question 12

Greater variability of SE

Answer 12

Wider interval

Question 13

Greater sample size

Answer 13

Narrower interval

Question 14

Greater confidence level

Answer 14

Wider interval

Question 15

If 95% confidence interval includes null value

Answer 15

Result would not be significant and p-value is greater than 0.05

Question 16

If null value not included in 95% confidence interval

Answer 16

p<0.05

Question 17

Point estimate

Answer 17

Best estimate of parameter is the sample mean

Question 18

If confidence interval doesn’t include null value

Answer 18

Statistically significant difference

Question 19

Clinical significance

Answer 19

Magnitude of effect determined with confidence interval
Part of interval that lies higher than clinical importance
If threshold included in range, it is potentially clinically important depending where the true mean lies

Question 20

Interpretation of 95% confidence interval

Answer 20

a range of values that you can be 95% certain contains the true mean of the population

Question 21

What percentage of 95% CIs omit the true population mean

Answer 21

5%

Question 22

Reject null hypothesis is CI does not include…

Answer 22

0
1 = if ratio

Question 23

If point estimate falls within 95% CI,

Answer 23

Consistent with overall population

Question 24

Positive likelihood ratio equation

Answer 24

sensitivity/ (1-specificity)