2 - Statistical Inference

Question 1

What is a confidence interval?

Answer 1

A way of conveying uncertainty about a dataset

95% CI = there is a 95% chance that the actual mean of YOUR dataset is in the interval you define

Question 2

Introduce the concept of hypothesis testing.

Answer 2

x = average of test group, u = true mean

1. Define null hypothesis (usually x=u)
2. Compute a test statistic: t = (x-u)/SE(x)
3. Draw a conclusion
   - –(if sample size is greater than ~50, reject null hypothesis if t is less than -2 or greater than 2 (5% chance of this)

Type I error:

Type II error:

Question 3

Interpret a P-value for an effect.

Answer 3

p = 0.05 means that the results seen would occur by random chance only 5% of the time

Question 4

Define central limit theorem.

Answer 4

A mathematical result stating that for a sufficiently large sample size, the sampling distribution of the mean will be approximately normal regardless of the underlying distribution of the data

Question 5

Define effect.

Answer 5

The magnitude of a difference or relationship

Question 6

Define event.

Answer 6

A clinical outcome of importance
–Ex: onset of a disease (such as cancer or heart disease), onset of a particular symptom (such as bleeding or depression), disease recurrence, or death

Question 7

Define hypothesis test.

Answer 7

A statistical analysis used to accept or reject a null hypothesis

Question 8

Define null hypothesis.

Answer 8

The hypothesis being tested about a population
Null = “no difference;” refers to a situation in which there is no difference (e.g., between the means in a treatment group and a control group)

Question 9

Define parameter.

Answer 9

An unknown summary value for an entire population

The purpose of a statistical analysis is to estimate and make inferences about a parameter

Question 10

Define power.

Answer 10

The power of a statistical test is the probability that it correctly rejects the null hypothesis when the null hypothesis is false (i.e. the probability of not committing a Type II error)

Question 11

Define p-value.

Answer 11

The probability of observing a result as extreme as or more extreme than the one actually observed based on chance alone (i.e., if the null hypothesis is true)

Question 12

Define random sample.

Answer 12

A subset of the population obtained by random selection

Question 13

Define sampling distribution.

Answer 13

The theoretical distribution of a statistic obtained from a random sample

Question 14

Define statistical significance level.

Answer 14

The probability of making a type I error in a hypothesis test

Question 15

Define test statistic.

Answer 15

The specific statistic used to test the null hypothesis (e.g., the t statistic)

Question 16

Define type I error.

Answer 16

The error that results when one rejects the null hypothesis when it is true or when one concludes that there is a difference when there is none (“false positive”)
–Saying there IS an effect when there isn’t

Question 17

Define type II error.

Answer 17

The error that results when one does not reject the null hypothesis when it is false or when one does not detect a difference when there is a difference (“false negative”).
–Saying there is no effect when there is

Question 18

How does standard deviation change from a sample of 100 to 1000? How is standard error different?

Answer 18

Standard deviation (SD) will be LARGER in a sample of 1000 vs 100 (because of individual variation)
--SD is a measure of SPREAD in a population, does NOT depend on sample size

Standard error = SD/sqrt(n)

• -A measure of PRECISION in a sample, depends on N and SD
• -This is the standard deviation of the AVERAGE rather than the individual

Question 19

Interscalene blocks have a mean duration of 24 hours with an SD of 8 hours.
The duration based on 100 blocks will have a mean duration of ____ and an SE of ____
The duration based on 1000 blocks will have a mean duration of ____ and an SE of ____

Answer 19

The duration based on 100 blocks will have a mean duration of 24 and an SE of 8/10

The duration based on 1000 blocks will have a mean duration of 24 and an SE of 8/sqrt(1000) (8/32)

Question 20

Looking at average length of stay (LOS):

1. First 100 patients: average LOS = 4.2 days, SD = 1.3 days: what do you think is the average length of stay is?
2. First 1000 patients: average LOS = 4.2 days, SD = 1.3 days: what do you think the average length of stay is?

Answer 20

1. Average = 4.2 days, SE = 1.3 days/sqrt(100) = 0.13 days
   –True value guess = 4.2 +/- (2 x 0.13) days = 4.2 +/- 0.26 days
   (Why multiply by 2? Creating a 95% confidence interval from the normal distribution)
2. Average = 4.2 days, SE = 1.3 days/sqrt(1000) = 0.04 days
   - -True value guess = 4.2 +/- (2 x 0.04) days = 4.2 +/- 0.08 days (95% CI)
   - -This provides better information

Question 21

Long-standing operative mortality from vascular surgery has averaged 3% at DHMC. Dr. X was recently hired at DHMC. In her last 220 cases, her operative mortality was 6% (SE = 1.6%).

What do you think? Would you send your mother to Dr. X?

Answer 21

Null hypothesis is that she is not dangerous

t = (0.06 - 0.03)/(0.016) = 1.875
–This value is

Question 22

T/F: If p > 0.05 or t is greater than 2 or less than -2, you accept the null hypothesis.

Answer 22

NO. You say you CANNOT REJECT the null hypothesis. This doesn’t mean it’s true or that the two groups are equal, so you can’t ACCEPT the null hypothesis

Question 23

Proportion dead under new treatment: 42% with SE of 5%
Standard of care = 30%
–What’s the likelihood that this new treatment is more deadly than the standard of care?

Answer 23

Null hypothesis: the new treatment has the same death rate as the standard of care

Calculate: t = (42-30)/5 = 2.4, so p = 0.016
–The proportion dead under the new treatment has a likelihood of ~1% of actually being 30% (the same as the standard of care), therefore we can reject the null hypothesis and say that it is more dangerous