Module 2

Question 1

What is the central limit theorem?

Answer 1

When “n” is sufficiently large, the sampling distribution for a particular statistic (e.g., sample mean) will tend towards a normal distribution, even if the underlying population distribution is NOT Gaussian. And if the sample size increases, then the distribution of averages becomes more normal and narrower.

Question 2

What’s the difference between the distributions of Gaussian observations and sample means.

Answer 2

Question 3

What is the (95%) confidence interval?

Answer 3

95% of the time, any given _X (“x bar”) should be within 2 standard errors (SEs) of the true population mean (mu).

Interpreted as “We are 95% confident that the true mean cholesterol level among persons with MSCD in he population could be as low as 231.8 mg/dL or as high as 268.2 mg/dL.”

Question 4

How do you calculate sample mean and variance?

Answer 4

Additional notes for variance: Take every value in sample, subtract the sample mean, square it, then divide by (n-1)

Question 5

How does the mean of the logs relate to the median of the logs?

Answer 5

They’re almost equal. As a result, when you exponentiate the mean of log10$ to return to the raw data, you get the median of the raw data (NOT the mean).

Question 6

How does the log of the median relate the median of the logs?

Answer 6

They’re equal

Question 7

How does the log of the mean relate to the mean of the logs?

Answer 7

They’re not equal

Question 8

What greek letter represents the mean with CLT?

Answer 8

lowercase mu

Question 9

What greek letter represents standard deviation with CLT?

Answer 9

lowercase sigma

Question 10

What is the standard error (SE) of _X (x bar)?

Answer 10

The standard deviation of the sampling distribution of _X

Question 11

How do you find variance?

Answer 11

Where sigma = standard deviation of the population
and n = size of sample

Question 12

How do you find standard error?

Answer 12

Where sigma = standard deviation of the population
and n = sample size

Question 13

How can the mean of the logs effect the interpretation of the confidence interval?

Answer 13

When you exponentiate the mean of log10$ to return to the raw data, you get the median of the raw data (NOT the mean). So in terms of CI interpretation, you’ve found the true median, not the true mean.

Question 14

Does your confidence interval increase of decrease with an increase in sample size?

Answer 14

As sample size (n) increases, the confidence interval decreases because your standard error goes down (you’re more sure, think CLT).

Question 15

How do you calculate margin of error (MOE)?

Answer 15

2*standard error

Question 16

What happens to the width of the confidence interval as n increases?

Answer 16

As sample size (n) increases, the width of the 95% CI decreases.

Question 17

Remember the question of interest for the module is: How much more did people with MSCD spend on medical care than (otherwise similar) people without MSCD?

How can you actually go about calculating that difference?

Answer 17

We estimate that the true value of the difference between population means is _X - _Y (the difference in the sample means). And we can find the 95% confidence interval with (_X-_Y) +/- 2SE(_X-_Y)

We can estimate SE(_X-_Y) using…

Question 18

How can you calculate the 95% CI for a difference in population means?

Answer 18

Question 19

How do you interpret a 95% CI for a difference in population medians?

Answer 19

Question 20

How do you calculate standard deviation?

Answer 20

Question 21

What is a null hypothesis?

Answer 21

A null hypothesis is a statement of no effect, no relationship, or no difference between groups.

Question 22

How do you perform a hypothesis test?

Answer 22

To perform a hypothesis test, we rephrase our question of interest in terms of a precise null hypothesis about the population. When we perform a hypothesis test, we make a decision about this null hypothesis– should we reject it? Or fail to reject it?

1. Specify a precise null hypothesis about the population. EX: Patients with MSCD in the population do not have higher cholesterol, on average, as compared to patients without MSCD.
2. Specify the exact outcome variable. EX: Each individual patient’s reported cholesterol level.
3. Specify the allowable Type 1 error rate (lowercase alpha) of rejecting the null hypothesis when it is in fact true – usually alpha = 0.05 (or 5%) EX: Concluding MSCD patients have higher cholesterol, on average, when in fact there is no difference in cholesterol levels.
4. Choose an estimator (use the mean for continuous outcome) from your data relevant to the hypothesis. EX: Difference in means comparing cholesterol in patients with MSCD to cholesterol in patients without MSCD.
5. Calculate a (1 - alpha)*100%, but when a=0.05 it’s 95% CI EX: For the difference in population means with 95% confidence
6. If the interval does not overlap the value in the null hypothesis, then reject the null hypothesis. If the interval includes the null value, then “fail to reject” the null hypothesis.

Question 23

What is a Type 1 error?

Answer 23

rejecting the null hypothesis when it is true

Question 24

What is a simulation?

Answer 24

Conduct an experiment repeatedly and then summarize the outcomes.

Question 25

What is a p-value?

Answer 25

A measure of consistency between the null hypothesis and the data. It is the probability (spanning from 0 to 1) of observing a sample relative risk (or some variable) as large as was observed or larger when the null hypothesis is true.

Question 26

When can you reject the p-value in relation to a selected lowercase alpha-level.

Answer 26

reject the null if p-value is less than a selected a-level. (usually a=0.05)

Question 27

What is a type 2 error?

Answer 27

False negative.

Question 28

What is the general form of t-statistic?

Answer 28