2.6.2. Basic Biostatistics II

Question 1

What is a correlation?

Answer 1

A measure of the strength of the association between two variables; used to determine whether an “association” exists and quantify its strength

Question 2

How do you prepare a plot of correlation coefficient? Relate this plot to the correlation coefficient.

Answer 2

1. Observe two variables (X, Y) for each member of a random sample of n subjects. 2. Plot pairs of points (X1,, Y1), (X2,, Y2), …, (Xn, Yn) on a scatterplot. 3. Inspect scatterplot for patterns of association. 4. Estimate population correlation coefficient ρ by sample correlation coefficient r

Question 3

What are the three extreme r values we use for correlation coefficient graphs and what do they tell us about our data?

Answer 3

r=0 => no linear association r=1 => perfect linear association r=-1 => perfect negative linear association

Question 4

What is a regression?

Answer 4

Regression: A family of methods for relating a predictor or multiple predictors) to an outcome

Question 5

“Determine whether an association exists and quantify its strength” This is an example of a correlation or regression?

Answer 5

Correlation

Question 6

“Use the relationship to predict one variable from the other” This is an example of a correlation or regression?

Answer 6

Regression

Question 7

Determine whether the observed relationship agrees with some theory or model and estimate the parameters of that model This is an example of a correlation or regression?

Answer 7

Regression

Question 8

The most common way to measure linear association is by the use of what?

Answer 8

The correlation coefficient

Question 9

Difference between p and r?

Answer 9

p is for the whole population. R is just the correlation coefficient for the sample

Question 10

What is the formula for the sample correlation r?

Question 11

How would you characterize the correlation of the variables below? Negative or positive? Weak or strong? Close to zero?

Answer 11

Good example of a zero correlation. Parabolas are always zero.

Question 12

How would you characterize the correlation of the variables below? Negative or positive? Weak or strong? Close to zero?

Answer 12

Strong positive

Question 13

How would you characterize the correlation of the variables below? Negative or positive? Weak or strong? Close to zero?

Answer 13

Weak positive correlation

Question 14

How would you characterize the correlation of the variables below? Negative or positive? Weak or strong? Close to zero?

Answer 14

Rather strong negative. Not a perfect line, but pretty darn good.

Question 15

How would you characterize the correlation of the variables below? Negative or positive? Weak or strong? Close to zero?

Answer 15

Weak negative or close to no correlation. There is a general negative slope but this would be an r of like -0.25 at best

Question 16

How would you characterize the correlation of the variables below? Negative or positive? Weak or strong? Close to zero?

Answer 16

No correlation

Question 17

How can we test if there is a significant correlation between variables X and Y? Go through the steps starting with already having the X and Y values.

Answer 17

1. Compute r
2. Compute t

You can use this to find your p-value in a confidence interval table. If p<0.05, you are significantly significant, which means you can reject the null hypothesis which states that there is no relation (meaning, your data supports a cause and effect)

Question 18

There are two reasons we would use a pearson correlation. What are they?

Answer 18

1. Observations are from a random sample
2. At least one variable follows a normal distribution

Question 19

What other tool can we use with regression to answer questions about the population?

Answer 19

Line of best fit

Question 20

When do we use a simple logistic regression?

Answer 20

When the dependent variable is continuous/categorical

It estimates odds ratios (log odds)

Question 21

When do we use a multiple logistic regression?

Answer 21

One dependent variable is categorical and we have multiple independent variables.

Question 22

Using a correlation or linear regression

vs.

Using a logistic regression

Answer 22

To assess association between two CONTINUOUS variables, use correlation or linear regression

To assess association between CONTINUOUS predictor and CATEGORICAL (binary) outcome, use logistic regression

Question 23

We are trying to see what affects BMD in women the most. We are testing weight and race (Black vs. White/other) against the BMDs. What type of stat method should we use?

Answer 23

Multiple regression

Question 24

If we wanted to predict a binary outcome, such as finding a disease to be present or absent, or finding the prognosis to be died or survived, what statistical method would help us best?

Answer 24

Logistic Regression

Question 25

Why do we need to adjust for certain variables?

Answer 25

Because they are confoudning