Correlation, regression, sample size & power

Question 1

Advantage(s) of a 2x2 table

Answer 1

Advantages:

• • Ease of interpretation
• • No distributional assumptions
• • Can easily stratify by other variables
• • Can calculate OR or RR

Question 2

Disadvantage(s) of a 2x2 table

Answer 2

sometimes requires arbitrary grouping of a continuous variable (loss of information)

Question 3

Advantage(s )of Correlation and Regression

Answer 3

Advantages:

• • Maintain continuity of data
• • Model one variable as a function of the other

Question 4

Disadvantage(s) of Correlation and Regression

Answer 4

Disadvantages:

• • Only measures linear relationship
• • Only useful when both variables are continuous

Question 5

Pearson Correlation Coefficient

Answer 5

to determine whether two continuous variables (X and Y) are linearly related.The correlation coefficient:

• measures linear relationship between X and Y
• ranges between -1 (perfect negative correlation) and 1 (perfect positive correlation).

Question 6

coefficient of determination (r2)

Answer 6

r2 is the proportion of the total variability in Y that can be explained by the linear association between Y and X

Question 7

Multiple Linear Regression

Answer 7

One dependent continuous variable (Y), several independent variables (X1, X2, …). Allows us to predict Y based on several variables.

Question 8

Logistic Regression (either simple or multiple)

Answer 8

Similar to linear regression, except that the dependent variable Y is dichotomous (e.g. Y=1 for diseased, Y=0 for not diseased), and we model the probability that Y=1.

Question 9

Type I error

Answer 9

incorrectly rejecting H0 when H0 is true, i.e. finding a statistically significant association based on a sample of data when there is truly not an association.

Question 10

Type II error

Answer 10

incorrectly failing to reject H0 when H1 is true i.e. finding not statistically significant association based on a sample of data when there truly is an association.

Question 11

α

Answer 11

Probability of a type I error. Also called significance level.

Question 12

β

Answer 12

Probability of a type II error.

Question 13

Power

Answer 13

1 - β is the chance of detecting a difference if the difference really exists

Question 14

Sample size determination steps

Answer 14

1. Type of alternative hypothesis (1 or 2 sided)
2. Significance level (α)
3. The difference between treatments that you wish to detect (delta) (i.e. the minimum difference that you consider clinically significant).
4. Power: the chance of rejecting the null hypothesis if the true difference is delta.
5. Standard deviation: an estimate of the standard deviation of the variable of interest (e.g. standard deviation of the mean difference between treatments). Obtained from small pilot study or literature.