Rates proportions, logs exponentials

Question 1

What are rates in statistics?

Answer 1

Rates describe how often an event occurs over a specified time period. It’s calculated as events per time unit, e.g., incidence rate = number of new cases / time period.

Question 2

What is a proportion?

Answer 2

A proportion is a type of ratio that represents a part of the whole. It is calculated as: proportion = part / total.

Question 3

What are exponentials in health statistics?

Answer 3

Exponentials model processes like disease spread where growth accelerates over time. Example: number of cases doubles at regular intervals.

Question 4

What are logarithms used for in health statistics?

Answer 4

Logarithms are used to reverse exponentials, allowing better visualization of skewed data or to simplify multiplicative processes.

Question 5

How are logarithms written?

Answer 5

Logarithms are written as log_b(x), where b is the base and x is the value. Common bases include 10 (log), e (ln), or 2 (log2).

Question 6

What is a key reason for using logarithmic scales in graphs?

Answer 6

Log scales compress large ranges of values, making it easier to visualize exponential growth and compare rates of change.

Question 7

How do you interpret log-transformed data in health research?

Answer 7

Log-transformed data often indicates relative changes or ratios rather than absolute differences, which is useful for multiplicative effects.