STA 210B/ENV 251
Statistics and Data Analysis for the Biological Sciences

Objective: To apply graphical analysis to univariate data.

Material: Use brthdth.jmp in the JMPin databook.

Background: The study of birth and death rates (usually per thousand persons) is fundamental to demography. Here we will examine these rates for many nations. There is a strong association between birth and death rates, but it is not a simple relationship. Death rates depend on the age and health of the population, while birth rates depend more specifically on the number of fertile individuals and cultural, social and economic factors. In most countries, the birth rate exceeds the death rate, indicating population growth.

Main Question: What is a sensible way to characterize the distributions of birth and death rates across the world?

Steps:
1. Examine histograms and boxplots for birth rates and death rates. (Include also region.) Are the distributions skew (long tailed), unimodal (only one mode or peak)? How are the two rate distributions different? Which countries appear to be outliers (stand far from the bulk of other observations) for either rate?

2. Use brushing (a dynamic graphical method of highlighting graphic elements) to discover which regions are associated with high or low rates. Which regions appear to be associated with high birth rates and which with low birth rates? What approximately is the natural break between high and low?

3. To compare regions more directly, fit rates by region (use Fit Y by X). Add quantile boxes. Do the regions have comparable central values (means and medians)? Do they have comparable spread (range or length of quantile boxes)? Which countries may be outliers from their region?

4. (Optional) To see if the two rates are correlated, fit death rate to birth rate. The pattern in this scatterplot is not linear. Add a quadratic (polynomial of degree two) fit to the plot. Now the pattern is unmistakable. How would you characterize the groups to the right and left of the parabola? (Use the lasso tool to highlight either of these groups, and look back at the other graphics.) Which side would have proportionately more elderly people and fewer children than the other? Which countries are experiencing zero or negative population growth?

Report:
The questions in the steps above are meant to stimulate analysis. Now summarize what you have discovered. This should be about two or three paragraphs. Be sure to include illustrative graphics. (Try out JMP's annotation tool, rightmost in the tool bar.)

Due: September 10, 1998