Section 3.4: Displaying Bivariate Numerical Data

The most important graph based on bivariate numerical data is the scatterplot.

Example: Vermont Sugarbushes The growth and decline of forests is a matter of great public and scientific interest. An article included a scatterplot of y = mean crown dieback (%), which is one indicator of growth retardation, and x = soil pH. The following observations were read from the scatterplot:

Observations X Y X Y 3.3 7.3 3.9 6.6 3.4 10.8 4.0 10.0 3.4 13.1 4.1 9.2 3.5 10.4 4.2 12.4 3.6 5.8 4.3 2.3 3.6 9.3 4.4 4.3 3.7 12.4 4.5 3.0 3.7 14.9 5.0 1.6 3.8 11.2 5.1 1.0 3.8 8.0

Scatterplot

Time-series plot – (time plot) A simple graph of data collected over time that can be invaluable in identifying trends or patterns that might be of interest. Consecutive observations are then connected by a line segment; this aids in spotting trends over time.

Example: Life Expectancy over Time The article “Americans Living Longer Than Ever” included a time-series plot that showed how life expectancy at birth for people living in the United States has changed over time. The plot was based on the following data from “The Vital Statistics Report,” published by the Center for Disease Control:

Data Year Life Expectancy at Birth (years) 1940 62.9 1950 68.2 1940 62.9 1950 68.2 1960 69.7 1970 70.8 1980 73.7 1990 75.4 2000 76.9

Time Series Plot

Section 3.5: Communicating and Interpreting the Results of Statistical Analysis

For Effective Communication: Be sure to select a display that is appropriate for the given type of data Be sure to include scales and labels on the axes In comparative plots, be sure to include labels or a legend A bar chart or histogram should always start at (0,0). A scatterplot does not have to. Keep graphs simple (clear and straightforward) Keep graphs honest (People look quickly at displays so 1st impression should be accurate data)

For categorical data, point out categories that were either common or rare compared to other categories For numerical data sets summarize the information that the display provides on 3 characteristics: center or location, spread, and shape For bivariate numerical data, the scatterplot would typically focus on the nature of the relationship between the two variables For data collected over time, any trends or patterns in the time-series plot would be described

When Constructing and interpreting graphical displays keep in mind: 1. Areas should be proportional to frequency, relative frequency or the magnitude of the number being represented.

When constructing and interpreting graphical displays keep in mind: 2. Be cautious of graphs with broken axes especially time plots, bar charts or histograms

When constructing and interpreting graphical displays keep in mind: 3. Watch out for unequal time spacing in time-series plots.

When constructing and interpreting graphical displays keep in mind: 4. Make sure the display shows the right first impression.