Graph Interpretation

This recognition and recall practice is based on a very simple graph in California Youth Authority's slide presentation on changing characteristics of youthful offenders.

• Ethnic Diversity of the California Youth Authority's Population
  

  Click on icon or on title above to see graph.

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1. Name the variable or variables in this graph, and tell whether they are measured as nominal, ordinal, or interval.

   One plausible response:

   One variable is ethnicity, measured as African American, Caucasian, Hispanic, and Other. Nominal measurement.

   Another variable is time. Measured intervally, by year.

   Another variable is age. Age is controlled. The population is that of the California Youth Authority, a population between the ages of 12-25.

   The data may also have been controlled on gender, since this seems to be based on data for juvenile males.

2. How did the CYA measure ethnicity? Is the answer readily apparent?

   One plausible response:

   No, the answer is not readily apparent because there is no accompanying written explanation of the graph. This is why having an explanatory paragraph is so important. In all likelihood, however, the CYA, accepted the ethnic designation on prior court records. To determine how ethnicity was actually measured, we would need to delve more deeply into CYA designation of ethnicity. This may be important to our understanding of the graph, because the ethnic categories do not appear to be, on the face of it, either adequately exhaustive or mutually exclusive.

   Consider, for example, the classification of African American and Hispanic. What if the youth's mother were Hispanic and father Black? How did the CYA categorize the youth? What about the many other kinds of confusion with marriages and relationships across ethnic boundaries? All that we can ascertain from the graph is that the CYA took care of any such anomalies by including the category Other. But in this case, especially since one of the CYA's concerns is the increasing diversity of the youthful offender population, such a broad Other category may mask information that is needed.

3. Could the population comparison of men and women over time, in Nan Chico's animated graph, have been shown in a graph like the one CYA used?

   One plausible response:

   Yes. You would have had to represent the males and the females by separate graph lines, and separate colors, to make it clear. You would have seen the change over the years by the shape of the graph lines. Try it. This way you won't need the animation.

4. Could we use the type of graph the CYA used to show the relationship between black and white male homicide? Scroll down to last chart on page.

   One plausible response:

   Yes, we could. We'd indicate the years along the x-axis, and we'd indicate the frequency of homicides per 100,000 along the y-axis. Then we would use a different graph line color or shape for white males and for black males. Try it. Which graph do you think is clearer? Which would help you most to understand the data? Which is catchier and more likely to be impressive in a presentation? How should you decide which approach to use?

5. How would the graph look if you threw out some data and graphed African Americans and Hispanics together as against Caucasians, with the Other category still separate? Would this be justifiable statistically?

   One plausible response:

   Messy question. You can collapse categories in statistics. It is justifiable if you can give a reasonable theoretical explanation for doing so. Perhaps you want to look at a Geographic Informations Systems Map for an area which is largely Hispanic/African American. Then you might have reason to collapse those categories. But if what you want to do is akin to racial profiling, then it's not justifiable, at least not in my world. Much will depend also on what your graph is intended for.

   You need to exercise caution in doing so, to be sure that you do not manipulate the data according to some pre-existing bias. The best way to do that is to give an explanation for collapsing data that will be apparent to the reader when the graph is presented.

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