# Statistics: Two Truths and a Lie – Part 1

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Anyone who has ever played the game Two Truths and a Lie knows that telling another person three things about yourself and deliberately lying about one of them is easy, and fun, to do. The same goes for statistics. Those who have taken a statistics course before, know that you must be cautious of how you interpret any kind of data that is presented to you. Sometimes, the data tells the truth. But, like people, data can also tell a lie. How you represent data can make all the difference.

For this exercise, my classmates and I were each asked to create a table using the data from one of our class readings. We were then instructed to create two very different graphs by only using the data in our table. The purpose of this post is to present my two different graphs and explain how I created them.

Here is the table that I created using Microsoft Excel:

Actual and Legal Process toward Sheff I Goal, 2003-2007 Chart – Data Source: Dougherty et al. “Sheff v O’Neill: Weak Desegregation Remedies,” Figure 5.1, p. 111

Next, I inserted the data from the table into a line graph (Line Graph #1). I gave the graph a title and labeled both the x- and y-axis. I also changed the minimum and maximum of the y axis to range from 0-100% , with 100% meaning that all of Hartford’ minority students were attending magnet and Project Choice schools. This range of minimum and maximum values makes the data in Line Graph #1 look like there was minor progress made toward the Sheff I goal.

Line Graph #1 – Minor Progress

Finally, I created a second line graph (Line Graph #2). This graph has the same data as Line Graph #1, as well as, the same title and axes. Thus, you would expect that the graphs would be identical. But, as you can see, this is not the case. In Line Graph #2, I changed the minimum and maximum of the y-axis to range from 10-35%. This new, smaller, range of y-axis values makes the data look like there was significant process made toward the Sheff I goal. Making the range between the minimum and maximum y-axis values smaller resulted in zooming in on the line in the graph. When looking at a zoomed in graph, or any graph, it is important to understand what the axes represent. Pay close attention to the numbers and do not be mislead by them.

Line Graph #2 – Significant Progress

If we had played Two Truths and a Lie with these statistics, could you have recognized the lie?

Source:

Jack Dougherty, Jesse Wanzer ’08, and Christina Ramsay ’09. “Sheff v. O’Neill: Weak Desegregation Remedies and Strong Disincentives in Connecticut, 1996-2008.” In From the Courtroom to the Classroom: The Shifting Landscape of School Desegregation, edited by Claire Smrekar and Ellen Goldring, 103–127. Cambridge, MA: Harvard Education Press, 2009. http://digitalrepository.trincoll.edu/cssp_papers/3/.