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2. Statistical thinking will one day be as necessary for efficient citizenship as the ability to read and write. – H.G. Wells Indeed, statistics may be one of our most effective and efficient vehicles for communicating information. It is the natural inclination of people to trust numbers over words, and statistics present numbers in an attractive format that even the most innumerate man can follow. In addition, statistics can be presented in a wide variety of forms, from line graphs to tables to pie charts. Each performs its own unique function and offers information from a new perspective. Yet with every benefit comes a setback. Many people do not realize that numbers in a graph can be easily manipulated to reflect the author’s own wishes. The problem with graphs is that even with missing information, incomplete figures, and vague captions, they can still be presented with reasonable realism. People have grown so accustomed to seeing graphs that they accept its information unquestionably. In the following presentation, we will show you two such misleading graphs, point out their errors, and attempt to recreate the same graph using more accurate forms of presentation. You will see how the same set of information can produce two completely different graphs, and learn about the many ways in which statistics can deceive you.

3. This graph is misleading in many ways. Here are some examples of the most commonly used graph-manipulation tactics. First of all, there is the title to consider. While retail sales do go down in April 2002, the title doesn’t accurately reflect what the rest of the graph shows. Yes, the sales do rise and fall over a period of a year and a half, but in general, they have been steadily rising since November 1998. Second, notice that the y-axis does not begin at zero, but at \$225 billion. This has the unfortunate effect of making the rising slope shown in the graph much steeper than it actually is. Third, the little white box that shows the rate of change from pervious months only includes the last three months in the graph. This immediately biases the graph in favor of the title, as it shows that sales have actually gone down since February. A reader just looking at the box will not know that sales have also gone down in May and September 1999, and that these did not affect the rising number sales one bit. Fourth, note that the year 1999 is written under June and July, and not January. This may be a minor transgression, but it will certainly lead some readers to believe that the time period spans three whole, consecutive years and not fragments of a year. One final observation: Is it fair to compare retail sales of the months of a year all together? Christmas in December, for example, would prompt gift buying, but slower months like February might now have any at all. Wouldn’t it be much fairer to compare the same months and calculate how much it has grown over the year?

4. On this second graph, the y-axis begins on zero, therefore making the rising slope much less dramatic. When presented like this it is also harder to tell which bars are higher and lower. The last two bars, for example – March and April – look almost exactly the same on this graph. If the reader wasn’t told that the sales had actually gone down from March in April, he would never know. The title, likewise, has been changed to something that can encompass all aspects of this graph. In addition, instead of labeling a group of months with one year, we have given each month its own year so that its easier to read. However, this graph still does not address the problem of comparing all months together as equals. In our next graph, we will show you what that might look like.

5. Comparing the months of consecutive years yields yet another perspective to the picture. From this graph, it is easy to see that sales have steadily risen for each month, and by a fairly predictable percentage at that. Nearly all the months are rising by the same margin from one year to the next. Even April sales, which the original graph proclaimed was falling, have risen compared to its sales from the previous year. Once again, while the original graph seems to be trying to convince us that April sales have very obviously fallen, these two graphs tell us the opposite. Appropriately, the title for this third graph has been changed completely to give the opposite minute.