As we move through the program, you will learn a variety of ways statistics can be used to massage data to support your point of view. Aside from the actual statistical calculations , one simple way to distort a situation is the visual presentation of the results. Let's see how this can be done.
A vertical bar chart titled in all capital letters: “MASSIVE INCREASE IN HOUSE PRICES THIS YEAR.” The vertical or y-axis is labeled “Average house price ($).” There are three prices indicated in the y-axis, ascending from $80,000 to $81,000 to $82,000. The horizontal or x-axis is labeled “Year.” The two years indicated on the x-axis are 1998 and 1999. For the year 1998, a vertical bar extends up to $80,000. For the year 1999, a vertical bar extends up to $82,000. The scale created on the y-axis shows the vertical bar for 1999 to be much higher than the vertical bar for 1998.
Here (above) the title of the figure and the scale on the y-axis suggest there has been a ‘massive increase' in price. A closer examination of the figure indicates the increase is only $2,000.
A vertical bar chart titled “Median Weekly Income for Ages 16-24.” The vertical or y-axis shows dollar amounts ascending from $300 to $400, increasing incrementally by $25. Two vertical bars extend up from the horizontal or x-axis. One bar is labeled “Men” and the other bar is labeled “Women.” The bar labeled “Men” extends up to nearly $400 on the y-axis. The bar labeled “Women” extends up to a little over $325 on the y-axis. The scale created on the y-axis shows the bar for “Men” to be much higher than the vertical bar for “Women.”
Here (above) the figure suggests a big difference between men and women in weekly income.
In the same bar chart as above, the dollar amount for the vertical bar for “Men” is shown to be $377 and the dollar amount for the vertical bar for “Women” is shown to be $331.
But the actual difference is $46.
A vertical bar chart that is the same in all respects to the previous chart, except that the vertical or y-axis shows dollar amounts ascending from $100 to $400, increasing incrementally by $100. As in the previous chart, two vertical bars extend up from the horizontal or x-axis. One bar is labeled “Men” and the other bar is labeled “Women.” The bar labeled “Men” extends up to nearly $400 on the y-axis. The bar labeled “Women” extends up to a little over $325 on the y-axis. The scale created on the y-axis shows the bar for “Men” to be only a little higher than the vertical bar for “Women” because the y-axis increments have changed.
Here the same data is presented [in the chart], but now the difference between men and women in weekly income appears very small.
Now, you try it. Switch between the income range increments to see how it changes the presentation of the exact same data. Click Next when you are finished.
For the same vertical bar chart as above, the student can choose income range increments of $10 or $25 or $50 or $100 or $200 on the y-axis. The visual display of the bars changes as the increments on the scale are changed. This activity shows the student how increments can be used to change the scale and therefore the visual presentation of bars on a chart.
A line graph with the vertical or y-axis labeled “Increase” and the horizontal or x- axis labeled “Year.” The y-axis ascends from 0 to 16 in increments of 1, 2, 4, 8, 16. The x-axis is divided into increments of 1, 2, 3 and 4. The graph line starts at the coordinate of 0 on the y-axis and 1 on the x-axis and extends up to the coordinate of 8 on the y-axis and the 2 on the x-axis. This line continues to the coordinate of 4 on the y-axis and 3 on the x-axis and then continues to the coordinate of 16 on the y-axis and 4 on the x-axis.
Here is another example. Here the y-axis has again been manipulated to distort initial impressions. It appears the biggest increase was between year one and year two. But that is because the year exponentially skips from an increment of one to an increment of eight. The biggest increase was actually from year three to year four.
A line graph that is the same in all respects as the previous line graph, but with a change to the increments of the y-axis. The y-axis now ascends from 0 to 16 in increments of 2, so that the scale reads 0, 2, 4, 6, 8, 10, 12, 14, 16. The line graph has the same coordinates as in the previous chart. However, the graph line is longest between the years three and four because there is no distortion in the scale of numbers on the y-axis.
Which you can clearly see when you adjust the increments on the y-axis to be consistent.
As you can see, statistics can be manipulated to support various viewpoints by how the data is displayed.