Misleading Graphs and Statistics Thanks to Mr. Hammond @ www.mrhammond.org/math/mathlessons/7-8.ppt

Review We have been looking at many different ways to present data. Now let’s see how people can use these charts and graphs to mislead you.

Questions to Ask When Looking at Data and/or Graphs Is the information presented correctly? Look at the title. Is the graph trying to influence you? Look at the labels. Does the scale use a regular interval? Look at the units What impression is the graph giving you? Do you feel the graph is trying to make a point?

Why is this graph misleading? This title tells the reader what to think (that there are huge increases in price). Is it presented correctly? The scale moves from 0 to 80,000 in the same amount of space as 80,000 to 81,000. The scale is not at regular intervals. The actual increase in price is 2000 £, which is less than a 3% increase. This graph was from England (their dollar sign looks like £ instead of $.) The graph shows the second bar as being 3 times the size of the first bar, which implies a 300% increase in price. The picture and the data do NOT agree. The orange box is three times the green box and there is only a 3% increase.

A more accurate graph: An unbiased title Change in house prices A scale with a regular interval. This shows a more accurate picture of the increase.

Why is this graph misleading? The scale does not have a regular interval. In other words, each square does not represent the same amount. In some cases the squares are 1, in one case the square is 8!!! Look at the units!!!

Graphs can be misleading in the news. The margin of error is the amount (usually in percentage points) that the results can be “off by.” Be wary of data with large margins of error.

From CNN.com

Problem 1. Margin of Error The difference in percentage points between Democrats and Republicans (and between Democrats and Independents) is 8% (62 – 54). Since the margin of error is 7%, it is likely that there is even less of a difference.

Problem 2: Misleading Units (it starts at 53) The graph implies that the Democrats were 8 times more likely to agree with the decision. In truth, they were only slightly more likely to agree with the decision.

Problem 3: 54% looks like a small number - the graph is trying to influence my opinion about Democrats. The graph does not accurately demonstrate that a majority of all groups interviewed agreed with the decision.

CNN.com updates the graph: Note: regular units, none of the graph cut off.

Notes Look at the title of the graph Look to make sure the intervals are the same throughout the graph Look at the labels on the axes

Let’s see some more . . . Sometimes people preparing the graph will pick the data to use. Here is some data on revenue growth in the US: First year 1953 1962 1969 1977 1981 1990 Last year 1961 1968 1976 1980 1989 1995 # of years in span 9 7 8 4 9 6 US Revenue growth 0.11 4.67 1.55 7.48 2.19 1.56

Somebody took that data and created a chart Somebody took that data and created a chart. They wanted to show that during the Kennedy and Reagan presidencies (where income tax rate was lower) the actual tax collected was higher (they were trying to show that without taxes, people spend more). Here is their chart: Problems: Intervals aren’t the same (is that because they set them to their advantage?) Kennedy dies in 1963. Why did they not show Carter administration on the chart (the revenue was the highest of all) . The truth is there was NO change in tax rate between 1970 and 1980, but the author of the chart decided to only include 1969 to 1976. First year 1953 1962 1969 1977 1981 1990 Last year 1961 1968 1976 1980 1989 1995 # of years in span 9 7 8 4 9 6 US Revenue growth 0.11 4.67 1.55 7.48 2.19 1.56

Conclusion This chart was presented March 1st, 2012 at the Senate Budget Committee hearing on tax reform. This was the testimony of expert Dr. Daniel J. Mitchell, a senior fellow at the Cato Institute. Moral – just because someone knows the facts does not mean they will not manipulate the facts with charts and graphs to make their point.

The following graphs are contributed from Naomi Robbins The following graphs are contributed from Naomi Robbins. Forbes’ magazine uses her. She specializes in the graphical display of data. She trains employees of corporations and organizations on correct use of data. “Some graph designers label the bars in bar graphs with data labels rather than including a scale. When I see a graph without a scale I take out my ruler and measure the heights of the bars. Too often, the labels don’t agree with the heights of the bars. It is [easier] to deceive in this manner [than if] there is a scale with tick marks at round numbers, since our eyes can judge if the scale is drawn evenly.” Inaccurate Correct

Most Common Bar Graph Deception – Not Starting at 0. Appeared on the news Correct display – note the word Scale – I had to add that to get Excel to display my data correctly

What’s wrong with this? More than 100%?

What’s wrong with this? What happened to 1993, 1996 and 1998?

Corrected – Notice: the “increase” disappeared

What’s wrong here?

Same data – 4 different graphs Put out by Democratic politician (Nancy Pelosi) in 2009. Problems Does not adjust for inflation Uses jobs lost as opposed to unemployment rate (there are more people therefore more jobs)

Same data – 4 different graphs Put out by Republicans in 2009. Problems Definitely political. Shows no comparison, so no point of reference

Same data – 4 different graphs This expands the data from the other two graphs. This adds on data back to 1974 (the green, black and red lines)

Same data – 4 different graphs This expands the data from the other three graphs. This adds on data back to 1948 (line the others were referring to is the mustard colored one).

All data show a problem, but in the top 2 the problem looks worse than it may be.