## How Not to Draw Graphs

Actually, the best places to get examples of graphs that should never have seen the light of day are newspapers (especially if they have a horoscope column, and most of all, if they also have a full-page weather map in color) and at presentations made to impress administrators. We're not as creative as Moses, so we'll present only four commandments.

First, Thou shalt not make thy bars look three-dimensional. They look sexy as all get-out, but it's difficult to see where the top is as we're often deceived by the back edge of the bar. This is particularly true if the y-axis also looks three-dimensional because we have to mentally extend the top of the box to the axis and then look down at an angle to read off the value. The more extreme the three-dimensional look, the worse the problem is. As if this isn't bad enough, one very popular program makes things infinitely worse by using the back of the box to indicate the magnitude whereas we expect the front to be the value.

Second, Thou shalt honor the bar and keep it holy. Displaying the number of people in each group by stacking up little people icons is cutesy, as is showing costs with piles of coins or dollar signs. Avoid the temptation; it's nothing but "chart junk" that should be exiled into the wilderness, yea verily, and declared outcast and anathema.

Third, Thou shalt not commit a stacked bar graph. An example of this abomination is shown in Figure 20-8. We can easily compare the relative number of single people across groups because they all have a common baseline. But are there more divorced people in Group B or Group C? That's much more difficult. We have to mentally shift the box in Group C down until the bottom lines up with Group B, keeping the height constant as we move it. It's not difficult; it's darned near impossible.

Fourth, Thou shalt not suffer multiple pie charts to grace thy pages. Pie charts aren't so bad if we're displaying the data for just one group, but they're useless for comparing groups. It's the same problem as with stacked bar graphs. We can compare the first wedge across groups because all first wedges start at the 12:00 position. After that, though, we have to mentally rotate the wedge from one group to make it line up with that from the other group in order to compare angles. Again, try to compare the proportions of divorced people in Figure 20-9. Now imagine the task if we drew pies for all five groups. If you have to put in numbers to make the pie charts understandable, then

Group

Figure 20-8 A stacked box plot.

Group

Figure 20-8 A stacked box plot.

either use a table or a different type of graph. Remember, the only time a pie chart is appropriate is at a baker's convention.

DEALING WITH MISSING DATA_

Open up any statistics book (including this one, so far) and you'll find beautiful tables of data to be analyzed. If the text describes a t test with 10 subjects in each group, there are the 20 numbers just waiting to be summed and squared and added; if the next chapter has a repeated measures analysis of

Figure 20-9 A pie chart.

variance (ANOVA) with five testing periods, then the numbers are nicely lined up, all in their proper place. This may reflect the situation in some psychology experiments. For example, if a rat shucks its mortal coil in the midst of an experiment, it's replaced with the next one in the cage; or if a student doesn't show up for the study, he or she is replaced (and often given demerit points, but that's a separate story). In the real world, though, life isn't so straightforward. If people refuse to be interviewed or if patients drop out of a trial of a new intervention, we can't simply replace them and pretend that nothing has happened. First of all, we may not be able to replace a participant, because of time or budgetary constraints or because the pool of eligible patients is limited. More important, though, most applied researchers believe in the dictum that people do not drop out of studies for trivial reasons. They may stop coming for follow-up visits because (1) they got better and don't see the need to waste their time filling out questionnaires or having blood drawn, (2) they didn't get better and are off looking for someone who can help them, (3) they find the side effects of the treatment too burdensome, or (4) they may have succumbed to the effects of the therapy or the lack of therapy. Some people may stop participating because of factors unrelated to the treatment, such as finding a job in a new town, but for the most part, the reasons for the loss of data are related to the treatment itself. If we replace the participant with someone who stays in the study, then we may be biasing the results by eliminating from the analysis people with positive or negative outcomes. The bottom line is that we have to find some way of dealing with the missing data. In this section, we'll discuss some of the ways that have been developed to work around the problems.