Quantitative Data Displays

The most basic display is called a frequency table. Let's say the team has given a short survey of 10 items to 100 students and that 88 of the students responded. The survey used the familiar 1-to-5 response scale, with 1 being "strongly disagree" and 5 being "strongly agree." Here's what a frequency table for one of the 10 items might look like:

I really like to read.

The display could be presented on a slide, and it could serve many purposes depending on what the team needs. (For calculating the percentage, the missing responses aren’t included. In other words, to find the percentage, the frequency is divided by the total number of people who actually responded, in this case 88 not 100.)

Cross-tabulations (cross-tabs) are a variation on frequency tables. Let’s say the team is curious about the differences between female and male students. Cross-tabulations report frequencies for the two groups, like this:

I really like to read.

Team members who prepare the display might swap out “total percentage” with a different calculation, perhaps the percentage of the total in each response category that were females (see below).

I really like to read.

Note that, for dramatic effect, this example stereotypes males as much less enthusiastic readers.

Another way to present the same information is to report averages (“means,” in the language of statistics). The advantage of this approach is that means can be reported in much less space.

To summarize the information in the frequency display and the cross-tabs displays above, we can be more efficient by showing the means.

In fact, we could present data summarizing responses to all 10 items in just a little more space than we needed for presenting the cross-tabs for just one item. So, why not use means all of the time? What’s the disadvantage of this approach to displaying data?

When we use means, we lose the detail about particular responses: how many were low, how many in the middle, and how many high. Still, we can format a table of means to include data that will help us make comparisons. For example, we can present means for several different subgroups in one display. For example, we might divide groups of students by classroom, by proficiency level, by gender (as in the above example) and so forth. We could then calculate and display means for each subgroup. A team could address lots of different questions using this approach.

Displays of means are also useful for tracking changes over time. Let’s say the TBT adopts a program to help boys engage better with reading and decides to use the 10-item survey four times over the course of the year to measure their attitudes towards reading (as well as the attitudes of the girls). Again, let’s keep our focus on just one item. Here’s what the display for the data after all four administrations might look like:

This is actually a relatively complicated display for a leadership team! Often, the displays they develop and use are simpler. But this one is useful for examining trends and perhaps for helping make instructional decisions. What are the helpful features of this display?

• It presents outcome data for a year-long effort.
• It provides four measures over the course of the year.

Two conditions would make the display even more useful:

• if data come from an instrument with established reliability and validity) and
• if the item for which it displays data is highly associated with overall scores on the 10-item scale.

But the display doesn’t show everything. In particular, it lacks information about variability in ratings. What a shame to lose that information!

In addition to means, those preparing data displays can include standard deviations. Think of the mean. It’s the average, but it’s produced by combining all of the scores—and those scores reflect a range: low, middle, and high. The standard deviation is a measure of how far those scores are from the average. Here’s what a display with both means and standard deviations (SD) might look like:

In this case, the ratings show improvement overall, with larger improvement for the boys. But for the boys, even though scores increased overall, the standard deviation also grew notably larger over time. This means that for some of the boys, there may have been no improvement at all, and for some, attitudes may actually have deteriorated. The increasing variability in scores tells us to dig deeper to figure out what might be going on.

These examples barely scratch the surface. Lots of other data analysis methods and data displays might also be useful. And they would address some of the other issues a team might want to understand. What are some of these issues?

• Is the difference we see in reading attitudes of males and females real? How large a difference would it have to be to be real?
• What do other subgroup comparisons look like (for instance, comparisons based on race, comparisons based on poverty)?
• What do the students whose attitudes remained low over the course of the year have in common?
• Is the relationship between reading proficiency and reading attitudes strong or weak?