Statistics for Dummies (16 page)
Sometimes, tables can be a bit confusing if you're not watching carefully. For example, the IRS reports "Tax Stats at a Glance" on its Web site, and some of those statistics (reported exactly as the IRS did) are shown in
Table 4-5
.
 |
Number of Returns (FY2001) | 129,783,221 |
Gross Collections (FY2001 in millions of dollars) | 1,178,210 |
Top 1% AGI break (TY1999) | $293,415 |
Top 10% AGI break (TY1999) | $87,682 |
Bottom 10% AGI break (TY1999) | $4,718 |
Median adjusted gross income (AGI, TY2000) | $27,355 |
Percent claiming standard deductions (TY2000) | 66.2% |
Percent claiming itemized deductions (TY2000) | 32.9% |
Percent using paid preparers (TY2000) | 53.4% |
Percent e-filed (TY2001) thru 5/3/2002 | 38.3% |
Number of returns with AGI > $1million (TY2000) | 241,068 |
Number of individual refunds (TY2000 in millions) | 93.0 |
Individual refund amount (TY2000 in billions of dollars) | 167.6 |
|
Two features of this table are noticeable right away. First, the IRS reports statistics for many different reporting years on the same table, for example FY2001 (which means fiscal year 2001, or the 12-month period from July 1, 2000 through June 30, 2001), TY1999 (which means tax year, or calendar year, 1999), and TY 2000. Note that the tax year and the fiscal year overlap, and that the tax returns for TY 2000, for example, are due to the IRS in April, 2001 (which is in FY 2001). How's that for confusion? Also notice that you can't compare the median adjusted gross income (median AGI) in this table to the top 1% or top 10% AGI in the same table, because these figures are listed for different years (TY 2000 and TY 1999, respectively).
Second, the way the IRS reports the dollar units can lead to confusion. For example, the gross collections for individual tax returns for FY 2001 (reported to be in millions of dollars) is listed as 1,178,210. This means that $1,178,210
million
dollars were collected from individual tax returns. Now you typically don't display dollar amounts that way. To put this into proper perspective, $1,178,210 million is actually $1,178,210,000,000, which is $1.178 trillion. No wonder the IRS didn't report these revenues that way, it's too big of a number to even fathom!
| REMEMBER | When looking at a table, be sure you understand the units that are being expressed and watch for changes in units (such as the year) throughout the table. |
Table 4-5
is intended to show several points; here are a few of them. In the tax year 2000, the ratio of people who claimed the standard deduction relative to people who itemized their deductions, is about 2 to 1. (A pie chart would show this very nicely.) About half of the people who filed for the tax year 2000 used tax preparers, and the percentage who e-filed for the tax year 2001 was about 38% (a percentage the IRS probably would like to see increase over time). The average refund for the tax year 2000 was $1,802.15 (the total amount of refund dollars in billions, divided by the total number of refunds, in millions). (Now, isn't it more impressive to report the total amount of refund dollars, as opposed to the average refund amount?) Also notice that the IRS didn't report the total number of tax returns filed for the tax year 2000 or the percentage of tax filers who received a refund for that tax year. Knowing this percent would be more useful than knowing the total number of refunds in a given tax year. After all, not everyone got a refund — plenty of people had to pay or paid exactly the right amount.
| HEADS UP | Tables are designed to make certain points more prominent and to make other points less noticeable. Sometimes, the de-emphasized information — or even the missing information — is the most telling! |
| Tip | To find out whether a table is sturdy enough, statistically:
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A
time chart
is a data display whose main point is to examine trends over time. Another name for a time chart is a
line graph
. Typically a time chart will have some unit of time on the horizontal axis (such as year, day, month, and so on) and some measured quantity on the vertical axis (such as average household income, birth rate, total sales, percentage of people in favor of the president, and so on). At each time period, the amount is represented by a dot, and the dots are connected to form the time chart.
In 1999, the U.S. Bureau of Labor Statistics put out a report on work trends in the United States, and what the outlook was for the future. Its report includes many time charts, including the two shown in
Figure 4-11
and
Figure 4-12
.
Figure 4-11
shows the trend over time in the average hourly wage for production workers from 1947 to 1998. (Because of inflation, it wouldn't make sense to simply show the actual hourly wages over this time period. You want to know the information in terms of "real wages" — in other words, something comparable over time. Here, the bureau shows everything in terms of 1998 dollars for equitable comparison over time.) You can see from
Figure 4-11
that wages for production workers increased from 1947 until the early 1970s, declined during the 1970s, and basically stayed in the same range until the late 1990s, when a small surge began.
Figure 4-11:Average hourly wage for production workers, 1947–1998 (in 1998 dollars).
Figure 4-12
makes the point that the gap in wages between educated and noneducated workers has widened between 1979 and 1997.
Figure 4-12:Weekly average earnings by educational level, 1979–1997 (in 1998 dollars).
| HEADS UP | Statistics tell you facts — in other words, they tell you what's occurring. But they don't explain why events are occurring as they are. The report put out by the Bureau of Labor Statistics not only presents data showing wage trends, but also goes beyond data presentation to discuss some of the reasons |
| REMEMBER | Many folks try to take a simple data display and use it not only to show what's happening, but also to try to explain why things are happening as they are. Without sufficient data, these people may be making false conclusions. If you suspect someone is going too far with his or her conclusions, you need to question whether these conclusions are justified. |
When showing birth statistics for Colorado residents, a time chart can be used to examine the trend in the rate of plural births over time. Such a time chart would look like the one in
Figure 4-13
. You can see that the percentage of plural births appears to be increasing over time, especially if you simply compare 1975 to 2000.
Figure 4-13:Percent plural births for Colorado residents, 1975–2000.
| HEADS UP | As with a bar graph, differences that are represented using a time chart can be played up or down by changing the scale on the vertical axis, so be sure to take the scale into account when interpreting the results of a time chart. |
For the Colorado plural births example, the increase in plural births over time can be made to look more dramatic by changing the increments on the vertical axis from 1% to 0.2%, which would stretch out the graph vertically. Likewise, the trend could be made to look almost nonexistent by changing the increments on the vertical axis from 1% to 5%. The most reasonable increment is something between 0.2% and 5%. I chose 1% increments for my version of this graph.
Another factor to consider with time charts is the time axis, or how close together or far apart the data points in the chart are. Data that are close together in time but have very different quantities will make the time chart appear jagged. This is typical of time charts that represent volatile data, such as stock market prices over the course of a day, as you may have seen on television business news programs. Other time charts may show more sweeping, long-term changes, such as those in
Figure 4-13
, which shows only the percentage of plural births every five years, rather than every single year. Again, this depends on how the person designing the chart wants you to look at the information. You need to really think about how the chart was set up and, potentially, ask additional questions in order to clear up any confusion.
| HEADS UP | You can also run into a problem in which a time chart presents the information in an unfair way, such as charting the |
| Tip | To see whether a time chart is on pace, statistically:
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