Statistics for Dummies (15 page)
A
table
is a data display that presents summary information from a data set in a row-and-column format. Some tables are clear and easy to read; others leave something to be desired. Although a pie chart or a bar graph is usually intended to make one or two points at most, a table can make several points at once (which can be good or bad, depending on the effect this has on the reader).
Statistical information is compiled by researchers not only for their own reports, but also so that others can use the information to do their own research and answer their own questions. Tables are often used in these situations.
The Colorado Department of Public Health and Environment compiles tables on birth statistics for Colorado residents.
Table 4-2
shows the number of live births by the sex of the child and the plurality status (single births versus the births of twins, triplets, and so on) for selected years from 1975–2000. Some questions that can be answered with this table are: What's the birth rate of males compared to females in Colorado? And is the rate of plural births changing? From this table, you can see that over a 25-year period, the percentage of female births remained steady at just under 49%, while the percentage of male births remained steady at just over 51%. (You may wonder why these percentages aren't closer to 50% each. This is a question for demographers — scientists who study human population trends — and biologists, not statisticians.) You can also see that the rate of plural births (as opposed to single births) seems to have changed over the years. It appears that the percentage of plural births is increasing, but which column do you look at: the number of plural births or the percentage of plural births? Does it matter? Yes, it does!
Year | Total Number of Births | Number of Female Births | % Female Births | Number of Male Births | % Male Births | Number of Single Births | % Single Births | Number of Plural Births | % Plural Births |
|---|---|---|---|---|---|---|---|---|---|
1975 | 40,148 | 19,447 | 48.4 | 20,701 | 51.6 | 39,385 | 98.1 | 763 | 1.9 |
1980 | 49,716 | 24,282 | 48.8 | 25,434 | 51.2 | 48,771 | 98.1 | 945 | 1.9 |
1985 | 55,115 | 26,925 | 48.9 | 28,190 | 51.1 | 53,949 | 97.9 | 1,166 | 2.1 |
1990 | 53,491 | 26,097 | 48.8 | 27,394 | 51.2 | 52,245 | 97.7 | 1,246 | 2.3 |
1995 | 54,310 | 26,431 | 48.7 | 27,879 | 51.3 | 52,669 | 97.0 | 1,641 | 3.0 |
2000 | 65,429 | 31,953 | 48.8 | 33,476 | 51.2 | 63,447 | 97.0 | 1,982 | 3.0 |
How do you draw conclusions about trends in plural births over time by using the statistics presented in this table? If you look only at the number of plural births for 1975 compared to 2000, they increase from 763 to 1,982. Someone may try to say that this represents a 160% increase, or about 1.6 times as many plural births in 25 years ([1,982 – 763] ÷ 763). More plural births occurred in the year 2000 than in 1975, but more single births also occurred over this same time period. Because of this, the only accurate way to compare these statistics is to calculate the percentage of single versus plural births and compare these percentages. Looking at
Table 4-2
, you can see that the percentage of plural births in 1975 was 1.9%, while in 2000 the percentage of plural births was 3.0%. You can conclude that the percentage of plural births did increase over time, even after taking the increased number of births into account. However, the increase is not 160%; it's closer to 58%: ([3.0 – 1.9]) ÷ 1.9) × 100%.
| HEADS UP | Beware of conclusions that are drawn from a data display that compares the |
Table 4-3
shows a breakdown of the number of live births in Colorado by the age of the mother for selected years from 1975–2000. The numerical variable age is broken down into categories that are of the same width (5 years) and are not overlapping. This makes for a fair and equitable comparison of age groups. However, the table gives only numbers of births in each case, so you can't look at the table and get a sense of any trends that may be developing over time in terms of the age of the mother. This problem can be solved by including the percents in parentheses along with the total number in each category, so that the reader can easily make a comparison. Another way to display the information is to include a pie chart for each year, showing the percent of the total births that were born to women in each of the eight nonoverlapping age groups.
 |
| | | Age of Mother (Years) | |||||||
|---|---|---|---|---|---|---|---|---|---|
Year | Total Number of Births | 10–14 | 15–19 | 20–24 | 25–29 | 30–34 | 35–39 | 40–44 | 45–49 |
1975 | 40,148 | 88 | 6,627 | 14,533 | 12,565 | 4,885 | 1,211 | 222 | 16 |
1980 | 49,716 | 57 | 6,530 | 16,642 | 16,081 | 8,349 | 1,842 | 198 | 12 |
1985 | 55,115 | 90 | 5,634 | 16,242 | 18,065 | 11,231 | 3,464 | 370 | 13 |
1990 | 53,491 | 91 | 5,975 | 13,118 | 16,352 | 12,444 | 4,772 | 717 | 15 |
1995 | 54,310 | 134 | 6,462 | 12,935 | 14,286 | 13,186 | 6,184 | 1,071 | 38 |
2000 | 65,429 | 117 | 7,546 | 15,865 | 17,408 | 15,275 | 7,546 | 1,545 | 93 |
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Note that because the totals are reported in this table, you can do the work of finding the percentages on your own, if you wanted to. (Had the table presented only percents, without any totals, you would have had an easier time comparing percents. But you would have been limited in the conclusions you could have drawn, because you would not have known the total numbers.) Just to save you time, I calculated those percents for you, for the combined group of mothers aged 40–49.
Table 4-4
shows those calculations. From this table, you can see that a trend in mother's age appears to be emerging. More women are having babies in their 40s than before, and the percentage is steadily increasing.
|
Year | Total Births | Number of Births to Mothers Aged 40–49 Years | % of Births to Mothers Aged 40–49 Years |
|---|---|---|---|
1975 | 40,148 | 238 | 0.59% |
1980 | 49,716 | 210 | 0.42% |
1985 | 55,115 | 383 | 0.69% |
1990 | 53,491 | 732 | 1.4% |
1995 | 54,310 | 1,109 | 2.0% |
2000 | 65,429 | 1,638 | 2.5% |
|
The footnote to
Table 4-3
(paraphrased from the note originally written by the Colorado Department of Public Health and Environment) indicates that any mothers who were aged 50 or older were not included in this data set. Recent studies suggest that a growing (albeit still small) percentage of women are having babies in their early 50s, so this data set may have to be augmented in time to include that age group.
Don't be fooled into thinking that just because certain percentages are small, they aren't meaningful and/or comparable. All of the percentages in
Table 4-4
are small (equal to or less than 2.5%) but the percentage for the year 2000 (2.5%) is over four times the percentage for 1975 (0.59%), and that represents a very large increase, relatively speaking. Similarly, don't assume that when a large percent increase is reported, the situation involves a large number of people. Suppose someone announces that the rate of a particular disease quadrupled over the past few years. That doesn't mean a large percentage of people are affected, it means only that the percentage is four times as large as it used to be. The percentage of people affected by the disease in question may have been extremely small to begin with. An increase is still an increase, but in some situations, reporting the percentage alone can be misleading; the prevalence of the disease needs to be put into perspective in terms of the total number of people affected.
| REMEMBER | A percentage is a relative measure. However, look for the total number, as well, to keep the actual amounts in proper perspective. |