Displaying meaningful data
It is important to think carefully about which values to present in tables. In some situations, the most obvious data are not the easiest to interpret, but a simple ratio or difference of values is much more easily understood and meaningful. A few examples will illustrate.
Percentages and proportions
In simple frequency tables, it is often easier to understand the proportions (or percentages) in the different categories than the raw counts.
This is even more important when comparing the distribution of a categorical variable in several groups, especially if the total number of individuals differs between the groups.
It is much easier to compare proportions or percentages between groups than to compare raw frequencies.
Tourists in Hawaii
In 2011, a questionnaire was mailed to tourists who had visited Hawaii, with respondents being given allowed to return it by mail or answer the questions online. The following table describes the region from which the respondents came and their 'lifestage'.
US West | US East | Japan | Canada | Europe | Oceania | |
Wedding/honeymoon | 120 | 210 | 647 | 117 | 221 | 74 |
Family (with children) | 722 | 637 | 888 | 721 | 184 | 311 |
Young (18-34) | 371 | 412 | 779 | 410 | 399 | 200 |
Middle aged (35-54) | 793 | 986 | 1363 | 834 | 630 | 398 |
Seniors (55+) | 1338 | 1507 | 2050 | 1255 | 440 | 659 |
Total | 3344 | 3752 | 5727 | 3337 | 1874 | 1642 |
Each column of this table is a frequency table for tourists arriving from one region. However it is difficult to make meaningful comparisons between the regions since their totals are so different.
The following table shows each column as percentages.
US West | US East | Japan | Canada | Europe | Oceania | |
Wedding/honeymoon | 3.6 | 5.6 | 11.3 | 3.5 | 11.8 | 4.5 |
Family (with children) | 21.6 | 17.0 | 15.5 | 21.6 | 9.8 | 18.9 |
Young (18-34) | 11.1 | 11.0 | 13.6 | 12.3 | 21.3 | 12.2 |
Middle aged (35-54) | 23.7 | 26.3 | 23.8 | 25.0 | 33.6 | 24.2 |
Seniors (55+) | 40.0 | 40.2 | 35.8 | 37.6 | 23.5 | 40.1 |
Total | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
In this form, it is much easier to understand the differences between the types of tourist from the different regions. In particular, it is clearer that:
A bigger proportion of tourists from Japan and Europe are Wedding/honeymoon than from the other regions. Also, very few tourists from Europe are Family, but many are Young or Middle aged.
Ratios
In some situations, the rows of a table correspond to items of different 'size'. Dividing values by a measure of size can then make it easier to compare rows. For example,
TB cases in SADC countries
The next table shows the incidence of TB in the countries of the Southern African Development Community (SADC) in 2012. (The values were reported to the nearest thousand in most countries.)
The largest numbers are associated with the countries with the biggest population, so the table mainly tells you about the sizes of the countries.
Click Show Cases per 1000 to add a column showing the populations of the countries and a final column containing the ratio of TB cases to the population size. This last column shows the TB cases per 1000 of population, so the values in different countries can be more meaningfully compared.
Note that the table only describes reported TB cases, so some of the smaller rates are caused by under-reporting, not just better health.
Finally, use the '-' button to reduce the digits displayed for the TB rates. Two significant digits would be sufficient in most reports.
Wine production in New Zealand
The table below gives the wine production (in tonnes) in New Zealand from 1998 to 2013.
Although these values show considerable variation in wine production between 1998 and 2013, with an increasing trend, there was also a great increase in the area of vineyards in this period. Click Show Yield to see the area of vinyards (hectares) and the yield (tonnes per hectare).
Use the '-' button to reduce the number of decimal digits in the column of yields.
There was considerable year-to-year variation, but the yield from vinyards in New Zealand changed very little in this period.