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Round off to meaningful decimal places!

Consider the following tables, containing data that I made up. Table 1 is simple, and it's easy to see (forget about statistical analysis for now) that treatment A produced the largest plants, treatment B produced the smallest, and treatments C and D produced plants of intermediate height and mass.

Table 1

Treatment

Plant height (cm)

Plant mass (g)

A

98.15 + 35.18

202.28 + 62.17

B

20.78 + 10.96

101.76 + 48.57

C

60.02 + 21.42

166.32 + 45.12

D

63.27 + 30.36

175.09 + 50.33

 

Table 2

Treatment

Plant height (cm)

Plant mass (g)

A

98 + 35

202 + 62

B

20 + 10

101 + 48

C

60 + 21

166 + 45

D

63 + 30

175 + 50

  

Note that the Table 1 contains 68 numbers. And also note that nearly 50% of the numbers in Table 1 do not provide useful, meaningful information. The decimal places in Table 1 do not provide meaningful information because the values represented by the decimal places are insignificant relative to the magnitude of the means and the magnitude of the variation. Now consider that including numbers that do not provide useful information increases the reader's work and therefore reduces the chances that he or she will read and understand the paper.

 

I rounded off to meaningful places in Table 2.

Which table is easier to understand? Table 2.

What has been lost by rounding off in Table 2? Nothing.

What has been gained by rounding off in Table 2? Reader attention and respect.

 

Inclusion of needless decimal places is a sign of inexperience and is also a form of academic, bureaucratic inflation. To the ignorant reader, the extra decimal places might indicate that the work is intricate, precise, sophisticated, and important. To the knowledgeable reader, the extra decimal places indicate a paper that he or she should probably skim or skip.

 

How does one decide whether the decimal places are meaningful? I don't know of any rule (there was one about significant figures but I have forgotten it). The key is to consider the magnitude of the differences between means and the magnitude of the variation. If the differences are relatively small and the variation is relatively small, the decimal places will provide information that will help the reader interpret the data. In Table 3, for example,I would retain the tenths decimal place but would not add the hundredths place.

Table 3

Treatment

Plant height (cm)

Plant mass (g)

A

9.8 + 3.5

20.2 + 6.2

B

2.0 + 1.0

10.1 + 4.8

C

5.8 + 2.1

16.6 + 4.5

D

6.3 + 2.0

17.5 + 5.0

  

Authors who include needless decimal places often commit another error: they repeat values from the tables or figures in the text. Again, this increases the quantity of stuff that the reader must look at and therefore increases his or her work. Let the tables and figures provide the data. If you want to maintain the attention of the knowledgeable reader, use the text to summarize the data, to compare and infer, but not to repeat the data.

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