How to decide on the number of decimal places to quote

By MUNGAI KIHANYA

The Sunday Nation

Nairobi,

28 August 2022

The question of rounding numbers isn’t going away easily. Last week I wrote that I did not understand why Wafula Chebukati, the Chairman of the Independent Electoral and Boundaries Commission (IEBC) chose to round off the percentages to two decimal places. I added that, if I had been consulted, I would have expressed the figures to just one decimal place.

Due to shortage of space (this column is just 400 words long), I wasn’t able to explain why. Rounding off numbers is not done for mere convenience. One must have good reason for choosing whatever number of decimals.

One such reason is to ask whether the differences in the numbers can be seen after rounding. In the case of the election results announced by Mr. Chebukati, it was clear that even if the percentages were rounded to one decimal place, the value for each of the four candidates would be different. Thus: Odinga’s score would 48.8; Ruto’s – 50.5; Wajackoya’s – 0.4 and Waihiga’s – 0.2 per cent.

However, if we rounded the figures to the nearest whole number, Wajakoya and Waihiga would both have zero per cent. This would be misleading – it implies that they had (nearly) equal number votes. Yet we know that Wajackoya had almost double what Waihiga got.

These relative scores are clearly seen when we use one decimal place: Wajackoya – 0.4 and Waihiga – 0.2. Adding the third decimal place does not give any additional information. It just opens room for criticism, as we so last week!

Another reason for rounding off numbers is to be consistent with margins of errors. In the case of votes garnered in an election, the values are exact. But in an opinion poll of a sample of voters, statistical errors are unavoidable.

Obviously, the values cannot be more accurate than the margin of error, hence they cannot have more decimal places! Thus, if the estimated error is, say, ±2 per cent, the results can only be quoted to in whole numbers only. Adding decimal places implies that the accuracy is greater than the stated margin of error – “a mathematical absurdity that defies logic”!

Nevertheless, political opinion pollsters alive to the repercussion of saying that a certain candidate has zero per cent support! For this reason, it is understandable to see poll results showing some candidates with less than one per cent yet the margin of error is greater than one.