Reducing number entry errors: solving a widespread, serious problem

Abstract

Number entry is ubiquitous: it is required in many fields including science, healthcare, education, government, mathematics and finance. People entering numbers are to be expected to make errors, but shockingly few systems make any effort to detect, block or otherwise manage errors. Worse, errors may be ignored but processed in arbitrary ways, with unintended results. A standard class of error (defined in the paper) is an 'out by 10 error', which is easily made by miskeying a decimal point or a zero. In safety-critical domains, such as drug delivery, out by 10 errors generally have adverse consequences. Here, we expose the extent of the problem of numeric errors in a very wide range of systems. An analysis of better error management is presented: under reasonable assumptions, we show that the probability of out by 10 errors can be halved by better user interface design. We provide a demonstration user interface to show that the approach is practical.To kill an error is as good a service as, and sometimes even better than, the establishing of a new truth or fact. (Charles Darwin 1879 [2008], p. 229).

Figure 1.

Errors in adding numbers in Microsoft Excel. Excel's SUM() function, which is used to total all columns in this figure, ignores values that are not numbers. No errors are reported in any of the examples. (a) Two apparently identical sums giving different results. The erroneous sum in the right-hand column is caused by 3.1. having a final decimal point/full stop, and hence being treated as text, and thus processed as zero by SUM. The difference between the column sums may not be noticed by a user, particularly since in normal use they are unlikely to double-check the ‘same’ columns, as used here for illustrative purposes. (b) The ‘show precedents’ feature is one way to help check calculations. It highlights the operands of a cell, but here the precedents for the incorrect total are shown as including the value that has been ignored. Evidently, Excel's notion of ‘precedents’ is the range of possible operands, rather than the actual operands, and therefore the feature is misleading. (c) Through innocent error or intentional mischief, even more unusual column sums can be produced. In the left column, the cell ‘3.1’ is generated by the formula ='3.1', which turns the apparently correct number 3.1 into a string, with value zero as before. In the right column, the cell ‘23’ is actually the number 995, but formatted as ‘23’ using a custom format.

Figure 2.

Snapshot of the error-blocking user interface after an error has occurred. The snapshot of the demonstration user interface shows handling a slip where the user has just entered a number with two decimal points (in our design, the device beeps and the screen also goes red to make the error more salient). An interactive demonstration is available.

Figure 3.

A plot of the probabilities of an out by 10 error and a blocked out by 10 error as found in a 5000 sample Monte Carlo method as a function of e for k = 10. The solid line shows the behaviour of a calculator-type device (all but the first decimal point is ignored); the dashed line shows the reduction in out by 10 errors by blocking syntax errors. Note that at certainty of error (e = 1), out by 10 errors are not certain; this is because e measures keying error rates, not out by 10 rates. (Some keying errors create numbers that are out by less than 10.)

Figure 4.

Plot of probability of an out by 10 error against probability of single key errors. As in figure 3, the solid line shows the behaviour of a simulated real device, and the dashed line shows the reduction in out by 10 errors by blocking syntax errors. The plot illustrates specifically how users with a given e (here 0 • 1) have their effective error rate approximately halved; since the graph is approximately linear for small e, this improvement in out by 10 rate would otherwise have to have been achieved by halving the user's keying error rate. The range of numbers covered in this plot is 0 • 1 to 99 • 9 with k = 10.