Systematic errors in data collection

You weigh the same sack ten times and the scale shows a slightly different number each time: 25.1; 24.9; 25.0; 25.2. That is random error, and on average it cancels out. Now a different case: the scale reads 0.4 kg too high every time. Repeat the weighing a hundred times and the error does not go away; the result merely looks more reliable. This is a systematic error: it pushes the result the same way every time. The more data, the more dangerous it is, because the result looks precise but is wrong.

Scatter and bias

You weighed a sample whose true weight is 25.0 kg five times on each of two scales. Scale A: 24.8; 25.3; 25.1; 24.7; 25.1, average 25.0. Scale B: 25.4; 25.5; 25.4; 25.3; 25.4, average 25.4. Scale B looks more consistent because its numbers sit close together, yet it reads 0.4 kg too high every time. Small scatter does not mean correctness: repeated measurement removes random error, but bias is revealed only by comparison with another scale or a known weight.

An example: the receiving scale

A receiving scale reads 25 kg sacks of chickpeas 0.4 kg too high. 480 sacks arrive a month: 480 × 0.4 = 192 kg of "extra" receipts. At 14,000 so'm a kilogram that is 192 × 14,000 = 2,688,000 so'm a month. Over a year it is 192 × 12 = 2,304 kg, or 32,256,000 so'm. The count at year-end reveals a shortage of 2,304 kg. Everyone thinks of theft, yet nobody stole anything: the scale is out of adjustment.

How to detect it

1. The signs of the discrepancies. Look at the signs of 20 differences between count and records (leave out zero differences). With random error the sign is like a coin toss: it splits roughly evenly. If 15 of 20 share one sign, the chance of that being random is about 4 percent; if 17 do, about 0.3 percent. In Excel: COUNTIF(differences, "<0") and COUNTIF(differences, ">0").
2. The distribution across slices. Break the differences down by shift, day, zone and counter. Random error is the same in every slice; systematic error gathers in one.
3. Round numbers. If 41 of 60 count results end in 0 or 5 (68 percent), whereas by chance you would expect 20 percent, that is 12, then most of them were estimated rather than counted.
4. An independent recount. Have a second employee recount the same 30 positions without seeing the book balance. The difference between the two counters should not lean one way. If the first always counts less than the second, the cause is that person's habit or counting method.

Typical sources

• Instrument: scales, tape measure, scanner settings.
• Routine: starting from the same place every day, or taking data only from the morning shift. If counters always start at the entrance, the last zones get counted tired and carelessly.
• Timing: if goods that arrived in the morning are documented in the evening, they look like a "surplus" at the count.
• Selection: only convenient, nearby or tidy shelves get counted, while the hard places are left "for later".
• People: if the counter sees the book balance, they stop when the figure comes close to it.
• Data entry: copying leaves the old value behind, and a default value (say "1" in every row) never changes.

How to reduce it

• Check the instrument once a week against a known weight. For example, if a 20 kg check weight reads off by more than 0.2 kg, take the scale out of use.
• Vary the routine: choose the starting zone by lot and rotate counters between zones.
• Set a cut-off: the hour the count starts, with later documents belonging to the next period.
• Blind counting: the second employee counts without seeing the book balance.
• If an error is found, correct past data too, or the trend is distorted.

Conclusion

Random error disappears with repeated measurement, while systematic error does not disappear but accumulates. Find it through the signs of discrepancies, through slices and through round numbers, and then change the process. The cheapest protection is to check the instrument once a week and to shuffle the counting order by lot. CountLab breaks stock-count results down by shift, zone and counter and shows signs of systematic bias separately in the report.