## How Fair is Your Scale?

Actually there are two things to consider when trying to determine how good your scale is, that is accuracy and precision.

1. Accuracy - Accuracy simply is how close to the "true" weight does the scale read.
2. Precision - Precision is the amount of variation in the measurements conducted on the same object as it is weighed repeatedly. Variation is unavoidable, since we don't live in a perfect world, but the amount of variation should be very small.

Both are very important. If your scale reads the exact same reading measurement after measurement, but is 0.1 ounce off, then you will have parents complaining that their child's car weighed exactly 5.00 ounces on some other scale. You will also have fairness issues if your scale cannot distinguish the weight difference between two closely weighted cars, but your timing system can. The heavier car will have the clear (and unfair) advantage.

Accuracy

If your scale cannot be calibrated to a standard weight, the only way to determine if your scale is accurate, is to compare it to a known standard weight. This can be done by purchasing an official 5 ounce weight or other certified weight to compare your scale against. Measure this weight several times and calculate the average of all the measurements. The average measurement should be within 0.1% of the standard weight's value.

If your scale can be calibrated to a known weight, you should include the calibration procedure in your weighing procedure prior to each car being weighed.

Precision

In trying to determine scale precision we must apply some simple statistics (don't worry, a spreadsheet does all of the calculations) and calculate the measurement error of the scale. If you have 2 object with weights within the region of the measurement error, the scale will not be able to tell them apart.

To calculate the measurement error we must first calculate the standard deviation of the measurement error from the following equation.

measurement)2 = (σrepeatability)2 + (σreproducibility)2

Where the square of the standard deviation of the measurement error is the sum of the squares of the standard deviation of the repeatability error and the standard deviation of the reproducibility error.

• Repeatability Error - The variation due to the same person using the same measuring instrument for repeated measurements.
• Reproducibility Error - The variation due to different people making repeated measurements using the same measuring instrument.

For our purposes, we will assume that each person using the scale knows the proper way to calibrate the scale and to take the measurements, so reproducibility error is assumed to be zero. Thus the equation simplifies to:

σmeasurement = σrepeatability

To accurately calculate the standard deviation of the repeatability error, you will need to gather at least 20 objects of varying weight for which you will weigh each of them twice. Groups of coins in varying numbers wrapped with tape works great for this.

This Excel spreadsheet has instructions on how to do this test as well as a worksheet to record your data and to calculate the measurement error. The spreadsheet also includes information on how to interpret the results.

Once we have calculated the standard deviation of the measurement error, we can finally calculate the scale's total measurement error, which is:

Measurement Error = +/- 3 (σmeasurement)

If your scale has a measurement error large enough for your timing system to detect (whether it be eyeball or electronics), you should consider replacing it with a more precise scale.