ERROR: How to be less wrong?
Updated: Nov 15, 2021
Being wrong means making errors. Therefore, to be less wrong, you need to make fewer errors. We will investigate them in a series made of three parts. Today, we will analyze the components of errors. In part II, we will dig deeper to understand what errors mean in terms of simple statistics. And in part III, we will discuss how to address them.
Firstly, let’s look at what errors are made of. For that, we need to understand the concepts of accuracy and precision:
Accuracy is an expression of distance to the truth. It tells you how close or how far you are from the true value that you are trying to measure.
Precision is an expression of variability of measurements. It tells you how far you are from other points of measurement and it gives you an idea of consistency (or lack thereof).
We can see how these two concepts apply through the 4 situations illustrated in the image:
Situation A: In this case, accuracy is high and precision is low. That is, each measurement is relatively close to the true value (illustrated by the center of the target) but there is high variability in the value of each measurement.
Suppose that you know for a fact that you weigh 70kg. You step on a scale and it returns 66kg. The next time you try it, it returns 74kg. These measurements are not far from the truth, but they are quite far from each other.
Since precision consists of variability, we also call it the random part of error. In political science, the variability (aka the amount of imprecision, aka random error, aka distance to other measures) is also called noise.
Situation B: This is the ideal situation, in which precision and accuracy are high. When you are both accurate and precise, the level of error is minimal.
You step on a scale and each time it shows 70kg, just like your true weight.
Situation C: When both accuracy and precision are low.
You step on a new scale. It shows 45kg. You step one more time and now it shows 82 kg. You step yet another time and now it shows 71 kg. Besides getting measurements that are far from the true value, you cannot reproduce the same numbers. You have high variability in measurement.
Situation D: When accuracy is low and precision is high.
Although 70kg is your true weight, each time you step on the scale, it returns 65kg. This scale is not that accurate, it always gives you 5 kg less than what you weigh. Therefore, we can say that the scale is biased, which expresses the level of systematic error (amount of inaccuracy).
Systematically wrong and precisely wrong. Although your aim is to be both accurate and precise (as in situation B), many times you will end up in a situation such as C, where there is both bias (aka inaccuracy, aka systematic error) and noise (aka amount of imprecision, aka random error, aka distance to other measures, aka variability).