This article explores the nuances of accuracy and precision. Included in the journey are their close cousins - bias and noise. We start with discussing contexts, including science, business, and our every day decisions. We then provide a dart board metaphor to build out our understanding. We conclude with practical car buying examples.
Scientists aim for the highest degree of precision and accuracy. This is another way of saying that scientists maximize explanatory power by minimizing error. There are times when they make rough estimates for making a scientific decision, like an inference. Their study may have uncertainty and need critical information. Minimizing study uncertainty is a key to success. To express uncertainty, they use these two values: accuracy and precision.
Business people and those of us purchasing and negotiating in our daily lives face similar challenges. This is especially true as related to potential bias and noise in our operating processes that may lead to accuracy and precision outcome challenges. This article helps relate traditional scientific principles in a way to make great decisions. [i]
In our everyday life, we face negotiation. Understanding our motivations and objectives is key to maintaining negotiation accuracy. Staying on an accurate (i.e., unbiased) path will enable our precision as we proceed through a negotiation. An accurate and precise negotiation process leads to the optimal outcome. In the case of a car buying negotiation, the optimal outcome is buying the best car at the best price. Without accuracy, precision loses its anchoring meaning. Without accuracy and precision, the outcome will likely be suboptimal.
People are naturally inclined to jump into the precision-related details of a purchase process. It is important to start with your guiding objectives as an accuracy beacon that will ground the precision-related details.
So, whether science, business, or our personal life, our understanding of how we make decisions is critical. To proceed down a good decision-making path, let us start with the nuanced definition of Accuracy and Precision.
Accuracy is defined as how close a measurement is to a standard or accepted value. This is impacted by the amount of bias in the process.
Precision is how close measurements are, or the closeness of the measurements/results with each other. This is impacted by the amount of noise in the process.
It is possible to be very accurate without being precise and to be very precise but not very accurate. We can suffer from both accuracy and precision problems. The holy grail is to be both accurate and precise.
The Dartboard Metaphor
To further explain, we use a dartboard metaphor to help distinguish between precision and accuracy. We use the bull's eye of the dartboard as the standard (true value). The closer the darts land to the bull's eye the more accurate. If all the darts land in one area, anywhere in the dartboard, and very close to each other, that is precision. Also, we use a distinction between process and outcome. Generally:
The amount of noise in a process maps to a similarly precise outcome (e.g., a high noise process leads to a low precision outcome).
The amount of bias in a process maps to a similarly accurate outcome. (e.g., a high bias process leads to a low accuracy outcome).
Also, in our dartboard example: 1) each team has 5 unique dart throwers, throwing 1 dart each, and 2) the "X" represents where the dart lands.
For Team A, all the darts landed close to the bull's eye and they are very close to each other. Therefore the outcome is both precise and accurate. Also, the outcome was the result of an unbiased, low noise process
For Team B, the darts all land very close to each other, but far away from the bull's eye. Therefore, it shows there is precision but is not much accuracy. Team B demonstrates a biased process because it is systemically off target.
For Team C the darts are not very close to the bull's eye but are equally spaced around the bull's eye. This shows that there is accuracy but not much precision. Team C demonstrates a noisy process because of the low precision outcome.
For Team D all the darts are widely scattered but to the left of the bull's eye. Like Team B, they lack accuracy. Also, like C, they lack precision. This results from both a noisy and biased process.
Please note, accuracy is based on distance from a standard. Standards are generally a human construct and can change. That is, what is accurate today may not be accurate tomorrow. Also, accuracy and bias are related. Since some standard is necessary to determine accuracy, it follows that the same standard could be related to a biased outcome. As such, bias is a function of the standard setter. The standard itself will drive the perception of bias. A related logical fallacy is called "Moving the goal post." This happens when the parameters for making an argument are changed after a conclusion is reached. As such, it is important to inspect both the standard and the measure when determining accuracy.
Daniel Kahneman’s book Noise uses the metaphor for "flipping the target." (see the graphic, this is the same as the prior dartboard graphic, except the bull's eyes have been removed.) The metaphor suggests bias (accuracy) requires an understanding of the standard (location of the bull's eye) whereas noise (precision) does not. Precision only requires understanding the relative distance of systems outcomes (dart cluster). When you flip the target, one may see the relative distance of the outcome, but one may not see the distance from the standard. In other words, you know that Teams D and C are not very precise as a result of a noisy process. Also, you know Teams B and A are very precise as a result of a low noise process. However, there is no way to determine bias or the resulting accuracy without the bull's eye standard.
A precise but low accuracy result is like someone being really good at NOT getting what they want.
This difference becomes important in the following car buying example.
Car Buying
Let’s face it, most people consider the car buying process as a “necessary evil,” right up there with visiting the dentist. But given the high cost, confusing criteria, and many alternatives, tackling the car buying process with a positive attitude and an informed approach is critical. To start, being clear about the car buying objective, such as “For Safe Transportation,” is like the bull's eye in the previous example. This becomes our decision beacon. Admittedly, there are many potential buying objectives. To minimize decision bias, one should:
Clearly initialize the objective, and then
Be true to the objective. Avoid “Moving the goal post.”
As in the dart-throwing metaphor, the car buying objective is what we are aiming for. Instead of a handful of darts, we now turn our attention to our car choices. The operative question becomes:
"How do we build a car choice set that accurately reflects our buying objective and in a precise manner leading to an optimal car purchase?"
The precision is related to the data and the car buying process. As long as we are precise in gathering and evaluating the car buying data, we will have a more precise outcome. Being true to the process minimizes decision noise.
In our article Cutting through complexity: A car buying approach is a recommended car buying approach. It is designed to optimize accuracy and precision. Our approach is designed for the best car purchase outcome. In this article, we suggest evaluating cost per remaining mile (CPRM) and car alternative preferences. These are precision metrics. Independently, it is your car buying objective that is the standard to determine accuracy. Since the precision metrics often involve some uncertainty, it is this objective beacon that serves to mediate that uncertainty. Keep in mind, some of the uncertainty is generated from auto dealers and other car sellers you may come across. Our approach provides buyer confidence when interacting with car sellers.
Accuracy in action
For example, if you are deciding between 2 car alternatives and they have different technology package options, it may be hard to evaluate. However, if you compare those options to your car buying objective, like “For Safe Transportation,” you will be able to quickly tell which option meets or exceeds that objective. If both options meet or exceed the objective, then you may choose the least expensive of the options. Think of a buying objective as a ready-made decision tiebreaker.
In Summary
Understanding the practical differences between precision and accuracy is important. When we are deep in the process of car buying or any other decision, we may lose sight of our objective. A lack of accuracy may reduce decision quality, regardless of the precision. A precise and accurate car buying process, or any decision process, will render a successful bull's eye outcome like Team A. An accurate and precise car buying process provides confidence:
the car was purchased at the best price, and
the car optimizes our preferences and needs.
Notes
[i] For a banking and business application of precision and accuracy, please see the article Statistics and AI-Enhanced Automation in Banking Transaction Testing