Wednesday, July 17, 2024

# Comparing Apples with Oranges?

The familiar saying, “Comparing apples to oranges,” suggests that it’s illogical to compare two distinct items. However, in the realm of statistics, such comparisons are not only possible but sometimes necessary. By establishing a uniform standard or metric, we can evaluate items that, at first glance, appear incomparable. In this article, I present some straightforward methods for drawing meaningful comparisons between disparate elements.

The general approach of comparing “Apples with Oranges” involves the following:

1. Find Comparable Metrics: Find metrics that can be applied to both items. For example, if you’re comparing the nutritional value of apples and oranges, you could compare their vitamin C content, calories, or fiber. If you’re trying to compare the popularity, you may consider the consumption per capita. If you’re trying to compare their weights, we’d consider their weights in a common scale.
2. Normalize the Data: Use per capita measurements or other forms of normalization to make the data comparable. For instance, if you’re comparing the popularity of apples vs. oranges, you might look at consumption per person rather than total consumption, which could be skewed by population size.
3. Contextualize the Data: Ensure that any external factors affecting the data are accounted for. For example, if one fruit was not available for a period while the other wasn’t, this should be factored into the timing of measurement of, say, consumption comparison.
4. Use Statistical Methods: Apply statistical methods such as t-tests or ANOVA to determine if there are significant differences between the groups you are comparing. t-tests give us pointers as to whether differences fall under Null Hypothesis or not, or put another way, if there are statistical differences between the two or just by random chance.
5. Consider the Purpose of Comparison: Always keep in mind why you are making the comparison and what you hope to achieve or understand from it.
With the right approach and statistical tools, you can make meaningful comparisons between different items. The key is to be clear about what is being compared and to ensure that the comparison is fair and takes into account all relevant factors.

Let’s consider some seemingly “ridiculous” questions and see if we can answer them sensibly.
Q1. What is more: a person who is 70 inches tall or an apple that weighs 250 grams?
A1:
Here we have to compare height of a human being in inches with an apple’s weight in grams!
To answer what is “more,” we need consider the following:
The height of a person who is 70 inches seems to be fall along the average height of men in North America. Similarly, the weight of an adult human varies by continent, but in North America, it’s about 80 kg or about 180 lb, which is 80,000 grams. So, the 70 inch tall person is likely to weighs around that.
In the other group, we have an apple that weighs 250 grams.
So, from strictly weight perspective, a person who is 70 inches tall and has an average weight of 80 kg is significantly “more” than an apple that weighs 250 grams.
As you can see here, we found a common ground here between the height and the weight of completely different things (human vs apple).
Simple enough, what if we asked another question?

Q2: Which one is extraordinary: a person of 70 inches height or a 250 grams apple?
A2:
Here we need to be cautious about defining the “extraordinary” as it is subjective. So, we need to qualify this further by taking the angle of “unusual”, or “outlier”, that is, outside of the mean measurements.
If we consider this in the context of height and weight
The term “extraordinary” is defined as something very unusual or remarkable¹. It’s a subjective measure and can depend on context or perspective.
In the context of height and weight:
A person who is 70 inches tall would be considered within the average range for adult human height in North America (average male height is around 69 inches in the USA).
An apple’s weight is typically under 100 grams (usually they’re in 70-100 grams range). So, a weight of 250 grams is unusually heavy for an apple.
In this perspective, the apple weighing 250 grams is an outlier, and therefore, extraordinary due to its weight being significantly more than an average apple. The height of a person on the other hand, is not as uncommon.

So, the apple is extraordinary in this case.
I hope this exercise was fun and enlightening. Thanks for reading! For more statistics and measurements, be sure to explore my other posts.

In another article, I share some of the ways to re-scale and normalize data from different scales to a common scale.

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