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Human personality is fantastically complex, which is why personality tests that try to shoehorn a person into binary, defined categories - e.g. thinking or feeling, but not both - are often considered problematic.
But there are indeed differences between people that can be tested.
One of the most common, preferred ways psychologists use to measure personality is what's called the "Big Five": extroversion, agreeableness, conscientiousness, neuroticism, and openness to experience.
People fit into a spectrum on these five dimensions. Everyone is more or less extroverted or more or less open to experience. (For a more thorough breakdown of what the big five personality dimensions mean, you can check out this page by the director of the Personality and Social Dynamics Lab at the University of Oregon.)
There are complex elements of personality that fit within these categories.
Captured within "conscientiousness," for example, are traits like "dutifulness," a person's sense of obligation, and characteristics like "self-discipline," referring to willpower or the ability to persist on a task. While these are related and both fall under the umbrella of conscientiousness, a person might have a very strong sense of obligation but a less developed sense of self-discipline. The most thorough personality tests make distinctions between these characteristics.
A full version of this test contains hundreds of questions and can take 30-40 minutes to complete. But retired Penn State psychology professor John Johnson has a page that offers not just the full test, but also a new, shorter version that takes only 10-20 minutes to finish.
More than 20,000 people have taken the short version of the test, giving it enough of a sample size to give scientifically valid results (more than half a million have taken the full version).
The questions are pretty simple. There's a five-point scale that goes from "very inaccurate" to "very accurate" and you note how true statements like "Worry about things" or "Love large parties" are for you.
When you're done, you get a complex report about your personality, with a score not only for each of the five dimensions, but also a subscore for six subcategories and an explanation for what they mean.
As an example, I scored highly in "Openness to Experience," particularly in the "Adventurousness" subcategory. As an explanation, they told me:
High scorers on adventurousness are eager to try new activities, travel to foreign lands, and experience different things. They find familiarity and routine boring, and will take a new route home just because it is different. Low scorers tend to feel uncomfortable with change and prefer familiar routines. Your level of adventurousness is high.
As someone who traveled abroad extensively, staying away for a year while traveling without a clear destination or end point, this rings true. Care to try it for yourself?