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The data table for my company's salesmen/women commission for FY23 follows.

enter image description here

Below, I compare the commission of each age group to know which age group is performing well (which I don't think matters), and please notice the groupings are arbitrary and hence meaningless. I compare commission for each age group not intending to see any causal relationship or correlation but rather for a descriptive view, i.e. to gain a deeper understanding of the data. In short, I'm summarizing the data.

enter image description here

Problem: Before I take you toward the problem, I want to clarify a term: Comparison. To compare means to note differences and similarities in characteristics between two or more things. I always thought I can only compare individuals (which are names in this data set) on a certain characteristic: maybe I compare the age of each individual, the commission of each individual, the gender of each individual, the salary of each individual, shirt color of each individual, and what not "of" individuals. Now, it starts to dawn on me that I can compare even the characteristics of individuals to other characteristics: in this case, age group and commission are being compared. My question is, which is unintuitive to me since to compare is to describe the differences in characteristics of two or more things, how in the world is commission a characteristic of age groups? Am I thinking wrong?

P.S. Even though the answers provided by the community were far more intuitive, I still didn't follow them. It is because I didn't make myself clear, which was my fault. To right the wrong, I edit the whole question (including the title).

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    $\begingroup$ Dependent on what? This is just data, if you are going to analyze it you have to define a model. What is your model? What are you trying to answer? $\endgroup$
    – user2974951
    Commented Jul 6, 2023 at 14:37
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    $\begingroup$ Why do you need to characterize any variable as "dependent" or "independent"? A more fundamental and important question is what do you mean by "age group"? $\endgroup$
    – whuber ♦
    Commented Jul 6, 2023 at 14:50
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    $\begingroup$ Please give your data not only as an image, but as text. Users can then easily copy&paste it into their choosen software, which is not possible now! $\endgroup$
    – kjetil b halvorsen ♦
    Commented Jul 6, 2023 at 14:56
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    $\begingroup$ If you can, you may also want to consider the expected commission's association with gender as well as with age. $\endgroup$
    – dimitriy
    Commented Jul 6, 2023 at 16:17
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    $\begingroup$ Put age on the x-axis and commision on the y-axis. Show each person as a dot. Make dots in two colours, one for each gender. Interpret the result. -- In this case, you might earn more or less with age but you cannot change your age by commision! Hence commision must be the dependent variable. $\endgroup$
    – Niels Holst
    Commented Jul 7, 2023 at 14:42

2 Answers 2

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"What makes commission dependent on age?"

The answer is not in statistics, but in substantive knowledge of what the two words mean and how they might relate. Age dependent on commission makes no sense. But if you run the regression that way, you won't get errors.

This is symptomatic of a larger problem: People asking statistics to solve problems that are substantive. When I was a consultant (now I'm retired) it was often hard to get my client to realize that a lot of the work had to be done by them.

But also note @whuber 's comment on Nuclear Hypothesis's answer. You not only have to think about what makes sense in terms of "dependence", but whether "dependent" is even the right term. (Statistics often uses ordinary English words in unusual and confusing ways.)

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At a very broad level, independent and dependent variables can often (but not always) be thought of as causes and effects. Independent variables are termed such because they do not depend on other variables, while dependent variables do. In other words, you can pick a value of the independent variables and see what the downstream effects are in the dependent variables, but you wouldn't generally set the dependent variable directly.

Note that these are generally rules of thumb, it's not always obvious which are dependent/independent variables or if those terms even truly apply - it more comes down to how you think about and use the variables in your analysis. Which one you call "dependent" should more be a function of how you plan to analyze the data, rather than your choice of label informing your analysis plan.

Here, you'd probably want to set age as the independent variable and commission as the dependent one, since that is the likely direction of cause-effect. It's quite possible that someone's commission is dependent on their age (if older more experienced people make more money, for example), but it would be hard to imagine a case where someone's age depended on their commission (implying that people might get older/younger if they make more/less). The choice of dependent/independent variables may also depend somewhat on what is readily observable and what you're trying to infer - you may build a model of causes as the dependent variables using observable effects as the independent variable.

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    $\begingroup$ This cause-effect characterization, although it often holds, is specious. Consider, for instance, the problem of estimating historical climate conditions from data like tree rings or fossils. In this problem the climate conditions are the target and therefore are the "dependent" variable, but then your characterization would have us suppose that tree growth caused the climate to vary! $\endgroup$
    – whuber ♦
    Commented Jul 6, 2023 at 14:52
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    $\begingroup$ @whuber Can you provide a non-specious, yet plausible definition for Independent and Dependent variables that holds every time? $\endgroup$
    – vs_1604
    Commented Jul 6, 2023 at 15:05
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    $\begingroup$ Yes: it's the one that appears in any good textbook that covers regression. The definition is made in terms of the model one applies to the data, which clearly distinguishes the roles. That begs the question of how to decide, in any application, what an appropriate model might be: and sometimes it's okay to model the data both ways, by switching the roles of the variables! Tukey describes this approach in his book EDA on exploratory data analysis, for instance. Thus, a full and correct answer to your question would have to discuss what it means to create and apply a statistical model. $\endgroup$
    – whuber ♦
    Commented Jul 6, 2023 at 15:39
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    $\begingroup$ It's worth commenting that this textbook definition does not invoke any sense of cause and effect, which therefore are irrelevant. Where such considerations become useful, as suggested by the present answer, is that often (but not always!) causal variables are regressors (independent), so that distinction can serve as a heuristic guide in model building. But it's not dispositive. Indeed, in many observational studies the cause/effect distinction is not present: one is interested in estimating how variables are associated or how the value of one might be predicted from values of others. $\endgroup$
    – whuber ♦
    Commented Jul 6, 2023 at 15:41

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