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Can descriptive statistics be completely devoid of inference?

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Let's say we are comparing two variables in a purely descriptive analysis, can there ever be a complete absence of any assumptions of the data?

Over 5 sports team A scores: 9, 7, 4, 6, 8.

Over 5 games sports team B scores: 1, 3, 4, 3, 3.

This I assume is where the descriptive analysis ends, other than to say that both teams drew in game 3. However, anyone analysing this would assume team A to be the better team, and they would be right, yet doesn't this then take this from being descriptive to inferential?

How can analysis be completely without an inference? Maybe it is just that any inference is left to the reader and not pointed out by the researcher, is this what would make something purely descriptive?

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  1. The word 'inference' in statistics has a technical meaning, referring to, uh, well, statistical inference.

    When you conclude something about a POPULATION, based on a SAMPLE, then you're engaging in statistical inference.

    Yes, descriptive statistics is that part of statistics that doesn't make that inferential step (which is NOT the same as saying there are no inferences, in the more common sense of 'inference).

    So, when the Census folk say that 14% of Americans self-identify as Black, there was no statistical inference there; it's descriptive.

    As for your example, you've left out the most crucial information. Am I right in assuming these are the SAME games? That is, if A played other teams, then I don't even know whether they won their games; or that B lost theirs.

    Assuming these are when they played each other, if they've played 80 games against each other, and B won all the other times, then B would be better.

    Thus, as I say, you'll left out way too much info. There are lots of other things, such as Bs 2 best players having been hurt and not playing, or all kinds of other things.

    Yes, when you say that one is better, you're engaging in inference, though not in statistical inference (which is a technical term, and you haven't performed its calculations).

    Statistical inference would ask, could you get these scores if the teams were equal quality, just by chance? Then you'd perform some hypothesis test thingy.

    My point is that, as with so many fields, words that have meaning in the ordinary language take on specialized meanings in statistics. You need to keep these distinct concepts straight in your mind -- do you mean the word in the technical sense, or the general sense.

    The word 'significant' gives a lot of trouble in this regard, as statistical significance is NOT the same as "important" (the more common meaning).


  2. One of the main purposes of statistics is to allow you to make inferences from data. Otherwise you're just collecting and manipulating data for no purpose.

    You can use your sports data to try and answer various questions. Is there any significant difference between teams A and B? Is team A better than team B? What will team A's score be next game? etc. This is inference. Any answer will have to be hedged around by things like confidence intervals, significance levels, probability distributions etc, so there won't be any definitive answer.

    The correct way to do inference is by using Bayesian techniques, at least according to Bayesians. David Mackay says you can't do inference without making assumptions, and Bayesian techniques force you to make your assumptions explicit.

  3. Yes, if there's no correlation to infer (unless you're counting that as the inference).

  4. to repeat the others, "inference" does not mean the same thing as it does in normal conversation when discussing statistics.  that said, descriptive statistics is separated from inferential quite easily.  descriptive will tell you the mean, median, mode, etc.  inferential will take those numbers farther, using the normal curve.

  5. "Inferential" statistics refers to the type of statistics where you draw conclusions about a larger population by studying the relations among variables in a sample and then "inferring" that the distribution found in the sample will be the same in the population. So by "inference" it means something quite specific, not any inferences at all but only those as described above.

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