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I am investigating the topic of Visual Pollution in my city, and have established some indicators such as Number of Visible Waste Bins and others but now, I am interested in building a single number index to measure and compare different areas within my city.

I have two questions.

First, what really differentiates an Index from any other Indicator?

Second, can an index of any kind be built on surveys (e.g. Satisfaction Level)?

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    $\begingroup$ In fields I know an indicator is a single measure and an index is usually some kind of composite such as a weighted average of indicators. I don't find people being very formal about the difference, but your wording seems standard. (There is a specific sense of an indicator being a variable with values 0 and 1, which doesn't apply here.) $\endgroup$
    – Nick Cox
    Commented Mar 23, 2021 at 11:00
  • $\begingroup$ Your second question seems very open to me. Why not? is a vague reply. I suggest you expand on that one. $\endgroup$
    – Nick Cox
    Commented Mar 23, 2021 at 11:02
  • $\begingroup$ @NickCox Thank you for your timely reply. What I meant by the second question is, can one develop an index which integrates different indicators some of which are subjective indicators? If so, how? $\endgroup$
    – Ronnie
    Commented Mar 23, 2021 at 11:14
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    $\begingroup$ Still very general. But as a weighted average, making sure that directions run the same way. Hard to say more specifically, e.g. many waste bins could mean less rubbish lying around, so that could be a positive for pollution. Much depends on what you're able to compute and/or know about already, e.g. Cronbach's alpha looks at how much indicators indicate the same or differently. Also, lumping several different things together can be a bad idea and isn't necessarily a good goal. $\endgroup$
    – Nick Cox
    Commented Mar 23, 2021 at 11:59
  • $\begingroup$ @NickCox, apologies for the bad wording. I just want to make my question clear. I now know that an index aggregates many indicators, can these indicators be based on survey results? $\endgroup$
    – Ronnie
    Commented Mar 29, 2021 at 7:46

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When I measure a physical quantity, like voltage, current, or resistance, or flow rate, volume, kilometers per hour and so forth, I would not call any one of them an "index," not because they are not indexed to something, indeed they are, it's just that they are physical measurements and calling them indices would be besides the point. Now an index can be defined as anything that is not physically interpretable in the context in which it is used but provides an indication of some target physical quantity is called an index. For example from medicine, a rate-pressure product would be heart rate times systolic blood pressure. which is indexed to cardiac work load, but cardiac work would be more accurately defined as both pressure-volume work and blood volume ejected acceleration work. So rate-pressure product is what we would call a quick and dirty approximation, and is indexed to cardiac workload.

Generalizing the above, we can define anything that is not an exact physical quantity can be called an index. So body mass index (BMI) which has units that do not relate to anything to do with how fat people are is most definitely an index. One could make the claim that AIC is an index, although AIC proponents might balk at that. So most generally there are measurements, and things indexed to measurements that are not themselves physical in the context in which they are used.

This answers both of your questions. Maybe this will help: "measurements measure and indices indicate."

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    $\begingroup$ (+1) When used formally an index is usually a composite, so that a price index is some kind of weighted average of different prices and (less subtly) a index of quality or merit is based on adding different things together, such as scores or grades under different headings. Your main examples can all be related to uncontroversial physical or biological science, but there are many fluffier or fuzzier fields. Does IQ really measure intelligence or is it just tautologically a measure of the ability to do well on IQ tests? $\endgroup$
    – Nick Cox
    Commented Mar 30, 2021 at 9:47
  • $\begingroup$ @NickCox Composites? Well, sometimes. More to do with context. For example, systolic blood pressure is a measurement that is indexed to risk of a cardiovascular event; heart attack, stroke. For IQ tests, what you get is a raw score, which measures performance on that test, and only when it is assumed that the conditions of the test and the raw score are indexed to intelligence, a context that is actually not that of the raw test score itself does the "indexing" occur. Using a measurement out of context is the magic "indexing" moment, as it were. $\endgroup$
    – Carl
    Commented Mar 31, 2021 at 0:22
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    $\begingroup$ I don't think we disagree. Systolic blood pressure being called an index is what I call an informal use. Some people might call systolic blood pressure a measure or indicator with (from my perspective) equal merit to the term. (I don't challenge your medical expertise or experience, naturally.) The touchstone is whether any term is essential, or at least customary, in definition. $\endgroup$
    – Nick Cox
    Commented Mar 31, 2021 at 7:26
  • $\begingroup$ @NickCox Yes, we were not disagreeing, just fleshing out context. As an aside, I often find that the commonly accepted context for things is somewhat illogical, and it troubles me because when I write I cannot always limit myself to exact constructs to prevent misinterpretation of my intent. $\endgroup$
    – Carl
    Commented Mar 31, 2021 at 12:05
  • $\begingroup$ Harold Jeffteys commented that mathematicians and statisticians are far behind botanists and zoologists in making their terminology systematic. $\endgroup$
    – Nick Cox
    Commented Mar 31, 2021 at 14:23

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