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Background

I have just been analysing some data where participants attempt to control a dynamic system with integer numeric inputs between 0 and 100. I've noticed that there is a general tendency for participants to give responses that are divisible by 10 (e.g., 0, 10, 20, 30, etc.). After that participants' second favourite input values are those divisible by 5 but not by 10 ( e.g., 5, 15, 25, 35, etc.). After that excluding some general patterns in the data, all the other input numbers appear about equally common (e.g., 1, 2, 3, 4, 6, 7, 8, 9, 11, 12, etc.).

Perhaps in a related way, I can also remember from market research that when you ask people how often they do certain things, as the number gets larger, they will often show a similar tendency to approximate and use numbers divisible by 10 or 100 and so on. I also seem to remember reading research where people report number of sexual partners, where a similar tendency was observed.

Thus, this tendency is consistent with a preference for what are informally referred to as "round numbers", where as in Wikipedia it is argued that "a number ending in 5 might be considered in a way more "round" than one ending in neither 0 nor 5. "

Question

  • What explains people's general tendency to prefer certain input values when trying to control a system (e.g., numbers divisible by 10 or 5)?
  • Is there any specific research that has quantified this effect in another system control task?
  • Does a similar mechanism underlie the popularity of such numbers in a system control task as does in a frequency estimation task?
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5  
I have an anecdote and an exception. The anecdote is that when I do quantitative analysis on a continuous data set, I sample it in tenths first, then finer if I have to. I think the goal is to gain intuition for the system by breaking it up evenly. The exception is when you ask people to name random numbers. Then suddenly, they NEVER hit a round number! And they tend to avoid hitting the same number twice in a row too (which is just as likely in a random set). –  Keegan Keplinger Jun 13 '12 at 6:57
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From my arm-chair it seems that the tendency is based on folk notion of sig-figs. If I say 10 without any further qualification as the magnitude of something, it is usually assumed to be $10 \pm 5$. I think when most people say 15 the also mean $15 \pm 2.5$, etc. When I say 11 though then I probably mean $11 \pm 0.5$. –  Artem Kaznatcheev Jun 13 '12 at 18:19
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1 Answer 1

up vote 8 down vote accepted

The effect you are referring to is called heaping. Unfortunately, I am not aware of a source discussing the psychological aspect of this phenomenon, but I found an article about a statistical approach to heaped data.

Roberts JM, Brewer DD. (2001) Measures and tests of heaping in discrete quantitative distributions. Journal of Applied Statistics 28(7), 887-896. http://www.tandfonline.com/doi/abs/10.1080/02664760120074960

Abstract Heaping is often found in discrete quantitative data based on subject responses to open-ended interview questions or observer assessments. Heaping occurs when subjects or observers prefer some set of numbers as responses (e.g. multiples of 5) simply because of the features of this set. Although heaping represents a common type of measurement error, apparently no prior general measure of heaping exists. We present simple measures and tests of heaping in discrete quantitative data, illustrate them with data from an epidemiologic study, and evaluate the bias of these statistics. These techniques permit formal measurement of heaping and facilitate comparisons of the degree of heaping in data from different samples, substantive domains, and data collection methods.

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2  
@JeromyAnglim Are you sure this "Answer" answers your question? It's certainly helpful, but it doesn't explain participants' preferences. (Sorry if I'm missing something obvious.) –  John Pick Jun 14 '12 at 5:12
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