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I have very little knowledge of statistics so please point me in the right direction if this question has already been answered. I tried searching but don’t know the correct keywords to search for.

I am conducting a survey to determine which factors (from a predefined set of 14 factors) motivates respondents the most. For each of the factors, respondents state whether that factor affects them positively (1), negatively (-1), or has no effect (0) on them.

What I would like to do now is to determine the importance of these factors so that I can order them accordingly. This will allow me to know which factors are strong motivators and which ones are weak. I could calculate the mean of each each factor and order them using that, but I have a feeling that that is not statistically correct. From what I have researched so far, I must use cumulative normal distribution. Is that right? If so, how do I do that? If not, what statistical methods do I use?

Hussein Abbas
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  • You need to decide *on the basis of your psychological knowledge* how you would quantify a "strong" motivator. For instance, if all the respondents answer $-1$, would that be the strongest possible motivator or the weakest possible? How about if no respondents answer $0$ but are split evenly between $1$ and $-1$: would this be a weak motivator or a strong one? If weak, how would you want it to compare to one where everybody answered $0$? If strong, how would you want it to compare to one where everybody answered $1$? – whuber Jan 13 '15 at 16:42
  • If all the respondents answer $-1$, that would be a weak motivator. Similarly, if most respondents answer $1$, that would be a strong motivator. Finally, if there is a split between the two, that would be neither strong nor weak. Therefore, I would want to sort based on the number respondents who answer similarly. So if many people answer $1$ for a factor ($f1$) compared to another factor ($f2$), then $f1$ would be a stronger motivator than $f2$. – Hussein Abbas Jan 14 '15 at 02:07
  • "The number ... who answer similarly" does not admit a linear ordering and so cannot be used as a basis for sorting. If you want to sort on the number (or better, proportion) of answers with $+1$, then by all means do so--but then what exactly is your question? – whuber Jan 14 '15 at 02:16
  • I do not know what is the best way to find out which factors are the strongest motivators. Is sorting by the proportion of answers with $+1$ the best way? If not, what is the better way? – Hussein Abbas Jan 14 '15 at 14:15
  • If *your definition* of "strongest" is in terms of proportion of $+1$s, then sort by that. If your definition is something else, then calculate your measure of "strong" and sort by it. I do not see what other kind of answer you could be looking for, given that such results are unique. What else are you hoping that "statistical methods" will supply? – whuber Jan 14 '15 at 15:09
  • Okay, I understand. So it is okay to simply sort the factors based on the number of people who answer $+1$. By the way, how would you approach this problem? Would you also sort by the number of people who answer $+1$? – Hussein Abbas Jan 14 '15 at 16:43
  • You are asking me a psychological question there, about which I am no authority. But I would think that a negative motivator could be as "strong" or important as a positive motivator, so I would hesitate to focus solely on the $+1$ answers as measures of strength. It seems your data cannot tell you how "strong" any particular factor is for motivating any particular person; all you can tell is how frequently people identify a factor as having some motivating influence--whether weak or strong seems impossible to say. – whuber Jan 14 '15 at 16:50
  • Great point. I agree that I must also consider the negatives in the study too, which I will. I would like to pick your brains one more time if you don't mind. Suppose we take the psychological aspect out of the question and assume that I want to rank some arbitrary elements based on responses where each respondent has scored the elements as $+1$ (Yes), $-1$ (No) and $0$ (Indifferent), would you still sort them based on the proportion of people who answered $+1$? – Hussein Abbas Jan 16 '15 at 17:17
  • That question cannot be answered with the information given. There is no intrinsic way of sorting three-tuples. Any specific consistent way of ranking them amounts to a *valuation* that implicitly reflects trade-offs between how much *you care* about $1$ *vs* $0$ *vs* $-1$. (See [tag:valuation] for some threads about this.) I cannot tell you how much you *should* care; at most I can apply an [underlying mathematical theory](http://stats.stackexchange.com/questions/9358) (giving criteria for any possible valuation to be consistent and meaningful) to help you quantify your own valuation. – whuber Jan 16 '15 at 17:42

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