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There is a sentence in Sokal and Rohlf's classic text [R.R.Sokal F.J.Rohlf; Biometry, 3rd ed., 1994: p.132, chapter 7 Estimation and Hypothesis Testing]:

The variance of means is therefore partly a function of the sample size on which the means are based.

In this specific case, I understand that the greater the sample size the lesser the standard deviation of sample means. But in general what does it mean to be a function of something? Relationship or dependence?

(Please provide answers/comments in plain language.)

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2 Answers

In layman terms as requested, a function takes input values and gives output values. It is like a blender. Put in apples and we get apple juice. Put in orange and we get orange juice. In your context, it means that the variance depends on sample size, just like what juice you get depends on what fruits you throw in!

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"$A$ is partly a function of $B$" means that if you change $B$, even if you don't change anything else, the chances are that $A$ will also change.

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Unless the function is constant, of course :-) –  Siminore Dec 9 '12 at 11:42
    
@Sim, if $A$ is constant, Sokal et al would not write $A$ is partly a function of $B$ --- and you know it --- so why confuse OP? –  Gerry Myerson Dec 9 '12 at 11:49
    
@Siminore That is what the phrase "chances are" is there for. –  Arthur Dec 9 '12 at 11:49
    
@GerryMyerson You should know that constant functions are functions. By the the way, a function is something that must be defined without any reference to "chances", "good luck" or equivalent words. –  Siminore Dec 10 '12 at 9:24
    
@Siminore, you should know that a teacher answers a question using language the student can be expected to understand. –  Gerry Myerson Dec 10 '12 at 11:47
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