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Aug 17, 2014 14:04
9 yrs ago
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Spanish term

igualar la probabilidad de equilibrio de error con la de acierto de error

Spanish to English Medical Mathematics & Statistics Sample size
Hi,

I am unsure as to what this means. I think it's to do with type I and type II error in determining simple size but I am not enough of an expert to really understand what it means. Are there any experts out there?

The heading is "Cálculo de tamaño muestral" for a clinical research study. The text under the heading reads:

Para determinar el tamaño de la muestra que representa la población en estudio, es necesario emplear la ecuación h = n / (P2 (n - 1) +1), la cual resulta de igualar la probabilidad de equilibrio de error con la probabilidad de acierto de error.

h = tamaño muestral
n= número de sujetos que constituye la población de estudio
P= probabilidad de error de la muestra
Proposed translations (English)
4 by balancing the margin of error and the confidence level
2 equating the probability of balance of error with the probability of certainty of error
Change log

Aug 17, 2014 15:27: Alison Imms changed "Field (specific)" from "Medical (general)" to "Mathematics & Statistics" , "Field (write-in)" from "Sampling / probability" to "Sample size "

Discussion

Muriel Vasconcellos Aug 18, 2014:
corresponds to? For the reasons mentioned here, perhaps you could say 'corresponds to' rather than 'equates'. I'm changing my answer; also changing 'with'' to 'to' in either case (that was an initial mistake).
DLyons Aug 18, 2014:
@Alison He's correct that "igualar" refers to the equal sign in the previous equation. But I'm pretty sure that the client is not a Statistician and is using the word in a "lay" sense here. He may be talking generally or misremembering where the equation comes from (he's using a very simplified version of the general equation). There's certainly an argument for translating literally what he says and I'd definitely check back with him whether he wants to tighten up the phraseology in English over the Spanish source.

I'm not aware of any version of this standard equation which actually equates two probabilities in its derivation (although some might certainly exist, there often are alternative ways of deriving results). If you read your reference carefully you'll notice that they are talking about SETTING both Type I and Type II error to be 0.05. "If one desired to set the probability of a Type II error equivalent to the 0.05 level used for the Type I error ...". They only use "equating" in the Abstract and this usage is similar to what's happening in your source.

http://www.saylor.org/site/wp-content/uploads/2011/06/MA121-... is a typical discussion.
Alison Imms (asker) Aug 18, 2014:
Type I and Type II Hi, thanks for all your help. I really do appreciate it. My concern is that although the equation given doesn't equate probabilities, the text actually states that this equation is derived from another in which it seems like two probabilities have been equated. I have spoken with my Spanish husband, who is an engineer and a mathematics tutor, and he says "igualar" definitely can only refer to the equal sign in the previous equation, which he says has been "despejada" in order to get the current one. Unfortunately he isn't sure what "equilibrio de error" and "acierto de error" refer to. Again, I am still wondering if this may have to do with Type I and Type II error, and have found a few references to "equating the probability of Type I and Type II errors at 0.05" in order to get a sample size, for example in the abstract of this document: https://journals.uair.arizona.edu/index.php/jrm/article/view... Any further thoughts?
DLyons Aug 18, 2014:
I'm not guessing. See the references. The underlying calculation does not equate probabilities.
Muriel Vasconcellos Aug 18, 2014:
I wouldn't try to guess at this I think it means what it says. If you look up 'balance of error' and 'certainty of error', they are both statistical terms.
Alison Imms (asker) Aug 17, 2014:
Thanks, I think it does belong in that category so I've changed it over. The rest of the document is very general, which is why I accepted it! It's just this part giving me trouble. So just to clarify, you believe "probabilidad de equilibrio de error" is the margin of error and "probabilidad de acierto de error" is the confidence level? What would "balancing" entail, exactly? I was thinking that "igualar" in the context of an equation was definitely "equate".
DLyons Aug 17, 2014:
It's really a Maths&Stats question.

Proposed translations

1 hr

by balancing the margin of error and the confidence level

Declined
It'll probably be accompanied by some version of the formula in the link. Quite possibly a simplified one, since this has the feel of being aimed at a fairly general audience.

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Note added at 1 hr (2014-08-17 15:24:02 GMT)
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Just noticed the formula! Yes, that's a very special case of the general formula given in the link.

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Note added at 1 hr (2014-08-17 15:30:38 GMT)
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Assumes equal proportions in the population, 95% confidence interval. Rounds off a bit.

Fine if the assumptions actually hold!

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Note added at 1 hr (2014-08-17 15:55:55 GMT)
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Perhaps a better way of putting it is "by trading-off the required level of confidence and the precision (as measured by the width of the confidence interval)" See e.g. discussion (especially fourth paragraph from the end) in https://www.utdallas.edu/~ammann/stat3355/node28.html

There's a trade-off between level of confidence and precision, increase one and you decrease the other (for a fixed sample size).

The formula derives from an error bound calculation, I think "igualar" is being used in a general way here rather than the more usual "equate".
Reference:

http://books.google.ie/books?id=WSQLAAAAQBAJ&pg=PA416

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19 hrs

equating the probability of balance of error with the probability of certainty of error

Declined
I think it should be translated literally. 'Balance of error' is a statistical term. See the following article:

https://blogs.oracle.com/darcy/entry/balance_of_error

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Note added at 1 day6 hrs (2014-08-18 20:18:32 GMT)
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Given all the doubts, it might be better to use looser language such as 'corresponds to' / 'is considered to be the same as'

Thus:

la cual resulta de igualar la probabilidad de equilibrio de error con la probabilidad de acierto de error

translates as:

'where the probability of balance of error corresponds to/is considered the same as the probability of certainty of error'
Peer comment(s):
neutral DLyons : Both terms are very occasionally used in Statistics and I've never seen them together. This would mean nothing to a reader. And "probability of certainty" is definitely not a possible term.
8 mins
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