# “Random variable” vs. “random value” (when translating from Russian into English)

In the introductory part of a Russian document I was translating, there was a simplified description of a control chart-based quality management system.

The description contained this sentence in Russian:

Контрольные границы определяют предел ожидаемых изменений процесса, когда действуют наиболее типичные для этого процесса факторы. Наносятся контрольные границы, как правило, на расстоянии трех стандартных отклонений случайной величины от линии средних значений.

I translated the Russian sentence this way:

Variations observed within the chosen control limits are considered natural for the process, arising from typical factors that influence the process. Control limits are usually set at a distance of 3 standard deviations ("sigma") from the mean line of the random variable.

The reviewer changed it to:

Control limits are usually set at a range of 3 standard deviations from the mean line of the random value.

Which is better?

I believe it is random variable, because we are talking about Shewhart charts here, and as far as I understand, statisticians use this term, "random variable". The original Russian phrase is "random value", but I thought it was better not to follow the original too closely.

• Both terms are essentially synonymous, are they not? So if random variable better accords to statistical practice, then use that one. – Chill2Macht Apr 9 '17 at 13:12
• It might help to add more context (before & after the sentence in question), I don't know. From a purely statistical perspective, I would prefer "variable", & thus I agree w/ you. Note that there are several high-rep CV users who are fluent in English & Russian, so it might be interesting to see what they have to say. – gung - Reinstate Monica Apr 9 '17 at 13:53
• Native Russian speaker here. "Случайная величина" is a Russian term for "random variable". Proof: go here en.wikipedia.org/wiki/Random_variable and switch to Russian; you will get here: ru.wikipedia.org/wiki/Случайная_величина. So I don't think it's correct to say that "The original Russian phrase is "random value"". (But note that the original Russian text says "st.devs. of the random variable from the mean line", not "st.devs. from the mean line of the random variable".) – amoeba Apr 10 '17 at 7:51
• @amoeba - thank you! I thought that the mean line is calculated from the values of this "random variable", so I remodeled the sentence a bit. – CopperKettle Apr 10 '17 at 9:04

I side with your editor. You plot the obtained values on the plot, then draw a mean (average) line, then calculate three standard deviations above and below the line to show the boundaries. There's really no modeling involved here, hence, there's no random variable defined explicitly. You could argue that implicitly the variables are introduced, of course, but I'd go with your editor's choice to de-emphasize modeling at this stage.

Here's the original page with a chart.

If you read the whole text they consistently use terms значение (величина) that stand for value or quantity, in my opinion, to emphasize the phenomenological nature of the approach. There's very little of statistical content in the paper. All they do is to watch control boundary breaches to detect stochastic controllability as they define it. I'd definitely stick with value here.

UPDATE: The link I gave was just one example how this paragraph is copied in Russian from one text to another. Google will spit you out dozens of example such as this one from medical field. There must be the original text from which this is copied, I suspect it's Russian translation of Chambers Wheeler book Understanding Statistical Process control. So, the precise answer would be to locate the English original in this (or other?) book.

UPDATE 2: I don't the have the original English text from translation of which the Russian paragraph was copied, but here's a control chart description on NIST web site. Notice how they never use the term "variable". Consistent with my answer they use "measurement", "value" and "data point".

• This answer makes sense when using "random values" (not value) as suggested by Alekos Papadopoulos as second option. – Pere Apr 9 '17 at 18:59
• @CopperKettle Is this indeed the document that you are translating? If so, then may I ask what for? – amoeba Apr 9 '17 at 19:04
• @amoeba I think that this document "borrows" the verbatim Russian translation from the reference [5]. If someone has that book it would be easy to locate the original in English and we'd have a precise answer! – Aksakal Apr 9 '17 at 19:05
• @amoeba - my document is a report on the analysis of the stability of manufacture of a drug. It only has a very short "theoretical" introduction. – CopperKettle Apr 10 '17 at 4:03

The correct phrase in order to make statistical sense, is "random variable". And this is because it refers to the "mean line" - and random values do not have a mean, only random variables do.

If the Russian word is "value", and even if the Russian author meant "value", (s)he was simply mistaken.

Alternatively, one could consider writing "...mean line of the random values" - plural, since probably here the theoretical expected value is unknown, and so "the mean line" is the sample mean of the observed values.

• Thank you, Alecos! The thing is, the Russian phrase is literally "random value", and this may have confused the reviewer. The word "variable" (peremennaya) has a slightly different range of usage in Russian. – CopperKettle Apr 9 '17 at 14:40
• @CopperKettle ..which makes no sense. You could settle for "random values" perhaps. This is perhaps even more correct statistically, if the theoretical expected value is unknown, and so "the mean line" is the sample mean of the observed values. – Alecos Papadopoulos Apr 9 '17 at 14:43
• Ah, I see! Thank you! "Variable" is more correct when speaking of this scheme generally, and "values" is okay, because at the manufacturing site we only have access to the values we obtain by measurement. – CopperKettle Apr 9 '17 at 14:46
• @CopperKettle As I wrote above, "случайная величина" is simply the Russian for "random variable"; the literal (non-statistical) meaning of the word "величина" is not really important here. There is no other way in Russian to say "random variable". – amoeba Apr 9 '17 at 18:22
• I was taken aback by your assertion in the first paragraph: any set of $n\ge 1$ values has a mean: it is $1/n$ times their sum. Regardless of what the Russian original might say, it would be incorrect to characterize this line as being set at the mean of a random variable, simply because the variable's mean usually is unknown! – whuber Apr 9 '17 at 20:06