Talk:Standard score

Standard Normal Deviate

I deleted this sentence, the subject of which is 'standard scores': "They are most frequently used to compare an observation to a theoretical deviate, such as a standard normal deviate."

1. Wasn't appropriate for intro. Roll into body?

2. Deviate (statistics) redirects to Random Variate, so, consider using that term?

3. 'Standard normal deviate' page was written ten years ago by someone who admits they don't know much about statistics and asked for help (which, sadly, never came). Shortly thereafter, it was nominated for deletion. But yet, it stays. It is not a very good page. OmneBonum (talk) 23:47, 3 March 2020 (UTC)

Other scores

• Just one quick addition/question. Standard score in statistics is not related only to (z) scores. "It should include (z), (t), deviation (IQS), stanine, sten scores, (others...)"(Drummond, 2004). —Preceding unsigned comment added by 65.182.95.67 (talk • contribs)

• Where can we add the value range standardization following

$y={\frac {x-minimum}{maximum-minimum}}$ - herr_blaschke 14:22, 3 Jan 2008 (UTC)

Modified content

I added stuff about standardization and standardized because a while back I created an article called "Standardized" that I'm now trying to get rid of (merging, then REDIRECTing -- note that the only page history Standardized had was the initial page creation by me on March 9, 2004 — I figured that wasn't important to keep).

I removed the following sentence because it was rendered mostly redundant by my discussion of comparing 2 students' exam scores.

A standard score is a way of placing a raw score in context. It is often used to compare test results within and between groups, and especially with reference to a norm group. - dcljr 21:11, 9 Aug 2004 (UTC)

I also removed the "external link" section and moved it to main text, and changed "\overline" back to "\bar". Not only do I prefer the look of "/bar", but it makes a little more sense, since the symbol is usually read, "x-bar". - dcljr 21:22, 9 Aug 2004 (UTC)

Question about normalising

How is normalising data different from standardising data? The Normalization (statistical) pages doesn't give much (enough) information about this. 129.97.80.128 21:51, 7 April 2006 (UTC)

Symbols question

Hi. Could somebody explain to me why sometimes symbols (like the Greek letters named mu and sigma) appear in pages while other times there are what seem like LaTeX codes (like \mu and \sigma)? I wonder why the codes appear, instead of their compiled output or the appropriate symbols. Thank you. Xinelo 11:11, 29 September 2006 (UTC)

Suggestion: Separate entry for [Normal Score]?

There should be a separate entry for [Normal Score]...maybe even a disambiguation page for [Normal Score], to separate [Standard Score]s or [Z-Score]s (same thing) from the [Normal Score]s of van der Waerden or Blom (altogether different from standard- or Z-scores...see http://www.statsdirect.com/help/data_preparation/normal_scores.htm or http://www.dnr.state.ak.us/ssd/whtest/sashtml/stat/chap47/sect17.htm for definitions.) -- —Preceding unsigned comment added by 68.33.196.22 (talk • contribs)

External Link Added

I added a link to a z-score table. z-score tables, though archaic, are definitely a part of the curriculum and should be mentioned somewhere. 68.19.125.93

That link is a commercial link and does not belong in Wikipedia. Please find a non-commercial link with the same or similar content. -- Chris53516 20:53, 25 October 2006 (UTC)

Granted, but, as the site itself admits, this is not proprietary material. (edit: I fail to see how this is not a fair use, considering, but I will admit that wiki has far more stringent policies on fair use than is normal, and that I may be entirely incorrect due to a faulty interpretation of wiki policy) Anyway, its not worth my time to comb google for a better one, so I'll leave it in the talk page and someone else can find something better. http://www.statsoft.com/textbook/sttable.html#index 68.19.125.93

Oh, it's fair to use, it's just that the website is a commercial entity, and linking to it may be seen as advertisement. See Wikipedia:External links for more info. -- Chris53516 21:37, 25 October 2006 (UTC)

Population versus Sample

"A key point is that calculating z requires the population mean and the population standard deviation, not the sample mean or sample deviation. It requires knowing the population parameters, not the statistics of a sample drawn from the population of interest."

My professor (Ph.D Electrical Eng.) says this is wrong, ether type can be use... Anyone care to offer up a third opinion or clarification?

---

The official definition of z involves the difference between a particular score and the population mean. So in order to calculate z you must know the population mean. Knowing the population mean is very easy with standardized testing because the population is all of the tests administered. For most natural phenomena, knowing the population parameters such as the population mean is practically impossible which is why sampling is done to try to estimate the population parameters by calculating sample statistics. If the sampling is done properly and the population has one of statistically correct types of distributions then the sample statistics can be used to approximate the population parameters. z score calculation requires that the population distribution be a normal curve.

So basically your professor is sort of right and sort of wrong. He is right if the population of interest is normally distributed and the sample statistics are good approximations of the population parameters. In many cases people will make that the distribution is normal and that the sample statistics do approximate the population parameters well enough. The nice thing about have the entire population such as the results of a standardized test is that the researcher can calculate the population parameters and can also check that the distribution is actually normal.

see http://mathforum.org/library/drmath/view/68384.html

Richardelainechambers 02:47, 22 April 2007 (UTC)

Totally incomprehensible jargon to this layperson

... and I say that as a Ph.D. who received good grades in her two graduate statistics courses. Is there anyone here who can decipher and "normalize" (sorry! :) the dense math-speak in this article to be a little more accessible? There's only so far it can be simplified, of course, being a mathematical concept, but surely it doesn't have to be this hard. As a guide, I clicked on this wikilink from an article that mentioned that the movie criticism site Metacritic is different from Rotten Tomatoes in that it uses normalized scores, so that may give you a clue as to how non-mathematical a person's motives might be in exploring this article. Lawikitejana (talk) 05:17, 8 February 2009 (UTC)

z-scores are not just for normal distributions

I think this article should mention that z-scores are applicable to ANY distribution where the population mean and standard deviations are known. All a z-score is, by definition, is the number of standard deviations away from the mean. It does not only apply to the normal distribution! This article intertwines z-scores and normal distributions which only leads to more confusion about z-scores. Z-scores make sense in uniform distributions, triangular distributions, and anything else you can think of. —Preceding unsigned comment added by ChevyC (talk • contribs) 16:35, 11 July 2009 (UTC)

Capitalisation

I came to this article to check to see whether "Z-score" should have a capital "Z", or a lower case "z". Both are used in the article, away from full-stops/periods. Is there a correct notation? Does the capitalisation refer to population, rather than sample properties?

Cheers! Buzwad (talk) 10:33, 6 May 2010 (UTC)

Table change

Hi, can someone please change the first row of the little table with Z scores to be 0.68ish and 1? I stopped in because I'm reverse engineering Excel's NORMINV() function (this version of Excel doesn't have function help) and I'm too busy to figure out how to update a wiki page (I never have before). The other three Z scores look right (the 95%, 99%, etc), but it looks like someone typed 0.68 and 0.67 or something accidentally, rather than 1 (68%ish is 1 std dev from the mean).

 Done Qwfp (talk) 19:22, 21 March 2011 (UTC)

Usefulness of the standard score?

Hi there, I read this article with interest. However, what seems to be missing to my (non-mathematical) mind is a section on the actual use and usefulness of the standard score. My very limited understanding is that this score is useful because it tells you how meaningful your results are: the more they deviate from (expected) normal distribution, the more likely it is that your data has something special to tell you. Now I am sure this is somewhat reductive or just part of the story, but more on this would be important, I think. -- Cheers, --PhilipWinter (talk) 11:16, 19 June 2011 (UTC)

There is an obvious lack of reference to the use of standard score with a standard normal table. There is no better use than I can think of. Stephen Charles Thompson (talk) 15:01, 7 May 2012 (UTC)

Here is a suggestion, an example from research within the medical field - is this suitable here? Please note: self-citation: In a study on dogs, plasma vasopressin concentration increased at removal of both ovaries, with a 15 minute pause between ovary removal. Blood pressure and vasopressin concentrations changed in parallel at use of z‐scores (standard scores) for comparison.

The suggested image has been remade from the publication: http://commons.wikimedia.org/wiki/File:Blood_pressure_and_Vasopressin_at_removal_of_ovaries,_Z-scores.jpg Odd Höglund (SLU) (talk) 20:24, 2 February 2019 (UTC)

References

Help in correcting the diagram

Diagram showing the cumulative distribution function for the normal distribution with mean (µ) of 0 and variance (σ²) of 1. The prediction interval for any standard score corresponds numerically to (1-(1-Φ_µ,σ²(standard score))*2). For example, a standard score numerically being x = 1.96 gives Φ_µ,σ²(1.96)=0.9750 corresponding to a prediction interval of (1-(1-0.9750)*2) = 0.9500 = 95%.

As a perceptive user noticed [1], I had mixed up variance and standard deviation in the diagram at Standard_score#Percentile_ranks_and_prediction_intervals. The text may be fixed now, but it seems that a correction in the diagram itself is necessary as well. I know how to easily change the letters in the image in Inkscape, but before I do so, can we conclude exactly how it needs to be changed? Is it enough to remove that little 2 above the σ at the top? Mikael Häggström (talk) 11:51, 14 November 2011 (UTC)

I've made an entry at Wikipedia talk:WikiProject Statistics for this issue now. Mikael Häggström (talk) 05:38, 30 November 2011 (UTC)

and when it's multivariate?

how dow you standardize when it's multivariate? 134.106.106.34 (talk) 16:36, 19 March 2013 (UTC)

Broken Link

External link to z-score calculator is broken. 173.246.13.195 (talk) 12:30, 9 August 2014 (UTC)

Incorrect formula for 'Z'

The formula given for 'Z' here is:

Z = [ (x-μ)/σ ]

Where:

• x is the raw score (the sample mean being tested)
• μ is the mean of the population
• σ is the standard deviation of the population
• s is the standard deviation of the sample

But, isn't that incorrect?

The actual formula is the following:

Z = [ (x-μ) / [σ/SqareRoot(N, the sample-size) ]

Since s = [σ/SqareRoot(N, the sample-size)]

then the correct formula might be rewritten:

Z = [ (x-μ)/s ] if they don't like the definition of 's'

Sources to prove my point:

https://www.cliffsnotes.com/study-guides/statistics/univariate-inferential-tests/one-sample-z-test

https://onlinecourses.science.psu.edu/stat414/node/269

As well as Duke University! http://sites.nicholas.duke.edu/statsreview/means/

and even: https://stats.stackexchange.com/questions/265615/z-test-for-a-population-proportion

and also this Canadian site: http://www.psych.utoronto.ca/courses/c1/chap7/chap7b.html

In all fairness, this website http://www.free-six-sigma.com/z-value.html has BOTH formulas, but does NOT explain why both are used.

Please either correct the error, or clarify why the formula in the Wikipedia article is correct.96.59.135.184 (talk) 06:49, 2 June 2017 (UTC)

Thehampshirehog (talk) 22:40, 25 September 2017 (UTC) I'm new to contributing to discussion pages so hope this helps and I am following correct etiquette ... You are referring to calculating a standard score from the *sample* mean and standard deviation, for example a couple dozen ball bearings taken randomly from a production line. The article here relates to calculating a standard score from the *population* mean and standard deviation. This formula is simpler but you need to measure all of the ball bearings which could be a bit tedious! This isn't always as impractical it may seem. For example if you were standardising the results of this year's UK's Chemistry GCSE exams you will already have ‘measured’ the population.

Sal from Khan Academy produced a short video explaining exactly why the *sample* standard deviation is different which is well worth checking out as he does an infinitely better job than I can. If you want to work through some examples, Excel provides functions for both, STDDEV.S() and STDDEV.P(). Thehampshirehog (talk) 22:40, 25 September 2017 (UTC)

You're combining both a z-score and a z-statistic.

${\frac {x-\mu }{\sigma }}$ is the formula for a z-score

${\frac {x-\mu }{\frac {\sigma }{\sqrt {n}}}}$ is the formula for a z-statistic, utilized for the Z-test

Jmbarbone (talk) 14:14, 8 July 2021 (UTC)

References

Copyright problem removed

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History?

Okay I'm gonna be upfront and say flat-out that I'm asking this because I can't find any information on this anywhere else: wouldn't a section on the history of z-scores and standardisation for this be prudent? I'm sure this technique is pretty old but I think it'd be an interesting addition to the page, at least. APenInSpace (talk) 10:17, 28 August 2023 (UTC)

Modified/Robust score

This article doesn't make any mention of the "modified" or "robust" 𝑧-score, which by my understanding makes fewer assumptions about the distribution from which the data is drawn. It would be good if a knowledgeable person is able to add information about this to the article. Vectro (talk) 19:39, 22 November 2024 (UTC)