Talk:Factor analysis

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Contradictory statements about variable indexes?

'"Subject" indices will be indicated using letters a,b and c, with values running from 1 to {\displaystyle N_{a}} N_{a} which is equal to 10 in the above example. ... "Instance" or "sample" indices will be indicated using letters i,j and k, with values running from 1 to {\displaystyle N_{i}} N_{i}. In the example above, if a sample of {\displaystyle N_{i}=1000} N_{i}=1000 students responded to the {\displaystyle N_{a}=10} N_{a}=10 questions, the ith student's score for the ath question are given by {\displaystyle x_{ai}} x_{ai}.'

These statements appear to me (a novice) to be contradictory; we say student indices are a, b, c then proceed to say that there are N_i = 1000 students, not N_a students. Using i, j, and k for students also seems to happen in the paragraphs following this one. Someone who knows what they are doing should confirm this and clean it up. — Preceding unsigned comment added by DanAtPearson (talk • contribs) 17:34, 30 January 2017 (UTC)

Your confusion is probably due to identifying two words which are different: the quote says "subject", not "student". The article text seems perfectly fine in this respect. 130.243.68.90 (talk) 13:10, 8 March 2017 (UTC)

Standard deviation formula

In the section "Mathematical model of the same example", the formula given for the standard deviation is

$\sigma _{a}^{2}={\tfrac {1}{N_{i}}}\sum _{i}(x_{ai}-\mu _{a})^{2}$

In particular, we're dividing by the number of samples $N_{i}$. However to get an unbiased estimate of the standard deviation of the distribution, one should rather divide by one less $N_{i}-1$ (since the average $\mu _{a}$ used in the calculation was computed from the same set of samples). The difference would of course be rather small (e.g. 1000 versus 999) in the typical case with this method, so it probably makes little practical difference, but what is theoretically correct? Further down it is claimed that the $z$ vector has unit length, which would not follow if dividing by $N_{i}-1$ instead. Is it standard practice with Factor Analysis to use the stated normalization to improve the linear algebra, even if that means employing a slightly biased estimate of the standard deviation? It is probably no big deal, but could warrant a remark. 130.243.68.90 (talk) 13:30, 8 March 2017 (UTC)

Possible typo??

I wonder if there is a missing comma in this sentence:

Factor analysis is not used to any significant degree in physics, biology and chemistry but is used very heavily in psychometrics personality theories, marketing, product management, operations research and finance.

amd maybe it should read:

Factor analysis is not used to any significant degree in physics, biology and chemistry but is used very heavily in psychometrics, personality theories, marketing, product management, operations research and finance.