Calculating Nσ for Table Area: Theory & Practice

[peripatein]

Supposing a table's width and length are measured a number of times using a ruler with a certain resolution. A manufacturer provides the theoretical values for both length and width. Thus we may calculate the practical and theoretical values of the table's area (S). How may Nσ for the area of the table S be calculated, given that Nσ = |X1 - X2|/SQRT(σ1^2 + σ2^2)? Will it be correct to say that Nσ equals |S practical - S theoretical|/SQRT[(σ of S practical)^2 + (σ of S theoretical)^2]?

 

[mfb]

I am a bit confused by your notation, but |S practical - S theoretical|/SQRT[(σ of S practical)^2 + (σ of S theoretical)^2] looks fine.

 

[peripatein]

What do you deem confusing in my notation? Wouldn't the latter determine the number of standard deviations between the two values? It is under the LSE section in my booklet and indeed resembles chi^2, does it not?

 

[mfb]

You did not define X1, X2, σ1 and σ1 (in addition, it is better to write indices like X₁ or X_1). And "Nσ" is N multiplied by σ? That is clearly not the result of such a formula.

 

[peripatein]

The booklet itself doesn't make that very clear. X_1 and x_2 are two values the difference of which, in terms of sigma, needs to be determined. Nsigma, presumably N_sigma, apparently denotes the number of sigmas that distance is equivalent to, which, the booklet states, ought to be less than three. Does that make more sense? Is my evaluation of N_sigma for the table's area then correct?

 

[mfb]

[...] looks fine.

3 is an arbitrary number, but it is frequently used to distinguish "not significant" and "probably significant"

 

[peripatein]

Thank you for your replies.