For a function f(x,y): The error is:(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \Delta f(x,y) = \sqrt{(\frac{df}{dx})^2+(\frac{df}{dy})^2} [/tex]

Is this a form of the approximation in algebraic error determination:

[tex] \Delta f(x,y) = \sqrt{f(x+\Delta x,y) + f(x,y+\Delta y)} [/tex]?

Now I was trying to do this in my bio lab for genetics and probability distribution. We had 27 samples, predicted 75% (20.25) to be purple and 25% (6.75) to be white. We observed that 23 were purple and 4 were white, so to calculate the deviation I used the above function and got:

[tex] \frac{df}{dx} = \frac{23-20.25}{20.25}, \frac{df}{dy} = \frac{4-6.75}{6.75} [/tex]

*For some reason latex doesnt want to show it, but I plugged in my numbers into the first equation above.

So the observed sample was 18.44% off?

They gave us an equation to find the deviation of a population from the expected value which is similar to the one above:

[tex] \chi^2 = {\frac{(Obs_p - Exp_p)}{Exp_p}^2+\frac{(Obs_w - Exp_w)}{Exp_w}^2} [/tex]

[tex] \chi^2 = {\frac{(2.75)}{20.25}^2+\frac{(2.75)}{6.75}^2} = 1.494[/tex]

It claims that "If the value for chi squared is less than or equal to 3.841, then your sample is within the expected range."

Is this a standard deviation?

This is pretty similar to the first equation, except we're squaring the numerator instead of the whole fraction. Did I get my error equation wrong, or are these truly diferent and unlinked?

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# Error analysis

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