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Hypothesis testing for ratio estimation

  1. Jun 11, 2012 #1
    1. The problem statement, all variables and given/known data
    Hi, this is a stats question, hope I'm asking it in the right place.

    I am estimating an animal populations health based on it's weight to length ratio, I have a population ratio (10grams/cm) from 5 years ago and a sample estimate made from recently gathered data.

    I am wanting to be able to say if the changed weight to legth ratio is of any significance or just due to sampling error.

    2. Relevant equations



    3. The attempt at a solution
    Should I be doing hypothesis testing such as ANOVA... I thought that was just for comparing means? Or is there another type of variance comparison I can do?
    Is it enough if the confidence intervals of estimates overlap to say there is no significant variation between the two?

    Cheers,

    Finn
     
  2. jcsd
  3. Jun 11, 2012 #2

    Simon Bridge

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    Welcome to PF;
    What level is this to be done at?

    If the only figure you have to compare is itself a mean then you pretty much have to compare means. How much work you need to do really depends on who it is for.
     
  4. Jun 11, 2012 #3
    Hi,
    It is for a third year under grad stats paper.
    I have two scatter plots of data, one for the "5 years ago" data set and one for the "present" data set. each is plotting SVL vs Weight. I have fit a regression line for both data sets when the two plots are overlaid the regression lines are quite different.
    So its not so much means as the two regression lines that I want to determine significant difference in, isn't ratio estimation a form of regression analysis?... does that make sense?

    I tried to copy some of the formula I've been using for similar questions to give an Idea of what sort of estimators etc I'm using but they turned into weird code when I pasted them? is it possiple to insert wquations into the posts?

    Any further help would be great.

    Cheers,
     
  5. Jun 12, 2012 #4

    Simon Bridge

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    You can use TeX markup. eg - the normal distribution:
    [tex]f(x;\mu,\sigma) = \frac{1}{\sigma\sqrt{2\pi}}
    e^{ -\frac{1}{2} \left ( \frac{x-\mu}{\sigma} \right )^2}[/tex] (quote me to see how I did it). If you don't know TeX/LaTeX you should learn, especially if you are planning on grad school.

    Since this is third year stats your courses to date will have included methods for hypothesis testing using arbitrary distributions. Use those. I'd automatically think of the Chi-squared test but you will have seen others by now.

    Comparing the ratios pretty much amounts to comparing human BMI - you'll be able to test if the modern population is generally heavier or lighter for their length and it gives you only one dimension to deal with. I'm afraid you'll have to decide if it is the appropriate thing to do in the context of your coursework to date.

    Making these judgement calls is one of the skills you have to learn.

    How you do the comparison depends on what kind of thing you want to comment on - if you want to be able to say that the population is, overall, of better or worse health these days then you need to establish weight/length regions which constitute good or bad health like the height/weight charts you see in doctors offices. You want to be able to say that the new sample is significantly different from the old one then you need to take the shape of the distribution into account.

    As soon as you identify the hypothesis you are testing, the test to use should become clear.
     
  6. Jun 12, 2012 #5
    Thanks for the advice, I think I have it sorted now.
    Also Cheers for showing me TeX/LaTeX, I wasn't aware of it, looks really useful!
     
  7. Jun 12, 2012 #6

    Simon Bridge

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    No worries - I've been noticing that the higher up the education ladder someone is the less technical my responses become - probably because I can rely on the competence of the recipient :)

    LaTeX is the standard for academic typesetting and second to none when it comes to getting math rendered. The (not so) short introduction to LaTeX is the canonical reference and covers the whole thing. There are tips and tutorials all over the interwebs. Enjoy.
     
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