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Thread: Algebra, two-sample t-statistic, variance

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    Algebra, two-sample t-statistic, variance




    Could someone help to start with the question. Question:

    http://s12.postimage.org/kvtyiacuj/question.png

    Thanks!

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    Re: Algebra, two-sample t-statistic, variance

    That clearly isn't the full question. There isn't enough information as it currently stands.

    This looks like a homework question though. Our homework help policy can be found here. We mainly just want to see what you have tried so far and that you have put some effort into the problem. I would also suggest checking out this thread for some guidelines on smart posting behavior that can help you get answers that are better much more quickly.
    I don't have emotions and sometimes that makes me very sad.

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    Re: Algebra, two-sample t-statistic, variance

    It's a full question and it is from homework. I am not asking for a solution. I am only asking for guidance. Thanks for your suggestions and recommendations for checking out 'posting behaviour'

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    Re: Algebra, two-sample t-statistic, variance

    I'm sorry but there has to be more background than that. I don't know what the "never and ever-had steroid groups" are. Also all we're asking is that you show us what you've attempted so far.
    I don't have emotions and sometimes that makes me very sad.

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    Re: Algebra, two-sample t-statistic, variance

    The question above is part of the question and the information provided for this part is in full.
    The question asks for a proof of t=b/s(b) is equal to two-sample t-statistic with pooled standard deviation
    b is least square regression with numerator and denominator parts: http://www.efunda.com/math/leastsqua...y1ddevsum4.gif

    The question posted above is the denominator of b and I need to show that the denominator of b is equal to n0n1/(n0+n1) where n0 and n1 are sample size.
    As I said the information for the part is in full. I don't require solution to the question. I seek for guidance and hints.

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    Re: Algebra, two-sample t-statistic, variance

    Quote Originally Posted by Dason View Post
    I'm sorry but there has to be more background than that. I don't know what the "never and ever-had steroid groups" are. Also all we're asking is that you show us what you've attempted so far.
    This information is irrelevant. Each steroid group is a sample. There are two samples in question as stated above and in the original heading of the question

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    Re: Algebra, two-sample t-statistic, variance

    Samples of what? Are we talking about a continuous quantity with a normal distribution? Is each X_i a binomial experiment? I still think we're missing some information.
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    Re: Algebra, two-sample t-statistic, variance

    Quote Originally Posted by Dason View Post
    Samples of what? Are we talking about a continuous quantity with a normal distribution? Is each X_i a binomial experiment? I still think we're missing some information.
    Two sample of people. The information is irrelevant. You can assume normal distribution by CLT, however.

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    Re: Algebra, two-sample t-statistic, variance

    Let's say X_1 = 1, X_2 = 2, X_3 = 3 and X_1, X_2 are in the never-steroid group and X_3 is the ever-steroid group. Then n_0 = 2 and n_1 = 1.

    Now \sum_{i=1}^3 (X_i - \bar{X})^2 = 2 but \frac{n_on_1}{n} = \frac{2}{3}

    So I'm thinking there has to be more to it than given because what is given doesn't work in general.
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    Re: Algebra, two-sample t-statistic, variance

    Hot ****. Was that so hard? Now I know that X is actually just a dummy coded indicator variable so that if a person is in the never-steroid group X_i = 0 and if they're in the ever-steroid group X_i = 1. It could be flipped around but that is very important information.

    So now we know that \bar{X} = \frac{n_1}{n} and we can break the sum apart into two pieces - one piece where all the X_i are 0 and one piece where they're all 1. Have you tried this yet?
    I don't have emotions and sometimes that makes me very sad.

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    Re: Algebra, two-sample t-statistic, variance

    Quote Originally Posted by Dason View Post
    Hot ****. Was that so hard? Now I know that X is actually just a dummy coded indicator variable so that if a person is in the never-steroid group X_i = 0 and if they're in the ever-steroid group X_i = 1. It could be flipped around but that is very important information.

    So now we know that \bar{X} = \frac{n_1}{n} and we can break the sum apart into two pieces - one piece where all the X_i are 0 and one piece where they're all 1. Have you tried this yet?
    I haven't tried this but it makes sense. Why is it \bar{X} = \frac{n_1}{n} and not \bar{X} = \frac{n_0}{n} ? and how can we break the sum in two parts?

    I guess I need to find a good paper on dummy variable in regression model to understand the concept.

    Thanks for your suggestion!

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    Re: Algebra, two-sample t-statistic, variance

    Quote Originally Posted by _joey View Post
    I haven't tried this but it makes sense. Why is it \bar{X} = \frac{n_1}{n} and not \bar{X} = \frac{n_0}{n} ?
    That's a good question - why don't you start by computing \bar{X} for this situation (instead of just taking my word for it). Working on that simpler problem will probably help build up your intuition about working with these dummy coded variables.
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    Re: Algebra, two-sample t-statistic, variance

    Quote Originally Posted by Dason View Post
    That's a good question - why don't you start by computing \bar{X} for this situation (instead of just taking my word for it). Working on that simpler problem will probably help build up your intuition about working with these dummy coded variables.
    I don't know how to apply the concept of dummy variable in solving the problem or computing \bar{X} in ' a situation' . I need to read on this first.

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    Re: Algebra, two-sample t-statistic, variance

    Okay, it's easy. The key part, the hint was n1/n for ever steroid to be X_i=1

    I appreciate your help!

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    Re: Algebra, two-sample t-statistic, variance


    What have you tried so far? You'll probably want to use the result from part (i).
    I don't have emotions and sometimes that makes me very sad.

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