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Thread: Would you help me? (Tranformations)

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    Thumbs up Would you help me? (Tranformations)




    Hi,


    I was looking for tranformations for ratio data. I find that arcsine tranformation is adecuate for that kind of data (ratio). For that reason i tranform my data with arcsine tranformation and the result was not satisfactory...

    In that moment i think i would make another kind of tranformation and it would result adecuate. But i also think:

    Ratio data allows not arcsine transformations?

    Or there is a matematical rule that prevent´s us to make this kind of transformation. it ocurred to me beacuse i have read various statistic books including Sokal & Rolph and Zar and they afirm that ratio data should be tranformed with arcsine transformation but not mention about transform ratio data with other transforamtions.

    Also i dont know how to realize arcsine transformations with SPSS.

    Thanks (if you read my text, if not FWcl you)

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    Re: Would you help me? (Tranformations)

    What are you trying to achieve by transforming this data?

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    Re: Would you help me? (Tranformations)

    Not your answer necessarily but perhaps you could do log transformation as this is common for ratio data. I personally don't know about the arcsine transformation.
    "If you torture the data long enough it will eventually confess."
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    Re: Would you help me? (Tranformations)

    I am trying to achieve similar distributions for a Kruskal Wallis test. But i also would like achieve normality and homocedascity.

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    Re: Would you help me? (Tranformations)

    If you're using the krustal wallis it's non parametric and doesn't assume normality. How do you know you've violated the linear model assumptions of normality and homocedascity ?
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    Re: Would you help me? (Tranformations)

    If you say that log transformation is common for ratio data, it could mean that another transformations are admissible for ratio data, provided that objectives of the transformation were meet.

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    Re: Would you help me? (Tranformations)

    Possible (even probable) but if you look at what CowboyBear asked and the second question I asked the answer to your question may be that you don't even need the transformation.
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    Re: Would you help me? (Tranformations)

    It is true, Kruskal Wallis is non parametric but it doesn´t means that it doesn´t have assumptions. Kruskal Wallis test assumption is that sample distributions are similar. This assumption would be meet even when the sample distributions are heteroscedastic and non normally distribuited.

    I test similar distribution assumption through Absolute diference ANOVA.

    Look:
    http://www.youtube.com/watch?v=Md8rqQ-oUH0

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    Re: Would you help me? (Tranformations)

    Why is an ANOVA out?
    "If you torture the data long enough it will eventually confess."
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    Re: Would you help me? (Tranformations)

    I don´t know the matematic reason, but Anova allows evaluation for similar distribution, through evaluation of absolute diference between the Rank and the mean rank of the variable of interest.

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    Re: Would you help me? (Tranformations)

    It's interesting that different sources vary as to whether or not the Kruskal-Wallis test requires the assumption of identical distributions (other than a possible shift in location). I've always found this a bit confusing. I think that whether we need to make this assumption depends on how we are actually interpreting the test. If we (perhaps foolishly) want to interpret the K-W as testing a null hypothesis that the population medians (or even means) are identical, then maybe we do need to assume identical distributions. But this isn't really what the test was designed to do. The following quote is from Fagerland & Sandvik, 2009:

    This usage of the WMW test [testing for differences in means or medians] is not in accordance with the original intentions, which is to test the null hypothesis that P(X<Y) = 0.5, where X and Y are random samples from the two populations at interest.
    More on this issue here (link). So I guess this all comes down to what you're trying to investigate here. Are you mainly interested in differences in means, differences in medians, or just whether a randomly chosen observation of X will tend to be a higher than a randomly chosen observation of Y?

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    Re: Would you help me? (Tranformations)

    Quote Originally Posted by CowboyBear View Post
    It's interesting that different sources vary as to whether or not the Kruskal-Wallis test requires the assumption of identical distributions (other than a possible shift in location). I've always found this a bit confusing. I think that whether we need to make this assumption depends on how we are actually interpreting the test. If we (perhaps foolishly) want to interpret the K-W as testing a null hypothesis that the population medians (or even means) are identical, then maybe we do need to assume identical distributions. But this isn't really what the test was designed to do. The following quote is from Fagerland & Sandvik, 2009:



    More on this issue here (link). So I guess this all comes down to what you're trying to investigate here. Are you mainly interested in differences in means, differences in medians, or just whether a randomly chosen observation of X will tend to be a higher than a randomly chosen observation of Y?
    Thanks

    That you say have sense since when the distributions compared are unequal there is a high possibility that distributions are significantly distinct. But if i understood that you send me, one of the propierties of ranking data and therefore Mann Witney test is that it is corretly used only when distributions are identical and have equal n.

    That i am comparing is fly abundance in different localities.

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    Re: Would you help me? (Tranformations)

    That isn't quite my reading of the article. What the article is saying that if you're using the Mann-Whitney test (and by extension the Kruskal-Wallis test) to compare means or medians, then the test is not robust to differences in distributions (among other things). OTH if you're using the test according to its original intention (testing a null hypothesis that the probability that a randomly chosen X is greater than a randomly chosen Y is equal to 0.5) then these things presumably aren't such a problem, although this usage wasn't the focus of the article.

    If it's really differences in means or medians that you're interested in, I wonder if you'd be better served by some kind of permutation test. Others here know more than I do about resampling tests like these. But doing transformations, then a non-parametric test, means that your results will surely be rather complex to interpret and make sense of.

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    Re: Would you help me? (Tranformations)

    I hesitate to write something here since it is labelled ”statistical research” and this is not statistical research.


    Sometimes I have seen that the arcsine transformation is used for data where there is a binomial distributed variable and it is approximately Poisson and the transformation is used to stabilize the residual variance.

    “That i am comparing is fly abundance in different localities.”
    Could it be that you have a random variable that is a count? And that you want to compare the mean of that count for different places (“localities”)?

    If it is so then you can use a generalized linear model with a Poisson distribution. “Poisson regression”.

    Sometimes some people say that the residuals in a regression model must be normally distributed. That is not true. The dependent variable can, given the explanatory variables, be Poisson distributed or negative binomial distributed. These distributions might be of interest for you. [Provided that I have not misunderstood.]

    “Thanks (if you read my text, if not FWcl you)”
    What does FWcl mean?

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    Re: Would you help me? (Tranformations)


    Quote Originally Posted by GretaGarbo View Post
    Sometimes I have seen that the arcsine transformation is used for data where there is a binomial distributed variable and it is approximately Poisson and the transformation is used to stabilize the residual variance.
    Yes arcsin is used to stabilize the variance for binomial distributed data converted to proportions. It can be shown that this transformation gives an asymptotic constant variance. It's not often mentioned but even after the arcsin transformation the variance is a function of the number of observations that went into the proportion so if you're looking at a bunch of proportions that came from variables with different sample sizes then the arcsin transformation might not be the best either.

    Then again I don't really like the arcsin transformation because as you mention there are better ways to deal with the data and I don't really think it's easy to interpret the results afterward.
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