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Thread: a series of T tests more appropriate than ANOVA here?

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    a series of T tests more appropriate than ANOVA here?




    Hi all,
    I'm writing up some experimental results, which I believe I know how to analyze, but wanted to get some frank and impartial feedback before I defend myself.

    I'm testing an insect to see if it is restricted to only one host plant. In the first experiment, I have two controls, one in which I place insects on their "native" host, and one control where insects are given no food at all. I also have a series of test host plants I place insets on. I count days survival as my response variable.

    So my 1st null hypothesis is that insect survival on the native host should be significantly higher than on ANY test host. The second null hypothesis is that survival on tests hosts should NOT be significantly higher than the starvation control.

    I am aware that some of my results fit between these two hypothesis, ie, they don't live as long on a test host as the native host, but it's better than starving to death, I can discuss that.

    For this experiment, I feel I should do a one sided t test for each test host against the native to test null 1, and separately, a one sided t test for each test host against the starvation control to test null 2.

    I was told by someone that I should do ANOVA, but I feel like they were reflexively saying that because they saw a bunch of different means. I don't think ANOVA is right though, because (as I understand it) it's going to compare all means to see if any differ from each other, but I don't really care if test host 3 is better or worse than test host 8, I'm only interested in how each test host compares to native and nothing.

    In my second experiment, I counted the numbers of eggs females laid on the native vs the test hosts. In this case there is no negative control as these insects require a leaf for egg laying. Again, ANOVA suggested, but I feel that a series of t tests against the native is more appropriate for the same reasons. The only difference being I'd use a 2 sided t test here, as the test hosts could have larger or smaller means than the native.

    Does this sound reasonable to you? Or am I missing something? Thanks for your feedback!

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    Re: a series of T tests more appropriate than ANOVA here?

    You can do post hoc tests with an ANOVA to get at those t-tests you're interested in. The only thing is that in the typical ANOVA setting you're assuming an equal variance. If this really is the case you gain a lot by doing the ANOVA over a whole bunch of t-tests because you get a much better estimate of the shared variance.

    But to tell you the truth it sounds like if you're dealing with number of eggs are being laid some sort of poisson regression might be better.

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    Re: a series of T tests more appropriate than ANOVA here?

    .... plus there's always that good ol' friend of ours, experimentwise error rate, which forces you to adjust your alpha-level of significance so that you might end up losing power and not detect any differences at all when they really are there...

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    Re: a series of T tests more appropriate than ANOVA here?

    Thanks for your advice,
    Yes, I've been checking the variance, it's not equal, Levene's Test p< 0.05. I too think a Poisson regression is the best way to go from what I've been reading, but I have a much weaker grasp about how to pull out a comparison between two factors with a test like that. Study continues...
    Cheers.

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    Re: a series of T tests more appropriate than ANOVA here?

    I doubt that survival times are normaly distributed. Maybe a survival anaylsis (like cox regression) would be more appropriate for this kind of experiment.
    Cheers,
    giordano

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    Re: a series of T tests more appropriate than ANOVA here?

    Hi

    If the sample meets requirements of ANOVA, afak you should do it first and then perform a dunett t-test (a post hoc test) to compare each group with the control.

    Don't use Student t-test here, because it would give you inflated significance (false positive error).

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    Re: a series of T tests more appropriate than ANOVA here?

    Thanks for the interest. With respect to the #s of eggs, I think the Dunnett t-test victorxstc mentions might be exactly right for what I was talking about at the start of the thread... trying to find documentation on how to do it in R.

    On the other hand, I think using a Poisson distribution for the egg count might be more appropriate, females produce between 0-15 eggs in all cases. If I create a Poisson glm though with host as the factor and eggs as the response variable, pretty much every host comes back as highly significant. If I understand this right, it's just telling me that host type is significantly influencing egg production. But I'm after the idea that some hosts are the SAME as the control. (null is that ALL are different) So my idea is to just keep dropping the host with the lowest mean egg production until the model returns no significant difference between factors. Then, all those hosts reaming essentially support the same egg production as the control. Is this the right idea?


    In case anyone comes across this thread with the same issue as me, a Dunnett t test is exactly the thing I was thinking I wanted to do when I started this thread, I just didn't know it! and here is a very clear explanation on how to perform this test in R-
    http://yatani.jp/HCIstats/PostHoc
    Thanks to everyone for the help!
    Last edited by BWGIA; 07-19-2011 at 08:09 PM. Reason: update

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    Re: a series of T tests more appropriate than ANOVA here?

    Cheers. Please note that the Dunett t test needs ANOVA F statistics to calculate the right P, so the ANOVA is still necessary.

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    Re: a series of T tests more appropriate than ANOVA here?

    Hi, after significant interaction in 2x2 Anova, when I am conducting paired t-test (2 time intervals/ 2 types of trial) I could possibly have 6 t-tests, but if I am only interested in: shorter times different type trials, and longer times different trial type, that would be only 2 t-tests and alpha would be adjusted to .025 am I thinking right?

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    Re: a series of T tests more appropriate than ANOVA here?

    You are on the right track for he Bonferroni correction. Though, I have seen different rules for how you should decide what to divide alpha by, including the number of all possible comparisons regardless if you perform them.

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    Re: a series of T tests more appropriate than ANOVA here?


    Quote Originally Posted by hlsmith View Post
    You are on the right track for he Bonferroni correction. Though, I have seen different rules for how you should decide what to divide alpha by, including the number of all possible comparisons regardless if you perform them.
    Thank you for reply, more I read abt Anova I get more confused, specially as I was not able to fing anything on exploring interaction in 2x2 within subject . in my experiment I have 2 conditions (RN, NRN) and two time intervals (8s and 32s) I want to examine participants accuracy and response time (2 separate 2x2 Anovas) but:
    1. for accuracy data (it was quite high anyway) is not normally distributed but Anova is apparently roboust so after conducting it I found some significant results-what do you think? what abt Friedman ?
    2. for response time I have significant effect for condition but not for time interval, but there IS an interaction- should I do paired t -tests for all possible 'pairs' and adjust alpha?
    3. just for my other experiment in one way within Anova 3 conditions (response times) to explore their 'connections' after significant Wilcoxon I just choose parawise comparisons in SPSS to do it for me
    if you could help me with that it would be much appreciated.

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