iSixSigma

Normality

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  • #53012

    ellzey
    Member

    HelloI´m having some statistical problems and would love to get some help. I have 8 groups of fish with different sample sizes from 8 different areas (243, 241, 302, 304, 369, 701, 360, 364 = N=2884) and I want to know if the fish length is equal between groups.If the data is normally distributed, should I use the one way Anova?Do I test the normality for each group or for all groups as a whole (N)? From Systat I get:
    N of Cases 2884
    Shapiro Wilk Statistic 0,991
    Shapiro Wilk p-value 4,663E-012
    Anderson Darling Statistics 3,884
    Adjusted Anderson Darling Statistics 3,885
    p-value < 0,01What is the next step for me? Please help I´m completely lost.Greetings, Susan

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    #187396

    Remi
    Participant

    Susan,
    So you have 2884 lengths of fishes divided over 8 groups.
    First make a picture: boxplot and decide if you want to perform analyssi on all the data or if some of the points should be analysed different.
    Then do 1-Way ANOVA.
    The data itself does not have to be normal distributed (and often is not if there is a large mean-difference); but the Residues should be (this is ‘the check for Normality’).
    You also have to check for equal variances. If the variances are not comparable the p-value outcome of the 1-way ANOVA should not be used. I generally recommend to postpone the mean-issue until you have resolved the sigma-issue (but some others of this forum do not agree with me).
    Remi

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    #187397

    StuW
    Member

    Here are some ideas:
    * Plot all the data, and look at the histogram.  Check the shape.
    * Plot all the data using a group color, or symbol, and check the overall group shapes with the various groups identified.
    * Run a boxplot for each group to look at the mean, quartile points, and any outliers for each group.
    * Run the 1-Way ANOVA, and check for differences.  With these large sample sizes you will be able to detect very small differences in means.
    * Run a multiple comparison test (Tukey, LSD, etc.) and look to segregate the areas into “like” groups.  Match the areas and look for patterns.
    As Remi suggests, look at the deviations after fitting each mean for Normality.   Also, how are these fish collected?  If all are collected in one shot by netting, then these are not independent observations and all bets may be off with this analysis. 

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    #187400

    Darth
    Participant

    I believe that if you check the underlying assumptions for ANOVA you might find that the individual groups need to be normally distributed as well as have equal variances. While robust to normality you are incorrect in stating that she can ignore the normality issue of the 8 groups.

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    #187402

    Tierradentro
    Participant

    Susan,
    What questions are you trying to answer or what problem are you trying to address with your analysis?
     

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    #187403

    MBBinWI
    Participant

    Susan:  The answer to your question : “I want to know if the fish length is equal between groups”, is no. 
    Now, if you’d like a statistical analysis on whether they are, let’s say, within 0.1″ of one another with a 95% confidence, then that’s another matter.
    Besides the other guidance you’ve received here, you will also want to evaluate whether you have sufficient sample sizes.  This is going to depend on just how much (or little in this case) difference you will want to be able to detect, and how much variation there is within the samples.  You’ll also need to identify your beta risk level (or test power).

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    #187460

    Remi
    Participant

    hai Darth,
    in my answer I mentioned that the residuals should be normal distributed. Y= f(x) + error; the ANOVA analysis can be usedIFF ((error is normal distributed) AND (equal variances test is passed)).
    I realize that “error is Normal” is not exactly the same as “each of the groups is normal” but don’t remember enough of my statistics to say which is more correct. Most of the times there is no difference, but once I encountered data where the residuals together were Normal distributed but the two groups were not. We found out that this was caused by how the line was split up in two parallel lines (the 2 groups)due to the weights of the products. We corrected for this and solved the problem.Remi

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    #187463

    Utter Chaos
    Member

    Darth,
    I’m glad that you replied, otherwise I may have thought that my SSBB mentor lied to me. Probably too much tequila.

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    #187464

    Darth
    Participant

    Mr. Chaos,
    Apparently you also have been misinformed about tequila…there is never too much tequila.Remi,
    You are correct in that the normality assumption of ANOVA does not refer to the combined data but to the individual groups.

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    #187467

    GB
    Participant

    Darth,
    Tequila is the Devil. I still have flashbacks of Army gatherings gone awry at the mere site of the wicked liquid.

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    #187469

    DarthDisturbererer
    Participant

    I am actually surprised to discover Darth and “normality” in the same chat. 
    PS. “Between” when talking about two groups. “Among” when taling about three or more groups.

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    #187471

    Darth
    Participant

    HeeBee,
    I doubt very much whether what you called tequila was in any way related to what I drink. My tequila is the nectar of the Gods, not the Devil. Mine is sipped in a brandy glass. Your’s was probably slammed with an involuntary full body shudder. Perhaps in SoBe we shall have an opportunity to partake of some fine liquor of the Agave.

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    #187472

    Mikel
    Member

    I vote for grappa

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    #187473

    MBBinWI
    Participant

    I’m sorry, Stan – the left over dregs of good wine making do not compare to gently malted barley, distilled into fine Scotch Whisky, preferably speyside – Glenfiddich distiller to be precise, and just reaching the age of majority.  Ahh, bliss for the pallet and nostrum.

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    #187478

    GB
    Participant

    MBB,You and your Grappa has a legacy stretching back aeons. I think some Romana Sambuca, or Ouzo would be a nice contemplative drink in light of the recent cold weather…

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    #187480

    Darth
    Participant

    Ahhh, but Ouzo with or without water?

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    #187481

    GB
    Participant

    During the day, Water, or even ice.
    At night, specifically close to bed time – straight upSome call it, “Greek Nyquil”

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    #187482

    Darth
    Participant

    Still trying to figure out how it turns milky when the water is added. My tequila doesn’t do it, nor does Scotch or even Grappa. It truly is a magic elixir.

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    #187483

    Leader
    Participant

    Tequila is definitely dangerous — especially low-grade tequila.  It might lend someone to not understanding normality of the initial data set vs the residuals after the analysis….

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    #187484

    Dard, Son of Zeus
    Participant

    It’s an emulsion. The oil which makes the delicate flavours of ouzo dissolves very nicely in alcohol, but it doesn’t dissolve very well in water. When you add water, it binds to the alcohol, which dissolves well in water. The oil eventually stops binding to the alcohol and starts hanging around with other oil molecules. These little aggregations of oil in the water make the drink turn milky white. If you were to zoom in with a very powerful microscope, you would see these tiny globules of oil being completely surrounded by water molecules. This is exactly how emulsion paint works, where you have globules of oily paint molecules surrounded by water. This is why it is the drink of the Gods and reminds us all of the milk of our beloved Mother Hera.

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    #187485

    Darth
    Participant

    As previously mentioned, Darth does not partake of low grade tequila. However, he has been known to keep the company of low grade women as does his hero Tiger Woods.As we also know, you can not prove normality….you may merely fail to reject the null hypothesis that your data is different than normal. We also know that control charts are robust to normality as well as are the assumptions of the two sample t test and ANOVA. But alas, you would know these things if you were a certified MBB and shared the worldly knowledge of Mayahuel, the Aztec Goddess of Agave.Perhaps, this knowledge will be imparted to you in the New Year.

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    #187486

    MBBinWI
    Participant

    Ouzo = Greek Licorice, not a real man’s drink.

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    #187487

    MBBinWI
    Participant

    I learned to drink it directly from a Greek army officer – and with water is the only acceptable method.  Still tastes like licorice to me.

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    #187488

    Darth
    Participant

    Let’s not take this thread down the Greek trail and inferences regarding HeeBee…..Webby will be yanking our posts in a second.

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    #187489

    MBBinWI
    Participant

    Ahh, here we are having a gentlemanly discussion about booze, and there you go spoiling things by injecting something relevant to the purpose of the forum.  Spoil sport.

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    #187490

    MBBinWI
    Participant

    So, Darth, are YOU inferring that HeeBee has more in common with the Greeks than just a fondness for Ouzo?  That wasn’t MY inference (and, no, I certainly want nothing to do with any trials to try to disprove any null hypothesis).

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    #187491

    MBBinWI
    Participant

    Let’s see if webby let’s that one slide through (wink, wink – Love ya Katie!)

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    #187492

    Mikel
    Member

    If anyone knows, it would be Darth.

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    #187493

    Darth
    Participant

    Stan, see ya in SoBe…oh, look, there is a dollar on the floor.

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    #187513

    GB
    Participant

    Webby, why on earth would you remove, “GLENN#[email protected]&*(” from my last post? I literall posted that, no cursing, or untoward comments were made.That’s just odd.

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    #187514

    GB
    Participant

    Nice…Nice…
    My answer is identical to the one i posted for “tool Share”.
    heh

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