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Hypothesis testing for discrete data

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  • #53761

    Draper
    Participant

    What are the most oftened used hypothesis testing for discrete data?

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    #191349

    Strayer
    Participant
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    #191365

    MBBinWI
    Participant

    Don Draper wrote:

    What are the most oftened used hypothesis testing for discrete data?

    The one that answers the question that I’m interested in, duh!

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    #191366

    MBBinWI
    Participant

    Straydog wrote:

    Cat got your tongue, Dog? Sometimes I kill myself!!!!!!!!!!!!

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    #191370

    Draper
    Participant

    MbbWii,

    Can you do a two sample T test (testing the means) on discrete data?

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    #191372

    Robert Butler
    Participant

    How discrete is discrete? If it is binary no, if it is Likert or count sure, go ahead.

    If it is something other than binary and if you are really worried – run the t-test and then run the Wilcoxon-Mann-Whitney on the same data and see what you see. The t-test is robust with respect to non-normality but if the data gets too extreme the test can fail to detect a difference in mean location when one exists. The Wilcoxon works under all conditions that would be appropriate for a t-test but it does a better job (has higher power) in cases of extreme asymmetry.

    If it’s binary and you are looking at samples from two independent populations then you would want to run a test on two proportions.

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    #191381

    Draper
    Participant

    Yes the data are binary. Patient has sepsis, yes / or no.
    Death would be binary as well correct?

    Suggestions, my good friend?

    How can you show a statistical imrprovement in a baseline of septic patients , after implementing a new process.

    Robert Butler wrote:

    How discrete is discrete? If it is binary no, if it is Likert or count sure, go ahead.

    If it is something other than binary and if you are really worried – run the t-test and then run the Wilcoxon-Mann-Whitney on the same data and see what you see. The t-test is robust with respect to non-normality but if the data gets too extreme the test can fail to detect a difference in mean location when one exists. The Wilcoxon works under all conditions that would be appropriate for a t-test but it does a better job (has higher power) in cases of extreme asymmetry.

    If it’s binary and you are looking at samples from two independent populations then you would want to run a test on two proportions.

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    #191382

    Robert Butler
    Participant

    The answer is too long to try to summarize in a forum of this type, however, it is not terribly involved. The exact answer to you question can be found in the book

    Statistical Methods for Rates and Proportions 3rd Edition – Fleiss, Levin, Paik – Chapter 9 The Comparison of Proportions from Several Independent Samples – subsection 9.3 Gradient in proportions: samples qualitatively ordered – which is the situation you have – controls, least likely, sepsis new method – more likely, sepsis old method – most likely.
    Based on your post the proportions would be: number of deaths/total number in population.

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    #191383

    Draper
    Participant

    Robert,

    Can this be completed in Minitab 16?

    Have you run such a hypothesis test?

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    #191386

    Robert Butler
    Participant

    I don’t know Minitab so I can’t comment on its capabilities, however, my guess would be that it can do this – at least the first part anyway.

    The first part of this kind of analysis is running a chi-square test on an mx2 contingency table. If that statistic is significant then the second part consists of the calculations needed to identify the proportions contributing to the significant difference.

    Just to see if Minitab can run the first part try this sample problem (from Fleiss pp.189)

    Group Smoker Count
    1 0 3
    1 1 83
    2 0 3
    2 1 90
    3 0 7
    3 1 129
    4 0 12
    4 1 70

    The table check would be group x smoker and the questions is the significance of the ratio of smokers to non-smokers.

    If Minitab can handle mx2 contingency tables you should get a chi-square value of 12.6 and the p-value should be .0056.

    The next piece would be identifying the samples or groups of samples contributing to the significance and you would need to talk to the folks at Minitab to find out if it is possible and if so how to proceed.

    As for running this kind of analysis – yes – many times. I do my work in SAS.

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    #191395

    Andrew Banks
    Participant

    Robert:

    Minitab is fine with mx2 tables, either in the format you provided or in two-way format. Just have to select “cross-tab & Chi square” for the table you provided. My results match your identically (Chi square 12.6 & p=0.006).

    “The next piece would be identifying the samples or groups of samples contributing to the significance and you would need to talk to the folks at Minitab to find out if it is possible and if so how to proceed.”

    I had Minitab calculate the contribution to chis square for each cell, and just by looking indicates that group 4 non-smoker contributes 9.05 to the statistic. The next highest are on the order of 1. This indicates that the proportion of non-smokers with cancer in group 4 is unexpectedly high, correct (12 versus an expected count of 5.16).

    Is there a next step?

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    #191396

    Andrew Banks
    Participant

    As long as the data has only two proportions (i.e. before & after an intervention) you can use the 2-proportions test in Minitab, which uses either raw data OR summarized data.

    The 2-Proportions test uses Fisher’s Exact Test which can be more accurate than the Chi Square test when counts are small (like counts of undesirable infections).

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    #191422

    khatri
    Participant

    Hi,

    If you have a discrete data, best test you can go for is Chi square test (for both Y&X are discrete). when u go to minitab, there are three test under it…
    1. Cross tabulation; used when both Y&X are in alphabet/character
    2. 1 Way variable : used when Y in number and X in character/alphabet
    3. 2 way : used when both Y & X are in number.

    Secondly, if ur Y is discrete and X is continuous, then u can go for Binary logistics regression (BLR). Please note, for this Y should be binary in nature.

    Hope this help.

    Regards
    Anil

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