2 x n Chi Square Contingency analysis, less than 5 and SPSS

Discussion in 'Scientific Statistics Math' started by Stefanie, Feb 18, 2005.

  1. Stefanie

    Stefanie Guest

    Hello everyone,

    I'm an ecology student having trouble deciphering whether or not
    Fisher's Exact Test is valid for 2x4 or 3x4 contingency tables. I'm
    also confused about whether or not SPSS 10 actually calculates either
    Fisher's Exact Test with a 2x4 table or the Chi Square with a Yate's
    Correction when it detects small values. To add to the confusion, I
    discovered that there is an exact tests add-on module that one has to
    purchase from SPSS to calculate exact tests (but the help menu in SPSS
    10 seems to imply that the regular old version calculates exact tests
    anyway..but the results are reported as Pearson's Chi Square ~ are
    they just pulling my leg or what?).

    My data is very simple. It is counts of species or individuals (in
    one case grouped into 3 functional categories) of butterflies at
    distances from a forest fragment in 2 different systems: shade and sun
    coffee.

    Any insight or advice would be greatly! appreciated.

    Thanks,

    Stefanie

    P.S.:
    It turns out someone else had a very similar question:

    I'm a pharmacy student having trouble with my statistics:) I hope
    some is
    able to help!
    I'm doing a study on compliance. I have a population of 45. (some
    questions
    were left blank by the respondents, so for some variables the
    population is
    less than 40!) Every case has been termed: "compliant" or
    "non-compliant". I
    now need to test the compliance parameter against numerous other
    parameters - like sex, age (grouped into four intervals), adverse
    effects,
    etc. I'm thinking that I can use the chi2-test. I remember it from my
    statistics class. My problem is that the approximation for chi2 isn't
    valid
    for any of my tests because I have an expected number of less than 5
    in all
    my tables. My question is now: What do I do?
    I know that when the approximation for the chi2-test isn't valid I can
    use
    Fisher's exact test for 2x2 tables but what about 2x3 or 2x4 tables?
    Is
    there an alternative test - like the exact test? I've looked around -
    in
    books and on the Internet, but I just can't find anything.
    (I have access to "Statistica", but can't find any help there either).

    Any help will be appreciated a lot.

    Thanks,
    Kata

    PS: If I have 9 compliant people and 36 non-compliant people, do I
    need to
    test if there is any difference between the two groups (9 against 36)?
    I
    don't think so, but a friend of mine says I do.
     
    Stefanie, Feb 18, 2005
    #1
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  2. Stefanie

    Bruce Weaver Guest

    "Fisher's Exact test" usually refers to the test for 2x2 tables. There
    are extensions of the test for larger tables. These are available in
    StatExact (from www.cytel.com), for example. The SPSS "exact tests"
    module is based on the StatExact procedures, AFAIK, so I expect you get
    the same tests there--but you will not get them (apart from Fisher's
    exact for 2x2 tables) if you do not have the exact tests module.

    My SPSS license was changed recently, and now includes the exact tests
    module. I've not used it yet, but did try this little demo just now.

    * ----- Start of Demo -------------- .
    data list list / r c count (3f5.0).
    begin data.
    1 1 5
    1 2 2
    2 1 6
    2 2 2
    3 1 2
    3 2 4
    end data.

    weight by count.

    CROSSTABS
    /TABLES=r BY c
    /FORMAT= AVALUE TABLES
    /STATISTIC=CHISQ
    /CELLS= COUNT
    /COUNT ROUND CELL
    /METHOD=EXACT TIMER(5).


    Crosstabs

    r * c Crosstabulation
    Count
    |----|-|----|-----|
    | | |c |Total|
    | | |--|-| |
    | | |1 |2| |
    |----|-|--|-|-----|
    |r |1|5 |2|7 |
    | |-|--|-|-----|
    | |2|6 |2|8 |
    | |-|--|-|-----|
    | |3|2 |4|6 |
    |----|-|--|-|-----|
    |Total |13|8|21 |
    |------|--|-|-----|

    Chi-Square Tests
    |---------------|--------|--|---------------|---------------|
    | |Value |df|Asymp. Sig. |Exact Sig. |
    | | | |(2-sided) |(2-sided) |
    |---------------|--------|--|---------------|---------------|
    |Pearson |2.928(a)|2 |.231 |.285 |
    |Chi-Square | | | | |
    |---------------|--------|--|---------------|---------------|
    |Likelihood |2.899 |2 |.235 |.285 |
    |Ratio | | | | |
    |---------------|--------|--|---------------|---------------|
    |Fisher's Exact |2.718 | | |.285 |
    |Test | | | | |
    |---------------|--------|--|---------------|---------------|
    |Linear-by-Linea|1.768(b)|1 |.184 |.265 |
    |r Association | | | | |
    |---------------|--------|--|---------------|---------------|
    |N of Valid |21 | | | |
    |Cases | | | | |
    |---------------|--------|--|---------------|---------------|
    a 6 cells (100.0%) have expected count less than 5. The minimum expected
    count is 2.29.
    b The standardized statistic is 1.329.

    * ----- End of Demo -------------- .

    There were two more columns of output in the last table (exact 1-sided
    p-value and point probability), but I deleted them, because they loused
    up the display due to wrap-around.

    In anycase, the exact 2-sided p-value of .285 (in the first 3 rows) is
    presumably for an extension of Fisher's exact test for 3x2 tables. You
    could check the SPSS aglorithms webpage to get details. Go to
    http://support.spss.com. Log in as guest with password guest. Select
    Statistics then Algorithms from the left hand list.
     
    Bruce Weaver, Feb 18, 2005
    #2
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