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    ASIF HANIF

    Analysis with Chi-Square

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    Pearsons Chi-Square: (2 X 2)

    Chi-Square test is employed to determine if there

    is an association between qualitative variables.

    When the word association is used in the

    statistical sense, a comparison is implied. For a 2X 2 table chi-square statistic is calculated as:

    2

    2 n ad bca b c d a c b d

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    Example

    The following represent mortality data for twogroups of patients receiving different

    treatments, A and B.

    Outcome

    Dead Alive

    Treatment A 41 216

    B 64 180

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    Example

    Classification Men Women Total

    Want T.V 80 120 200

    Dont Want T.V 170 130 300

    Total 250 250 500

    A random sample of 250 men and 250 womenwere pooled as to their desire concerning theownership of television sets. The following data

    results

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    Formation of Hypothesis

    Ho: The two variables of classification are

    independentH1: The two variables of classification arenot independent

    Level of Significance

    = 0.05Decision

    P-Value = .0000

    Hence P- Value is less than , so we reject Ho andwe may conclude that variables of classificationdepends upon each other.

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    Example

    The following data (as above) describe the state of grief of 66

    mothers who had suffered a neonatal death. The table relates this to

    the amount of support given to these women:

    SupportGood Adequate Poor

    Grief State

    I 17 9 8

    II6 5 1

    III 3 5 4

    IV 1 2 5

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    Fishers Exact Test:

    When expected count is less than 5 we use

    this techniques

    1 2 1 2! ! ! !

    '! ! ! ! !

    R R C CFisher s Exact Test

    n a b c d

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    Example

    The following data relate to suicidal feelings in

    samples of psychotic and neurotic patients:

    Psychotics Neurotics Total

    Suicidal feelings 2 6 8

    No suicidal feelings

    18

    14

    32

    Total 20 20 40

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    Example

    The following data compare malocclusion of teethwith method of feeding infants.

    Normal teeth Malocclusion

    Breast fed 4 16 =20

    Bottle fed 15

    21 = 2237 = 42

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    Pearsons Chi-Square: (RXC)

    For a R x C table the Chi-Square Statistics can

    be calculated as:

    And Yates Corrected Chi-Square for R X C

    contingency table can be calculated as:

    2

    2 ij ij

    i j ij

    O E

    E

    2

    20.5ij ij

    ij

    O E

    E

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    Co-efficient of Contingency

    Contingency coefficient. A measure of association based

    on chi-square. The value ranges between zero and 1,

    with zero indicating no association between the row and

    column variables and values close to 1 indicating a highdegree of association between the variables.

    2

    2C n

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    Phi & Cramers V

    The Phi coefficient is a degree of association

    between two attributes and is calculated as:

    2

    ad bcPhina b c d a c b d

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    Kendalls Tau b

    Kendall's tau-b: This test is used to measure strength ofcorrelation when we have ordinal data. The sign of thecoefficient indicates the direction of the relationship, and itsabsolute value indicates the strength, with larger absolutevalues indicating stronger relationships. Possible valuesrange from -1 to 1, but a value of -1 or +1 can only beobtained from square tables.

    Where S=P-Q P=Concordant pairs of observation Q=Discordant pairs of observation

    m=min(r,c)

    0 0b

    S

    P Q X P Q Y

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    Example An animal epidemiologist tested dairy cows for the presence of a

    bacterial disease. The disease is detected by the analysis of

    blood samples, and the disease severity for each animal was

    classified as None (1), Low (2) and High (2). Moreover, the size

    of the herd that each cow belongs to a category is classified as

    Large (3), Medium (2) and Small (1). The number of animals ineach of the 9 cells are recorded as:

    Size of theherd

    None (1) Low (2) High (3) Total

    Small (1)9 5 9 23

    Medium (2) 18 4 19 41

    Large (3) 11 88 136 235

    Total 38 97 164 299