Stats I Final Pitt 5

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Stats I Final Pitt 5
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2012-12-05 13:46:24
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Nonparametric Statistics
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Stats I Final Pitt part 5
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  1. Nonparametric Statistics

    nonparametric
    statistics performed on nominal/ordinal dependent variables

    do not require normality
  2. Chi-square tests

    nonparametric
     one of the most popular nonparametric tests

    examines differences in proportions involving either one or two variables
  3. One-way  chi-square

    nonparametric
    involves only one varaible with 2 or more levels
  4. Two-way chi-square

    nonparametric
    utilizes two variables with 2 or more levels
  5. Chi-square assumptions

    nonparametrc
    1. independence of subjects

    2. Not more than 20% of the expected frequencies is less than 5
  6. Proportion

    nonparametric
    one of the simplest statistics that can be computed

    number of responses (subjects) in a category divided by a total number of responses (subjects)

    • where ni is the number of responses in the ith category; N is the total number of responses

    typically, the population is written as pi,
  7. Properties of X2 Distribution

    nonparametric
    • positively skewed distribution with ranges from 0 to positive infinity
    • -never negative

    • critical region of the distribution only appears in teh right side
    • -not a directional test

    As df increases, the critical value of the distribution decreases

    As df incerases, the distribution is less skewed

    The mean of X2 distribution is equal to df

    The variance of the X2 distribution is equal to the 2 x df
  8. Chi-square Distribution

    nonparametric
    X2 tests have their own distribution

    family of distributions denoted by a degrees of freedom
  9. One-way X2

    nonparametric
    • can be computed using either proportions or frequencies
    • -more common to use frequencies of categories

    Example: Is there a difference in proportion of people who support and oppose abortion?
  10. Two-way X2

    nonparametric
    often seen as a test of independence (association)

    both variables can be DVs or one variable can be a DV while the other is an IV
  11. Cross Tabulation

    nonparametric
    • Both variables are categorical variables with 2 or more levels
    • Variable 1 has c levels and variable 2 has r levels

    r = row; c = column

    Oij will have a double subscript to indicate position in table

    • dot in 1st subscript = row total
    • dot in 2nd subscript = column total
  12. Phi

    nonparametric
    • used to measure effect size in a two way X2
    • -can only be used in a 2 x 2

    range from 0 to 1

    • similar interpretation as r
  13. Cramer's V

    nonparametric
    • used to measure effect size in a two way X2
    • - larger than a 2 x 2 design

    range from 0 to 1

    similar interpretation as r
  14. Assumptions

    nonparametric
    even though the assumption is on the expected frequencies, there is a higher chance of violating the assumption when the number of participants is small
  15. Fisher's Exact Test

    nonparametric
    for a two-way X2 test with dichotomous variables (i.e. 2 X 2) where the assumption is most often violated
  16. Yates' Correction for Continuity

    nonparametric
    when the test statistic becomes inaccurate

    2 x 2
  17. Cohen's w

    nonparametric
    w = phi

    w = (Cramer's V)(square root of q)
  18. Within-subject Design

    nonparametric
    (categorical)

    Test of marginal homogeneity can be performed to examine a change in categorical variable from time 1 to 2 (within-subjects [repeated measures] design).
  19. McNemar's Test

    nonparametric
    test of homogeneity for a dichotomous variable

    corrects for continuity

    df = 1

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