SOCY 211 Test #3 Review
Chapter 11:
• Statistical significance ensures tests aren’t a result of mere chance
• Test of Significance: detect non random relationship
• Measures of Association: provide information about the strength and direction of
relationships, trace causal relationships among variables, cannot prove two
variables are causally related ▯association is not proof that a causal relation exists
11.2
• Variables can be said to be associated if the distribution of one of them changes
under the various categories or scores of the other
• Independent Variable = X = Column
• Dependent Variable = Y = Row
• Assesing table from column to column we can observe the effects of the
independent variable on the dependent variable – Within Column Frequencies =
Conditional distributions of Y; they display the distribution of scores on the
dependent variable for each condition of the independent variable
• Chi Square (typically used for test of significance), any nonzero variable
obtained for chi square indicates association – If Chi square is zero, the variables
are independent and not associated
• Possible for two variables to be associated (by a non zero Chi Square) but still be
independent (fail to reject null hypothesis)
11.3 Three Characteristics of Bivariate Association
1) Does an association exist?
2) If an association exists, how strong is it?
3) What is the pattern or the direction of association?
1)
• Look at Y column changes or chi square
• Compute percentages within the columns – down each column and then compare
horizontally “Percentage down, compare across”
2)
• An issue of determining the amount of change in the conditional distributions of
Y
• Perfect relationship is strong evidence there is a causal relationship between
variables
• Measures of association provide precise, objective indicators of strength
• 0.0 no association 1.00 perfect relationship
• Maximum difference: compute column percentage, skim across each row to find
the largest difference between column percentages
• Magnitude of chi square bears no strength on association 3)
• Max Diff between 0 – 10% strength of relationship is weak
• Max difference between 1130% moderate
• Max difference more than 30% strong
• Ordinal can be described in terms of direction as well
• Positive association: high scores of one variable is associated with high scores of
another variable ▯one variable increases in value, the other increases
• Negative Association: high scores of one variable associated with low scores of
another variable, one variable decreases the other increases
• Measures of association take on positive values for position associations and
negative values for negative associations
11.5
• Calculate column percentages, to asses strength use PHI – measure of association
for 2 x 2 tables
• Phi – closer to 1, the stronger the relationship
• Cramers V; Tables larger than 2x2
• Find the lesser of the number of rows minus 1 or the number of columns minus 1
• Interpreting: value of statistic and the strength of the relationship for phi and
cramers v
• Same strength difference as max difference
11.6
• PRE: developed to complement the older chi square measures of association,
however provides a more meaningful interpretation
• Makes two different predications about the score of cases – first, ignore
information about the independent variable, therefore make many errors in
predicting the score of the dependent variable. Second, take account of the score
of the case of the independent variable to help predict the score on the dependent
variable
• If there is an association between the variables, we will make fewer errors when
the independent variable is taken into account
• Perfect association – make no errors when predicting Y from the form of X
• Using information about the independent variable will reduce the number of
errors
Lambda
• A PRE measure
• First, number of prediction errors made while ignoring the independent
variable (gender) must be found. Then, we will find the number of prediction
errors made while taking gender into account – sum of these two will then be
compared to derive the statistic
• First independent variable is ignored (gender) work only with row marginal –
E1 = the total number of cases minus the largest row total • E2 = the sum of the following: for each column, the column total minus the
largest cell frequency
• Lambda ranges from 0.0 to 1.0
• An index of the extent to which the independent variable (X) helps us to
predict or understand the dependent variable (y)
• Limitations of Lambda
▯Lambda is asymmetric the value of the statistic will vary depending on
which variable is taken as dependent
▯When one of the row totals is much larger than others, it can be misleading,
it can be 0.0 even when other measures show association, chi is then preferred
Chapter 12: Association Between Variables at the Ordinal Level
• Collapsed ordinal variable – has a few, no more than 5 values or scores and can be
created by either collecting data in collapsed form of by collapsing it on a
continuous scale
• Continuous Ordinal level variables = Spearmans rho
12.2
• Gamma, Kendal A and C, and Somers D ▯measure strength and direction of
association by comparing each respondent to every other respondent, called a pair
of respondents, in terms of their ranking on independent or dependent variables
• Total number of unique pairs can be found when n(n1)/2
• Pairs can be divided into subgroups.
• A pair is “similar” when the larger value on the independent variable also has a
large value on the dependent variable
• A pair is “dissimilar” when if the respondent with the large value on the
independent variable is small
More
Less
