Chapter 10 Flashcards
Chi-square requires no
assumptions about the shape of the
population distribution from which a sample is drawn. It can be applied to nominal or
ordinal data (including grouped interval-level data).
Chi-square test
An inferential statistical technique designed to test for significant relationships between two
nominal or ordinal variables organized in a bivariate table.
Statistical independence
The absence of association between two cross-tabulated variables. The percentage
distributions of the dependent variable within each category of the independent variable are identical.
The chi-square test requires no assumptions about the shape of the population distribution
from which the sample was drawn. However, like all inferential techniques, it assumes
random sampling. It can be applied to variables measured at a nominal and/or an ordinal
level of measurement.
Like all other tests of statistical significance, the chi-square is a test of the null hypothesis.
The null hypothesis (H0
) states
that no association exists between two cross-tabulated variables in the population, and therefore, the variables are statistically independent.
Expected frequencies (fe )
The cell frequencies that would be expected in a bivariate table if the two
variables were statistically independent.
Observed frequencies (fo) T
The cell frequencies actually observed in a bivariate table.
Chi-square (obtained) T
The test statistic that summarizes the differences between the observed (fo) and the
expected (fe
) frequencies in a bivariate table.
Statistical significance only helps us evaluate w what and what does it not tell abt
Statistical significance only helps us evaluate whether the
argument (the null hypothesis) that the observed relationship occurred by chance is reasonable. It does not
tell us anything about the relationship’s theoretical importance or even if it is worth further investigation.
Another limitation of the chi-square test is that it is sensitive to small expected frequencies in one or more of
the cells in the table. Generally
when the expected frequency in one or more of the cells is below 5, the chisquare statistic may be unstable and lead to erroneous conclusions. There is no hard-and-fast rule regarding
the size of the expected frequencies. Most researchers limit the use of chi-square to tables that either have no
fe values below 5 or have no more than 20% of the fe values below 5.
measure of association
A single summarizing number that reflects the strength of a relationship, indicates
the usefulness of predicting the dependent variable from the independent variable, and often shows the
direction of the relationship.
proportional reduction of error (PRE)
Proportional reduction of error (PRE) A measure that tells us how much we can improve predicting the
value of a dependent variable based on information about an independent variable.
lambda
An asymmetrical measure of association, lambda is suitable for use with nominal variables and may
range from 0.0 to 1.0. It provides us with an indication of the strength of an association between the
independent and dependent variables.
asymmetrical measure of association
n A measure whose value may vary depending on which variable is
considered the independent variable and which the dependent variable.
cramers v
V A chi square related measure of association for nominal variables. Cramer’s V is based on the
value of chi-square and ranges between 0 and 1.
gamma
A symmetrical measure of association suitable for use with ordinal variables or with dichotomous
nominal variables. It can vary from 0.0 to ±1.0 and provides us with an indication of the strength and
direction of the association between the variables. Gamma is also referred to as Goodman and Kruskal’s
gamma.
kendalls tau b
A symmetrical measure of association suitable for use with ordinal variables. It can vary
from 0.0 to ±1.0. It provides an indication of the strength and direction of the association between the
variables. Kendall’s tau-b will always be lower than gamma
symm measure of association
A measure whose value will be the same when either variable is
considered the independent variable or the dependent variable
The chi-square test is
an inferential statistical technique designed to test for a significant relationship
between nominal and ordinal variables organized in a bivariate table. This is conducted by testing
the null hypothesis that no association exists between two cross-tabulated variables in the
population, and therefore, the variables are statistically independent
The obtained chi-square (χ
2
) statistic summarizes
the differences between the observed frequencies
(fo) and the expected frequencies (fe
)—the frequencies we would have expected to see if the null hypothesis were true and the variables were not associated. The Yates’s correction for continuity is
applied to all 2 × 2 tables.
The sampling distribution of chi-square tells
the probability of getting values of chi-square,
assuming no relationship exists in the population. The shape of a particular chi-square sampling
distribution depends on the number of degrees of freedom.
Measures of association are
single summarizing numbers that reflect the strength of the relationship
between variables, indicate the usefulness of predicting the dependent from the independent
variable, and often show the direction of the relationship.
Proportional reduction of error (PRE) underlies the definition and interpretation of several measures
of association. PRE measures are derived by
comparing the errors made in predicting the dependent
variable while ignoring the independent variable with errors made when making predictions that use
information about the independent variable.
Measures of association may be symmetrical or asymmetrical. When the measure is symmetrical, its… and what abt when its asymmetrical
value will be the same regardless of which of the two variables is considered the independent or
dependent variable. In contrast, the value of asymmetrical measures of association may vary
depending on which variable is considered the independent variable and which the dependent
variable.
Lambda is an asymmetrical measure of association suitable for use with
nominal variables. It can
range from 0.0 to 1.0 and gives an indication of the strength of an association between the
independent and the dependent variables.
kendalls taub v gamma
Gamma is a symmetrical measure of association suitable for ordinal variables or for dichotomous
nominal variables. It can vary from 0.0 to ±1.0 and reflects both the strength and direction of the
association between two variables.
Kendall’s tau-b is a symmetrical measure of association suitable for use with ordinal variables.
Unlike gamma, it accounts for pairs tied on the independent and dependent variable. It can vary
from 0.0 to ±1.0. It provides an indication of the strength and direction of the association between
two variables.
cramers v
a measure of association for nominal variables. It is based on the value of chi-square
and ranges between 0.0 to 1.0. Because it cannot take negative values, it is considered a
nondirectional measure.
