1.1.1.3.1.5 Frequencies:tables for relative and
absolute. Consider requesting n-tiles
1.1.1.3.1.6 Peakedness: compute the
kurtosis of a variable
1.1.1.3.1.6.1 To test departures from normality: for N greater
than 1000, refer the critical ratio of the kurtosis
measure to a table of the unit normal curve; for N
between 200 and 1000, refer the kurtosis measure
to a table for testing kurtosis; for N less than 200,
use Geary's criterion.
1.2 2 VARIABLES
1.2.1 Scale of Measurement?
1.2.1.1 1 Interval,
1 Nominal
1.2.1.1.1 Is interval
variable
dependent?
1.2.1.1.1.1 YES: measure of
strength or test of
significance?
1.2.1.1.1.1.1 Test of
significance:
1.2.1.1.1.1.1.1 assuming homoscedasticity
across levels of ind. variable,
perform an analysis of variance
and F-test for significance
1.2.1.1.1.1.1.2 With no homoscedasticity across
levels of ind. variable, use ANOVA.
For hypothesis testing use the
Welch statistic, the Brown-Forsythe
statistic, or the t-test
1.2.1.1.1.1.2 Measure of strength:
1.2.1.1.1.1.2.1 Use the
ANOVA, and Omega Squared
Intraclass Correlation Coefficient
Kelley's Epsilon Squared
1.2.1.1.1.2 NO: ANOVA to perform
an analysis of variance
1.2.1.2 1 Nominal,
1 Ordinal
1.2.1.2.1 compute the Friedman test and
probability of chance occurrence.
1.2.1.2.2 Use Freeman's
coefficient of
differentiation, theta
1.2.1.3 1 Interval,
1 Ordinal
1.2.1.3.1 If ordinal is based on an
underlying normally
distributed interval variable,
use Jaspen's Coefficient of
Multiserial Correlation
1.2.1.4 Both Nominal
1.2.1.4.1 Both variables
2-point scale?
1.2.1.4.1.1 YES: What will
be measured?
1.2.1.4.1.1.1 Symmetry: Use McNemar's test of
symmetry; it is equivalent to Cochran's Q
1.2.1.4.1.1.2 Covariation: use
Yule's Q Phi
1.2.1.4.1.2 NO: At least one is not a
2-point scale and one
is considered an
independent variable
1.2.1.4.1.2.1 Statistic based on
number of cases
in each category
1.2.1.4.1.2.1.1 use Goodman and
Kruskal's tau b
1.2.1.4.1.2.2 Statistic based on
number of cases in
modal categories
1.2.1.4.1.2.2.1 calculate the asymmetric
lambdas A and B
1.2.1.5 Both Ordinal
1.2.1.5.1 Distinction between dependent
& independent variables?
1.2.1.5.1.1 YES: use
Somer's d for 2
ordinal variables
1.2.1.5.1.2 NO: What do you
want to measure?
1.2.1.5.1.2.1 Agreement: no applicable statistic,
but data may be transformed to
ranks and r or Krippendorff's r used
1.2.1.5.1.2.2 Covariance: depending on if the
ranks are treated as interval scales,
use Kendall's tau-a, tau-b, tau-c
Goodman and Kruskal's gamma,
Kim's d, or Spearman's rho (rs)
1.2.1.6 Both Interval
1.2.1.6.1 Distinction between dependent
& independent variables?
1.2.1.6.1.1 YES: looking for
linear relationship?
1.2.1.6.1.1.1 YES: use the F-test, also
computed by Regression
1.2.1.6.1.1.2 NO: Curvilinear relationships- use the
F-test, computed by Regression, equal
to t-squared, for each coefficient
1.2.1.6.1.2 NO: looking for equal
means on both variables?
1.2.1.6.1.2.1 YES: calculate the t-test
for paired observations
1.2.1.6.1.2.2 NO: treat the relationship as linear
What do want to measure?
1.2.1.6.1.2.2.1 Agreement: penalty
without same distribution?
1.2.1.6.1.2.2.1.1 YES: Robinson's A or
the intraclass
correlation coefficient.
The test is the F-test.
1.2.1.6.1.2.2.1.2 NO: Use Krippendorff's
coefficient of agreement
1.2.1.6.1.2.2.2 Covariance:
1.2.1.6.1.2.2.2.1 Use Pearson Product-Moment r (correlation
coefficient), Biserial R, or Tetrachoric r depending
on how many of the variables are dichotomous