Measures Of Association

Front 1

Two nominal variables, both dichotomous

Back 1

Phi

Phi=√(X^2/N)
N= number of subjects
X^2=Chi-square statistic

Front 2

Two nominal variables, not dichotomous, equal number of categories

Back 2

C coefficient
C=√(X^2/(N+X^2 ))

Front 3

Two nominal variables, proportion reduction in error

Back 3

Lambda and asymmetric lambda
How much improvement do we make in predicting Y if we consider X?
Lambda assumes DV and IV. Asymmetric assumes neither.

Front 4

Dichotomous nominal variable and ordinal variable

Back 4

Rank-biserial
r_pb=(2(¯Y_1-¯Y_2))/n

Front 5

Dichotomous nominal variable and interval variable

Back 5

Point-biserial
Use Pearson r formula

Front 6

Nominal variable and interval variable

Back 6

Eta
η=√(〖SS〗_(Between Groups)/〖SS〗_Total )

Front 7

Two ordinal variables

Back 7

Spearman's rho
ρ=1-(6∑d^2 )/(n(n^2-1))

Kendal's tau-b adjusts for ties
τ_b=(s(N_C-N_D))/√((N(N-1)+T_X)(N(N-1)+T_Y))

Front 8

Two dichotomous variables, both with underlying continous distributions

Back 8

Tetrachoric

Front 9

Two ordinal variables, both with underlying continous distributions

Back 9

Polychoric

Front 10

Dichotomous variable with underlying continuous distribution, and interval variable

Back 10

Biserial

Front 11

Dichotomous or Ordinal variable with underlying continous distribution, and interval variable

Back 11

Polyserial

Front 12

Two interval variables

Back 12

Pearson's r
r=S_xy/(S_x S_y )
Ho: ρ=0
t_((n-2))=(r√(n-2))/√(1-r^2 )

Front 13

Compare observed frequencies against hypothesized distribution, called goodness of fit.

Back 13

Chi-square
x^2=∑〖(O-E)〗^2/E
Effect size=(O-E)/√E
df=C-1, where C is number of categories

Front 14

Two nominal variables, unequal number of rows and columns

Back 14

Cramer's V
V=√(X^2/(N(q-1)))
X^2=Chi-square statistic
q=number of categories

Front 15

What is concordance

Back 15

With two ordinal variables, does a higher score on X also go with a higher score on Y? If so, X and Y are a concordant pair.

Front 16

Testing hypothesies about r when the population r is not assumed to be zero.

Back 16

Fisher's Z transformation

Front 17

Correlation between two variables, while removing the influence of a third variable from both.

Back 17

Partial correlation.

Front 18

Correlation between two variables, while removing the influence of a third variable from one of the two.

Back 18

Part correlation, or semi-partial correlation

Front 19

Testing the hypothesis that there is no relationship between two nominal variables (test of independence)

Back 19

Chi-square
x^2=∑〖(O-E)〗^2/E
Effect size=(O-E)/√E
df=(C-1)×(R-1), where C is # of columns and R is # of rows