Statistical Notation Reference.md

APA7 Statistical Notation, Abbreviations, and Symbols

Abbreviation or symbol	Descriptor
a	In item response theory, the slope parameter
AIC	Akaike information criterion
ANCOVA	analysis of covariance
ANOVA	analysis of variance
AVE	average value explained
b, bi	in regression and multiple regression analyses, estimated values of raw (unstandardized) regression coefficients; in item response theory, the difficulty-severity parameter
b$\ast$, bi$\ast$	estimated values of standardized regression coefficients in regression and multiple regression analyses
BC, aBIC	Bayesian information criterion, sample-size-adjusted Bayesian information criterion
CAT	computerized adaptive testing
CDF	cumulative distribution function
CFA	confirmatory factor analysis
CFI	comparative fit index
CI	confidence interval
d	Cohen's measure of sample effect size for comparing two sample means
d'	discriminability, a measure of sensitivity in signal detection theory
df	degrees of freedom
DIF	differential item functioning
EFA	exploratory factor analysis
EM	expectation maximization
ES	effect size
f	frequency
fe	expected frequency
fo	observed frequency
F	F distribution; Fisher's F ratio
F($v_{1},v_{2}$)	F with $v_{1}$ and $v_{2}$ degrees of freedom
Fcrit	critical value for statistical significance in an F test
Fmax	Hartley's test of homogeneity of variance
FDR	false discovery rate
FIML	full information maximum likelihood
g	Hedges's measure of effect size
GFI	goodness-of-fit index
GLM	generalized linear model
GLS	generalized least squares
H$_{0}$	null hypothesis, hypothesis under test
H1 or Ha	alternative hypothesis
HLM	hierarchical linear model(ing)
HSD	Tukey's honestly significant difference
IRT	item response theory
k	coefficient of alienation; number os studies in a meta-analysis; number of levels in an experimental design or individual study
k2	coefficient of nondetermination
KR20	Kuder—Richardson reliability index
LGC	latent growth curve
LL	lower limit (as of a Cl)
LR	likelihood ratio
LSD	least significant difference
M (or $\bar{X}$)	sample mean; arithmetic average
MANOVA	multivariate analysis of variance
MANCOVA	multivariate analysis of covariance
MCMC	Markov chain Monte Carlo
Mdn	median
MLE	maximum likelihood estimator; maximum likelihood estimate
MLM	multilevel model(ing)
MS	mean square
MSE	mean square error
n	number of cases (generally in a subsample)
N	total number of cases
NFI, NNFI	normed fit index, nonnormed fit index
ns	not statistically significant
OLS	ordinary least s uares
OR	odds ratio
p	probability; probability of a success in a binary trial
prep	probability a replication would give a result with the same sign as the original result
PDF	probability density function
q	probability of a failure in a binary trial; 1-p
Q	test of homogeneity of effect sizes
r	estimate of the Pearson product—moment correlation coefficient
rab.c	partial correlation of a and b with the effect of c removed
ra(b.c)	partial (or semipartial) correlation of a and b with the effect of c removed from b
r2	coefficient of determination; measure of strength of relationship; estimate of the Pearson product-moment correlation squared
rb	biserial correlation
rpb	point biserial correlation
rs	Spearman rank-order correlation
R	multiple correlation
R2	multiple correlation squared; measure of strength of association
RMSEA	root-mean-square error of approximation
s	sample standard deviation (denominator $\sqrt{n-1}$
S	sample variance—covariance matrix
s2	sample variance (unbiased estimator) — denominator n — 1
S2	sample variance (unbiased estimator) — denominator n
SD	standard deviation
SE	standard error
SEM	standard error of measurement; standard error of the mean
SEM	structural equation model(ing)
SRMR	standardized root-mean-square residual
SS	sum of squares
t	Student's t distribution; a statistical test based on the Student t distribution; the sample value of the t-test statistic
T2	Hotelling's multivariate test for the equality of the mean vector in two multivariate populations
Tk	generic effect-size estimate
TLI	Tucker—Lewis index
U	Mann—Whitney test statistic
UL	upper limit (as of a Cl)
V	Pillai—Barlett multivariate trace criterion; Cramér's measure of association in contingency tables
Wk	fixed-effects weights
Wk*	random-effects weights
W	Kendall's coefficient of concordance and its estimate
WCS	weighted least squares
z	a standardized score; the value of a statistic divided by its standard error

APA7 Greek Character Set

Abbreviation or symbol	Definition
$\alpha$ (alpha)	in statistical hypothesis testing, the probability of making a Type Cronbach's index of internal consistency (a form of reliability)
$\beta$ (beta)	in statistical hypothesis testing, the probability of making a Type 11 error (1 — $\beta$ denotes statistical power); population values of regression coefficients (with approriate subscripts as needed)
B (capital beta)	in SEM, matrix of regression coefficients among dependent constructs
$\Gamma$ (capital gamma)	Goodman—Kruskal's index of relationship; $\Gamma$, matrix of regression coefficients between independent and dependent constructs in SEM
$\delta$ (delta)	population value of Cohen's effect size; noncentrality parameter in hypothesis testing and noncentral distributions
$\Delta$ (capital delta)	increment of change
$\epsilon^{2}$ (epsilon squared)	measure of strength of relationship in analysis of variance
$\eta^{2}$ (eta-squared)	measure of strength of relationship
$\theta_{k}$ (theta k)	generic effect size in meta-analysis
$\Theta$ (capital theta)	Roy's multivariate test criterion; $\Theta$ ;matrix of covariances among measurement errors in SEM
K (kappa)	Cohen's measure of agreement corrected for chance agreement
$\lambda$ (lambda)	element of a factor loading matrix; Goodman—Kruskal measure of predictabiliy
$\Lambda$ (capital lambda)	WilksS multivariate test criterion; A, matrix of factor loadings in SEM
$\mu$ (mu)	population mean; ex ected value
$\nu$ (nu)	degrees of freedom
$\rho$ (rho)	population product—moment correlation
$\rho_{I}$ (rho I)	population intraclass correlation
$\sigma$ (sigma)	population standard deviation
$\sigma^{2}$ (sigma-squared)	population variance
$\Sigma$	population variance—covariance matrix
$\tau$ (tau)	Kendall's rank-order correlation coefficient; Hotelling's multivariate trace criterion
$\phi$ (phi)	standard normal probability density function
$\Phi$ (capital phi)	measure of association in contingency tables; standard normal cumulative distribution function; $\Phi$ ;matrix of covariances among independent constructs in SEM
$\chi^{2}$ (chi-squared)	the chi-square distribution; a statistical test based on the chi-square distribution; the sample value of the chi-square test statistic
$\Psi$ (capital psi)	in statistical hypothesis testing, a statistical contrast; matrix of covariances, among prediction errors in SEM
$\omega^{2}$ (omega-squared)	strength of a statistical relationship
$|a|$	absolute value of a
$\Sigma$ (capital sigma)	summation