# Statistical Notation

**Topics:**Statistics, Analysis of variance, Normal distribution

**Pages:**10 (840 words)

**Published:**March 27, 2014

APA format for statistical notation and other things:

Statistical abbreviations:

ANCOVA

ANOVA

α

β

Analysis of Covariance

Analysis of Variance

alpha, the probability of

making a Type 1 error in

hypothesis testing

beta, the probability of

making a Type 2 error in

hypothesis testing

CI

d

d’

df

confidence interval

Cohen’s measure of

effect size

d-prime (a measure of

sensitivity, used in

Signal Detection Theory)

degrees of freedom

F

Fmax

H

Ha

F-ratio (used in

ANOVA, ANCOVA and

MANOVA)

Hartley’s Fmax test

value (a test for

homogeneity of

variance)

Kruskal-Wallis test value

Alternative hypothesis

Ho

HSD

LSD

MANOVA

Null hypothesis

Tukey’s Honestly

Significant Difference

Fisher’s Least

Significant Difference

Multivariate Analysis of

Variance

M (or �)

𝑋

Mdn

MS

MSE

Mean (usually, the

sample mean)

Median

Mean Square

Mean square error

µ

n

N

ns

mu, designating the

population mean

Number in subsample

Total number in sample

Not significant

p

%

σ

r

Probability

Percentage

sigma, designating the

population standard

deviation (n version of

the SD formula)

Pearson's correlation

R

s (or σn-1)

s

coefficient of

determination

multiple correlation

sample standard

deviation (n-1 version of

the SD formula)

sample variance (n-1

version)

rs

SD

SE (or SEM)

SS

Spearman’s rho

Standard deviation

Standard error

Sum of Squares

r

2

2

Graham Hole, Research Skills 2012: page 2

t

T

U

x

t-test value

Wilcoxon test value

Mann-Whitney test value

Horizontal axis on a graph

y

z

Σ

2

Χ

Vertical axis on a graph

z-score

Sum

Chi square test value

Other commonly used abbreviations :

°C

cm

°F

g

Degrees Centigrade

h

Centimetre(s)

IQ

Degrees Fahrenheit

kg

Gram(s)

km

Hour(s)

kph

Intelligence Quotient

L

Kilogram(s)

m

Kilometre(s)

m²

Kilometres per hour

mg

Litre(s)

min

Metre(s)

ml

Square metre(s)

mm

Milligramme(s)

ms

Minute(s)

Millilitre(s)

RT

Millimetre(s)

s

Reaction Time

Second(s)

Millisecond(s)

Jeffrey Kahn's guide to APA format is reproduced below. Find the original here: http://my.ilstu.edu/~jhkahn/apastats.html

Reporting Statistics in APA Style

Dr. Jeffrey Kahn, Illinois State University

The following examples illustrate how to report statistics in the text of a research report. You will note that significance levels in journal articles--especially in tables--are often reported as either "p > .05," "p < .05," "p < .01," or "p < .001." APA style dictates reporting the exact p value within the text of a manuscript (unless the p value is less than .001). Please pay attention to issues of italics and spacing. APA style is very precise about these. Also, with the exception of some p values, most statistics should be rounded to two decimal places.

Graham Hole, Research Skills 2012: page 3

Mean and Standard Deviation are most clearly presented in parentheses: The sample as a whole was relatively young (M = 19.22, SD = 3.45). The average age of students was 19.22 years (SD = 3.45).

Percentages are also most clearly displayed in parentheses with no decimal places: Nearly half (49%) of the sample was married.

Chi-Square statistics are reported with degrees of freedom and sample size in parentheses, the chi-square value (rounded to two decimal places), and the significance level: The percentage of participants that were married did not differ by gender, χ2(1, N = 90) = 0.89, p = .35.

T Tests are reported like chi-squares, but only the degrees of freedom are in parentheses. Following that, report the t statistic (rounded to two decimal places) and the significance level.

There was a significant effect for gender, t(54) = 5.43, p < .001,...

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