Alphabetical Statistical Symbols:
Symbol
Text
Equivalent
a
Y- intercept of least
square regression line
Slope of least
squares regression
line
b
B (n, p)
Binomial
distribution with
parameters n and
p
c
n
C
C
Meaning
n-c-r
r
n, r
Cov (X, Y)
n-c-r
Covariance
between X and Y
Formula
Link to Glossary
(if appropriate)
a = y  b x , for line y = a + bx
Regression: y on x
 ( x  x)( y  y)
b=
 ( x  x)
Regression: y on x
2
for line y = a + bx
Discrete probability
If X follows B (n, p) then,
n
distribution for the
P (X = r) = C r p r (1  p) nr ,
probability of number
of successes in n
Where, 0 < p <1,
independent random
r = 0,1,2, ...n
trials under the
identical conditions.
Confidence level
c  P( z c  Normal(0,1)  z c )
Combinations
n!
n
, where n  r

C
r
(number of
r!(n  r )!
combinations of n
objects taken r at a
time)
Combinations
n!
C n,r  r!(n  r )! , where n  r
(number of
combinations of n
objects taken r at a
time)
Covariance between
Cov (X) =E [(X-E (X))(Y- E (Y)]
X&Y
Binomial Distribution
Confidence interval
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Symbol
Text
Equivalent
Meaning
Formula
CV
Coefficient of
variation
CV=
df
E
Degree(s) of freedom
Maximal error
tolerance
E  zc
E (f (x))
Expected value of
f (x)
f
F
S tan dard Deviation
.
Arithmatic mean

for large samples.
n
E (f (x)) =
Frequency
F-distribution
variable
Link to Glossary
(if appropriate)
 f ( x) P( x )
f = number of times score.
 12
F=
n1

where n1 and n2
2
2
F-distribution,
Hypothesis testing for
are the equality of 2
variances.
n2
corresponding degrees of freedom.
F (x) or F x
Distribution function
f (x) or f x
Probability mass
function
Depends on the distribution.
f x  0 &  f x dx = 1.
The null hypothesis is the hypothesis Testing of hypothesis
about the population parameter.
An alternate hypothesis is constructed in Testing of hypothesis
such a way that it is the one to be
accepted when the null hypothesis must
be rejected.
Measures of central
IQR = Q - Q
3
1
tendency.
Fx

x
 f x dx

x
H0
H-naught
Null hypothesis.
H1
H-one
Alternate hypothesis.
IQR
Interquartile range
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Symbol
MS
Text
Equivalent
M-S
n
N
Meaning
Mean square
MS=
p-hat
Sample size.
Population size
Permutation (number
of ways to arrange in
order n distinct
objects taking them r
at a time)
Permutation (number
of ways to arrange in
order n distinct
objects taking them r
at a time)
Sample proportion
P (A | B)
Probability of A
given B
Conditional
probability
P (x)
Probability of x
Probability of x
P
n
n, r
Pr
p̂
p-value
Q
n-p-r
n-p-r
Formula
The attained level of
significance.
Probability of not
happening of the
event
SS
df
Link to Glossary
(if appropriate)
Analysis of variance
(ANOVA)
n = number of units in a sample.
N = Number of units in the population.
n!
Pn,r  (n  r )! , where n  r
n
Pr 
n!
, where n  r
(n  r )!
Binomial distribution
number of success
.
number of trials
P( A  B)
P (A | B) =
P( B)
No.of favorable outcomes
P (x) =
Total no.of outcomes
P value is the smallest level of
significance for which the observed
sample statistic tells us to reject the null
hypothesis.
q=1–p
pˆ 
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Symbol
Text
Equivalent
Q
Q-one
Q
Q-two
2
Q
3
Meaning
First quartile
1
Q-three
Second quartile
Or Median
Third quartile
Sample Correlation
coefficient
2
r-square
R2
r-square
S
= Median of the lower half of the Measures of central
tendency
data that is data below median.
of central
Q2 = Central value of an ordered data. Measures
tendency
of central
Q3 = Median of the upper half of the Measures
tendency
data that is data above the median.
Co var iance ( X , Y )
r
[ SD( X )] * [ SD(Y )]
Q
Coefficient of
determination
Multiple correlation
coefficient
Sample standard
deviation
2
r  (Correlatio n coefficien t)
R2  1
s
S e2
S-square
s-e- square
Sample variance
Error variance
2
mean square error
S y2
 (x  x)
2
for ungrouped data.
n 1
 f (x  x)
 f   1
 (x  x)

for grouped data.
2
s
2
s
2

S e2 
n 1
 f (x  x)2
 f   1
Measures of
dispersion
2
s
s2
Link to Glossary
(if appropriate)
1
R
r
Formula
for ungrouped data.
Measures of
dispersion
for grouped data
sum of squares of residuals
.
n
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Symbol
Text
Equivalent
SD
Meaning
Sample standard
deviation
Formula
 (x  x)
s
Bowley’s coefficient
of skewness
skb
Pearson’s coefficient
of skewness
skp
Sum of Squares
SS x
2
for ungrouped data.
n 1
 f (x  x)
 f   1
s
skb =
2
for grouped data.
(Q3  Q2)  (Q2  Q1)
skp =
Link to Glossary
(if appropriate)
(Q3  Q1)
Mean  Mode
S tan dard Deviation
Measures of skew
ness
Measures of skew
ness
SS x   ( x  x) 2 for ungrouped data.
SS x   f ( x  x) 2 for grouped data.
Student’s t variable.
t
tc
Var (X)
X
t critical
The critical value for
a confidence level c.
Variance of X
Variance of X
Independent variable
or explanatory
variable in regression
analysis
t
Normal (0,1)
 n
t-distribution
2
n
t c =Number such that the area under the Testing of hypothesis
t distribution for a given number of
degrees of freedom falling between
 t c and t c is equal to c.
Var (X) = E (X-  ) 2
Eg. In the study of, yield obtained & the
irrigation level, independent variable is,
X= Irrigation level.
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Symbol
x
Text
Equivalent
x-bar
Meaning
Formula
Arithmetic mean or
Average of X scores.
x
x
y
Z
Z-score
zc
z critical
Dependent variable
or response variable
in regression analysis
Standard normal
variable
(Normal variable
with mean = 0 & SD
= 1)
The critical value for
a confidence level c.
x
n
 fx
f
for ungrouped data.
Link to Glossary
(if appropriate)
Measures of central
tendency
for grouped data.
Eg. In the study of, yield obtained & the
irrigation level, dependent variable is,
Y= Yield obtained.
Standard normal
x
, where X follows
z
distribution

Normal (  ,  ).
z c = Number such that the area under Testing of hypothesis
the standard normal curve falling
Confidence interval
between  z c and z c is equal to c.
Greek Statistical Symbols:
Symbol

Text
Equivalent
Alpha
Meaning
Type I error or
Level of Significance.
Formula
 = P [Rejecting the null hypothesis |
Link to Glossary (if
appropriate)
Hypothesis Testing
Null hypothesis is true].
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Symbol
Text
Equivalent
Meaning

Beta
Type II error or
Power of the test.

Epsilon
“Error Term” in
regression/statistics; more
generally used to denote
an arbitrarily small
positive number

2
Chi-square
Chi-square distribution

2
Chi-square
Chi-square distribution
Gamma-n
Gamma function

Lambda

Mu
Parameter used for
Poisson distribution
Arithmetic mean or
Average of the
population.
(n)
Formula
 = P [Accepting the null hypothesis |
Null hypothesis is False].
y = 0+ 1 *x + 

= Sum of n independent Standard Chi-square distribution.
normal variables
Goodness of fit test
(O  E ) 2
where O is the
2  
E
observed frequency and E is the
expected frequency.
Or
(n  1) s 2
2
(?)
 
2
2

Mu-r
th
r central moment
r
 'r

Hypothesis Testing
Regression

(n)

Mu-r-dash
rth Raw moment
Rho
Population correlation
coefficient

= (n-1) !
= Mean of Poisson distribution
Poisson distribution
x
N
 = E (x) =

Link to Glossary (if
appropriate)
 xP(x)
= E [(X-  )r]
Measures of central tendency.
 'r = E (Xr)
Covariance ( X , Y )

SD( X ) * SD(Y )
Measures of central tendency.
r
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Symbol


Text
Equivalent
Meaning
Sigma
Summation
Sigma
Population Standard
Deviation
Formula
 x = Sum of x scores.
 (x  )

2
Sigma square Population variance
Measures of dispersion
2
N
=

Link to Glossary (if
appropriate)

2
E[( x   ) 2 ] 
 (x  )
 ( x   ) P( x )
2
Measures of dispersion
2
N
Mathematical Statistical Symbols:
Symbol
Text
Equivalent
Meaning
!
Factorial
c
Complement
Product of all integers up
to the given number
not

Union
or

Intersection
And
Formula
Link to Glossary
(if appropriate)
n! = n (n-1) (n-2) …….. 1.
0! = 1
c
For example: A is not A
For example:(A  B) is happening of
either event A or event B
For example: (A  B) is happening of
both event A and event B
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