Alphabetical Statistical Symbols: Symbol
Text Equivalent
a
b
B (n, p)
Binomial distribution with parameters n and p
c n
C
n-c-r
r r
C
n , r
Cov (X, Y) CV df
n-c-r
Covariance between X and Y
Meaning
Formula
Link to Glossary (if appropriate)
Y- intercept of least a = y − b x , for line y = a + bx square regression line Slope of least ( x − x)( y − y ) b = for line y = a + bx squares regression 2 line ( x x)
Regression: y on x
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 )
Binomial Distribution
∑ ∑ −
Combinations (number of combinations of n objects taken r at a time) Combinations (number of combinations of n objects taken r at a time) Covariance between X&Y Coefficient of variation Degree(s) of freedom
n
n!
C = r !(n − r )! , where n ≥ r r
C
n , r
=
n! r !(n − r )!
r
, where n ≥ r
Cov (X) =E [(X-E (X))(Y- E (Y)] CV=
S tan S tan dard Deviation Arithmatic mean
.
Regression: y on x
Confidence interval
Symbol
Text Equivalent
E
Meaning Maximal error tolerance
E (f (x))
Expected value of f (x)
f F
Formula σ
E = z c
Frequency F-distribution variable
for large samples.
n
E (f (x)) =
Link to Glossary (if appropriate)
∑ f ( x) P ( x)
f = number of times score. 2
χ 1 F=
n1
where n1 and n 2
2
χ 2
F-distribution, Hypothesis testing for are the equality of 2 variances.
n2 corresponding degrees of freedom. Distributi Distribution on function function
F (x) or F x x
Probabilit Probability y mass function
f (x) or f x
F x
=
x
∫ f x dx
−∞
Depends on the distribution. f x ≥ 0 & ∫ f x dx = 1. x
H 0
H-no H-nott
Null Null hypo hypoth thes esis is..
H 1
H-one
Alternate hypothesis.
IQR
Interquartile range
MS
M-S
Mean square
The The null null hypo hypoth thes esis is is the the hypo hypotthes hesis 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. Analysis of variance SS MS= (ANOVA)
df
n
N
Sample size. Population size
n = number of units in a sample. N = Number of units in the population.
Symbol
n-p-r
n , r
n
Text Equivalent
n-p-r
P r
pˆ
p-hat
P (A | B) P (x)
Conditional probability
Probability of x
Probability of x
Q
Q
Q-one
Q
Q-two
1
2
3
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
Probability of A given B
p-value
Q
Meaning
Q-three
Formula
P
n , r
n
=
P r =
pˆ =
n! (n − r )!
n! (n − r )!
, where n ≥ r
, where n ≥ r
number of success number of trials
P (A | B) = P (x) =
Link to Glossary (if appropriate)
.
Binomial distribution
P ( A ∩ B)
P ( B) No.of favorable outcomes Total no.of outcomes
The attained level Pof value is the smallest level of significance. significance for which the observed sample statistic tells us to reject the null hypothesis. Probability of not q=1–p happening of the event First quartile Q1 = Median of the lower half of the Measures of central tendency data that is data below median. Second quartile Q2 = Central value of an ordered data. Measures of central Or Median tendency Third quartile Q3 = Median of the upper half of the Measures of central tendency data that is data above the median.
Symbol
Text Equivalent
R
Meaning Sample Correlation coefficient
2
r
r-square r-square
R 2
r-square
S
Coeffici Coefficient ent of determination Multiple correlation coefficient Sample standard deviation
Formula r =
Co var iance( X , Y ) [ SD( X )] * [ SD(Y )]
2
r = (Correlatio n coefficien t ) R 2 = 1 −
S y2
∑ ( x − x )
s =
s
S e2 SD
S-square
s-e- square
Sample variance
Error variance Sample Sample standard standard deviation
2
for ungrouped data.
n −1
∑ f ( x − x ) (∑ f ) − 1 ∑ ( x − x ) =
s s
2
=
S e2 =
sk p
for grouped data.
n −1 f ( x − x ) 2
∑ (∑ f ) − 1
for ungrouped data.
n
∑ ( x − x )
.
2
for ungrouped data.
n −1
∑ f ( x − x ) (∑ f ) − 1
2
for grouped data.
(Q3 − Q 2) − (Q 2 − Q1)
Bowley’s coefficient of skewness
sk b =
Pearson’s coefficient of skewness
sk p =
Measures of dispersion
for grouped data
sum of squares of residuals
s =
Measures of dispersion
2
2
2
s = sk b
2
mean square error
s = 2
Link to Glossary (if appropriate)
(Q3 − Q1)
Mean − Mode S tan dard Deviation
Measures of skew ness Measures of skew ness
Symbol
Text Equivalent
Meaning Sum of Square Squaress
SS x
Formula
t
Student’s t variable.
t c
Var (X)
t critical
Variance of X
x
x-bar
The critical value for a confidence level c.
t =
Z
Z-score
z c
z critical
2
2
Normal (0,1) 2
χ n
n
t distribution for a given number of degrees of freedom falling between − t c and t c is equal to c.
µ ) 2
Variance of X
Var (X) = E (X-
Independent variable or explanatory variable in regression analysis Arithmetic Arithmetic mean or Average of X scores.
Eg. In the study of, yield obtained & the irrigation level, independent variable is, X= Irrigation level.
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.
t-distribution
t c =Number such that the area under the Testing of hypothesis
x = x =
y
∑ ( x − x) for ungrouped data. = ∑ f ( x − x) for grouped data.
SS x = SS x
Link to Glossary (if appropriate)
∑ x n
∑ fx ∑ f
for ungrouped data.
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 − µ , where X follows z = distribution σ Normal ( µ , σ ).
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
α
Alpha
β
Beta
2
χ
Chi-square
Meaning
Formula
Link to Glossary (if appropriate)
Type I error or Level of Significance. Type II error or Power of the test.
α = P [Rejecting the null hypothesis | Null hypothesis is true]. β = P [Accepting the null hypothesis | Null hypothesis is False].
Chi-square distribution
χ
2
Hypothesis Testing Hypothesis Testing
= Sum of n independent Standard Chi-square distribution.
normal variables 2
χ
Γ (n)
Chi-square
Chi-square distribution
χ 2 =
∑
(O − E ) 2
where
E observed frequency expected frequency. Or (n − 1) s 2 χ 2 = (?) σ 2 Gamma-n
λ
Lambda
µ
Mu
Γ ( n)
Gamma function Parameter used for Poisson distribution Arithmetic Arithmetic mean or Average of the population.
and
O E
is is
∑ x N
µ = µ = E (x) =
Goodness of fit test
the
= (n-1) !
λ = Mean of Poisson distribution µ =
the
∑ xP ( x)
Poisson distribution
Symbol
Text Equivalent Mu-r
Meaning
Formula
th
r central moment
'
r
th
= E [(X- µ ) µ ) ]
Mu-r-dash
r Raw moment
µ r = E (Xr )
Rho
Population correlation coefficient
ρ =
∑
Sigma
Summation
σ
Sigma
Population Standard Deviation
2
Sigma square
Population variance
Measures of central tendency.
'
Co var ianvce( X , Y ) SD( X ) * SD(Y )
∑ x = Sum of x scores. ∑ ( x − µ ) σ =
Measures of dispersion
2
N
σ =
σ
Measures of central tendency.
r
r
µ r ρ
Link to Glossary (if appropriate)
σ = 2
E [( x − µ ) 2 ] =
∑ ( x − µ )
∑ ( x − µ ) 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 n! = n (n-1) (n-2) …….. 1. 0! = 1 For example:
c
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
Link to Glossary (if appropriate)
