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
r
n, r
Cov (X, Y) CV df
Meaning
n-c-r
n-c-r
Covariance between X and Y
Formula a = y − b x , for line y = a + bx b=
∑ ( x − x)( y − y) ∑ ( x − 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 Coefficient of S tan dard Deviation . CV= variation Arithmatic mean Degree(s) of freedom
Link to Glossary (if appropriate) Regression: y on x Regression: y on x
Binomial Distribution
Confidence interval
Symbol
Text Equivalent
E
E (f (x))
Meaning Maximal error tolerance
Expected value of f (x)
f F
Formula σ
E = zc
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.
χ 12 F=
n1
χ
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
Fx
=
x
∫ f x dx
−∞
Depends on the distribution. f x ≥ 0 & ∫ f x dx = 1. x
H0
H-naught
Null hypothesis.
H1
H-one
Alternate hypothesis.
IQR MS
Interquartile range M-S
Mean square
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. Analysis of variance SS (ANOVA) MS=
df
n N
Sample size. Population size
n = number of units in a sample. N = Number of units in the population.
Symbol
P
Text Equivalent
Pr
n-p-r
pˆ
p-hat
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
n
n, r
n-p-r
Meaning
p-value
The attained level of significance.
Q
Q
Q-one
Q
Q-two 2
Q
3
Probability of not happening of the event First quartile
1
Formula
P
n
n,r
Pr =
Q-three
n! , where n ≥ r (n − r )!
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 =
Q
= 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. 1
Second quartile Or Median Third quartile
=
Link to Glossary (if appropriate)
Symbol
Text Equivalent
R
Sample Correlation coefficient
2
r-square
R2
r-square
r
S
s
2
Meaning
Coefficient of determination Multiple correlation coefficient Sample standard deviation
S-square
Sample variance
Formula r=
Co var iance( X , Y ) [ SD( X )] * [ SD(Y )]
2 r = (Correlation coefficient )
R2 = 1−
∑ (x − x)
s=
SD
s-e- square
Error variance Sample standard deviation
2
for ungrouped data.
n −1
∑ f (x − x) s= (∑ f ) − 1 ∑ (x − x) = s n −1 ∑ f (x − x) s = (∑ f ) − 1
skp
Bowley’s coefficient of skewness Pearson’s coefficient of skewness
for grouped data. for ungrouped data.
Measures of dispersion
2
for grouped data
sum of squares of residuals . n
S e2 =
∑ (x − x)
s=
skb =
Measures of dispersion
2
2
2
2
for ungrouped data.
n −1
∑ f (x − x) (∑ f ) − 1
s=
skb
2
mean square error S y2
2
S e2
Link to Glossary (if appropriate)
2
for grouped data.
(Q3 − Q 2) − (Q 2 − Q1)
skp =
(Q3 − Q1)
Mean − Mode S tan dard Deviation
Measures of skew ness Measures of skew ness
Symbol
Text Equivalent
Meaning Sum of Squares
SS x
Formula SS x = ∑ ( x − x) 2 for ungrouped data.
Link to Glossary (if appropriate)
SS x = ∑ f ( x − x) 2 for grouped data.
t
Student’s t variable.
tc
Var (X) 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 Arithmetic mean or Average of X scores.
x-bar
t=
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.
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- µ ) 2 Eg. In the study of, yield obtained & the irrigation level, independent variable is, X= Irrigation level.
x= x=
y
Normal (0,1) χ n
∑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 z= , where X follows 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
α
Text Equivalent Alpha
β
Beta
∈
Epsilon
Meaning Type I error or Level of Significance. Type II error or Power of the test. “Error Term” in regression/statistics; more generally used to denote an arbitrarily small positive number
χ
2
Chi-square
Chi-square distribution
χ
2
Chi-square
Chi-square distribution
Γ(n)
λ
Formula
Link to Glossary (if appropriate)
α = P [Rejecting the null hypothesis |
Hypothesis Testing
Null hypothesis is true]. β = P [Accepting the null hypothesis | Null hypothesis is False].
Hypothesis Testing Regression
y = β0+ β1 *x + ∈
χ
= Sum of n independent Standard Chi-square distribution. normal variables Goodness of fit test (O − E ) 2 χ2 = ∑ where O is the E observed frequency and E is the expected frequency. Or (n − 1) s 2 χ2 = (?) 2 2
σ
Gamma-n
Gamma function
Lambda
Parameter used for Poisson distribution
λ
Γ(n)
= (n-1) !
= Mean of Poisson distribution
Poisson distribution
Symbol µ
Text Equivalent Mu
Meaning
Formula
Arithmetic mean or Average of the population.
µ=
∑x N
µ = E (x) =
µ
Mu-r
µ
rth central moment
r
µ 'r ρ
∑ σ
r
2
Mu-r-dash
rth Raw moment
µ 'r = E (Xr)
Rho
Population correlation coefficient
ρ=
Sigma
Summation
Sigma
Population Standard Deviation
Sigma square Population variance
∑ xP(x) Measures of central tendency.
= E [(X- µ )r]
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
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
∪
Formula 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
Link to Glossary (if appropriate)
Symbol â&#x2C6;Š
Text Equivalent Intersection
Meaning And
Formula For example: (A â&#x2C6;Š B) is happening of both event A and event B
Link to Glossary (if appropriate)