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)) =

∑ 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

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

=

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

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.

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

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

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

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