Statistical Symbols

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Alphabetical Statistical Symbols


Symbol

Text Equivalent

Meaning

Formula

Link to Glossary (if appropriate)

a

 

Y- intercept of least square regression line

, for line

Regression: y on x

b

 

Slope of least squares regression line

for line

Regression: y on x

Binomial distribution with parameters n and p

Discrete probability distribution for the probability of number of successes in n independent random trials under the identical conditions.

If X follows then, ,

Where, ,

r = 0,1,2, …….,n,

 

Binomial Distribution

c

 

Confidence level

Confidence interval

nCr

n-c-r

Combinations (number of combinations of n objects taken r at a time)

, where

 

n-c-r

Combinations (number of combinations of n objects taken r at a time)

, where

 

Covariance between X and Y

Covariance between X & Y

 

CV

 

Coefficient of variation



df

 

Degree(s) of freedom

 

 

E

 

Maximal error tolerance

for large samples

 

E (f(x))

Expected value of f(x)



 

f

 

Frequency

number of times score.

 

F

 

F-distribution variable

where n1 and n2 are the

corresponding degrees of freedom.

 

F-distribution, Hypothesis testing for equality of 2 variances.

or

 

Distribution function

.

 

f(x)

or

 

 

Probability mass function

 

Depends on the distribution.



H0

H-naught

Null hypothesis

The null hypothesis is the hypothesis about the population parameter.

Testing of hypothesis

H1

H-one

Alternate hypothesis

An alternate hypothesis is constructed in such a way that it is the one to be accepted when the null hypothesis must be rejected.

Testing of hypothesis

IQR

 

Interquartile range

Measures of central tendency.

MS

M-S

Mean square

Analysis of variance (ANOVA)

n

 

Sample size.

number of units in a sample.

 

N

 

Population size

Number of units in the population.

 

n-p-r

Permutation (number of ways to arrange in order n distinct objects taking them r at a time)

where

 

n-p-r

Permutation (number of ways to arrange in order n distinct objects taking them r at a time)

, where

 

p-hat

Sample proportion

Binomial distribution

Probability of A given B

Conditional probability

 

Probability of x

Probability of x

 

p-value

 

The attained level of significance.

P value is the smallest level of significance for which the observed sample statistic tells us to reject the null hypothesis.

 

Q

 

Probability of not happening of the event

 

Q1

Q-one

First quartile

Median of the lower half of the data that is data below median.

Measures of central tendency

Q2

Q-two

Second quartile Or Median

Central value of an ordered data.

Measures of central tendency

Q3

Q-three

Third quartile

Median of the upper half of the data that is data above the median.

Measures of central tendency

R

 

Sample Correlation coefficient

 

r2

r-square

Coefficient of determination

 

R2

r-square

Multiple correlation coefficient

 

S

 

Sample standard deviation

for ungrouped data. for grouped data.

Measures of dispersion

S2

S-square

Sample variance

for ungrouped data.

for grouped data.

Measures of dispersion

s-e- square

Error variance

 

SD

 

Sample Standard deviation

for ungrouped data. for grouped data.

 

 

Bowley’s coefficient of skewness

Measures of skew ness

 

Pearson’s coefficient of skewness

Measures of skew ness

 

Sum of squares

for ungrouped data

for grouped data

 

t

 

Student’s t variable

t-distribution

tc

t critical

The critical value for a confidence level c.

Number such that the area under the t distribution for a given number of degrees of freedom falling between and is equal to c.

Testing of hypothesis

Var(X)

Variance of X

Variance of X

 

 

X

 

Independent variable or explanatory variable in regression analysis

Eg. In the study of, yield obtained & the irrigation level, independent variable is, Irrigation level.

 

x-bar

Arithmetic mean or Average of X scores.

for ungrouped data.

for grouped data

Measures of central tendency

y

 

Dependent variable or response variable in regression analysis

Eg. In the study of, yield obtained & the irrigation level, dependent variable is, Yield obtained.

 

Z

Z-score

Standard normal variable (Normal variable with mean = 0 & SD = 1)

, where X follows Normal .

Standard normal distribution

z critical

The critical value for a confidence level c.

Number such that the area under the standard normal curve falling between and is equal to c.

Testing of hypothesis Confidence interval


Greek Statistical Symbols


Symbol

Text Equivalent

Meaning

Formula

Link to Glossary (if appropriate)

Alpha

Type I error or Level of Significance

[ Rejecting the null hypothesis | Null hypothesis is true ] .

Hypothesis Testing

 

Beta

Type II error or Power of the test

[ Accepting the null hypothesis | Null hypothesis is False].

Hypothesis Testing

Epsilon

“Error Term” in regression/statistics; more generally used to denote an arbitrarily small positive number

Regression

Chi-square

Chi-square distribution

Sum of n independent Standard normal variables

Chi-square distribution

Chi-square

Chi-square distribution

where O is the observed frequency and E is the expected frequency.

Or

Goodness of fit test

(n)

Gamma-n

Gamma function

 

Lambda

Parameter used for Poisson distribution

Mean of Poisson distribution

Poisson distribution

Mu

Arithmetic mean or Average of the population

 

Mu-r

rth central moment

Measures of central tendency.

Mu-r-dash

rth Raw moment

Measures of central tendency.

Rho

Population correlation coefficient

 

Sigma

Summation

Sum of x scores

 

Sigma

Population standard Deviation

Measures of dispersion

Sigma square

Population variance

Measures of dispersion


Mathematical Statistical Symbols


Symbol

Text Equivalent

Meaning

Formula

Link to Glossary (if appropriate)

!

Factorial

Product of all integers up to the given number

;

 

c

Complement

not

For example: is not

 

Union

or

For example: is happening of either event A or event B.

 

Intersection

And

For example: is happening of both event A and event B.

 

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