Statistical Symbols

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

ⁿC_r

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

t_c

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