Alphabetical Statistical Symbols

Alphabetical Statistical Symbols: Symbol Text Equivalent a C C Regression: y on x b =∑ 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. Confidence level If X follows B (n, p) then, n-c-r 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 r n, r Cov (X, Y) CV df Link to Glossary (if appropriate) a = y − b x , for line y = a + bx c n Formula Y- intercept of least square regression line Slope of least squares regression line b B (n, p) Meaning n-c-r Covariance between X and Y Degree(s) of freedom ( x − x)( y − y) ∑ ( x − x) n 2 for line y = a + bx Binomial Distribution P (X = r) = C r p (1 − p) n −r , r Where, 0 < p <1, r = 0,1,2, ...n c = P( − z c < Normal (0,1) < z c ) n n! C r = r!(n − r )! , where n ≥ r C n, r = n! , where n ≥ r r!( n − r)! Cov (X) =E [(X-E (X))(Y- E (Y)] CV= S tan dard Deviation . Arithmatic mean Confidence interval Symbol Text Equivalent E E (f (x)) Meaning Maximal error tolerance Expected value of f (x) f F F (x) or F x Formula σ E = zc for large samples. n E (f (x)) = Link to Glossary (if appropriate) ∑ f ( x) P ( x) Frequency F-distribution variable f = number of times score. Distribution function F x = ∫ f x dx χ 21 F-distribution, Hypothesis testing for 1 n where n1 and n2 are the equality of 2 F= 2 χ2 variances. n2 corresponding degrees of freedom. x −∞ f (x) or f x Probability mass function Depends on the distribution. f x ≥ 0 & ∫ f x dx = 1. 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 MS= (ANOVA) x H0 H-naught Null hypothesis. H1 H-one Alternate hypothesis. IQR MS Interquartile range M-S Mean square df n N Sample size. Population size n = number of units in a sample. N = Number of units in the population. Symbol Text Equivalent 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 P n n, r Pr p̂ n-p-r Meaning n-p-r p-value The attained level of significance. Q Q-one Q Probability of not happening of the event First quartile 1 2 Q 3 P n n ,r Q-three Second quartile Or Median Third quartile = Pr = Link to Glossary (if appropriate) n! , where n ≥ r ( n − r)! n! , where n ≥ r (n − r )! number of success Binomial distribution . 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 ˆp = = Median of the lower half of the Measures of central tendency data that is data below median. Measures of central Q2 = Central value of an ordered data. tendency of central Q3 = Median of the upper half of the Measures tendency data that is data above the median. Q 1 Q-two Q Formula Symbol Text Equivalent R Sample Correlation coefficient 2 r-square R2 r-square r Meaning S Coefficient of determination Multiple correlation coefficient Sample standard deviation Formula r= Co var iance ( X ,Y ) [ SD( X )] * [ SD(Y )] 2 r = (Correlation coefficient) R 2 = 1− ∑ (x − x ) s= S-square Sample variance 2 for ungrouped data. n −1 ∑ f (x − x ) (∑ f ) −1 ∑ (x − x ) = for grouped data. 2 s 2 for ungrouped data. n−1 ∑ f (x − x ) s = ( ∑ f ) −1 SD s-e- square Error variance Sample standard deviation skp Measures of dispersion 2 for grouped data sum of squares of residuals . n S e2 = ∑ (x − x ) s= 2 for ungrouped data. n −1 ∑ f (x − x ) (∑ f ) −1 s= skb Measures of dispersion 2 2 S e2 2 mean square error S 2y s= s2 Link to Glossary (if appropriate) 2 for grouped data. ( Q 3 − Q 2) − (Q 2 − Q 1) Bowley’s coefficient of skewness skb = Pearson’s coefficient of skewness skp = (Q 3 − 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 Link to Glossary (if appropriate) 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 tc =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 zc 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. 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 “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) Gamma-n Gamma function λ Lambda Parameter used for Poisson distribution Link to Glossary (if appropriate) Regression y = β0+ β1 *x + ∈ χ = Sum of n independent Standard Chi-square distribution. normal variables 2 Goodness of fit test (O − E ) where O is the χ 2=∑ E observed frequency and E is the expected frequency. Or 2 ( n − 1) s (?) χ2 = 2 2 σ Γ(n) = (n-1) ! λ = Mean of Poisson distribution Poisson distribution Symbol µ Text Equivalent Mu Meaning Formula µ=∑ Arithmetic mean or Average of the population. x N µ = E (x) = µ Mu-r µ rth central moment r r rth 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. 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 ∑ xP(x) = E [(X- µ )r] Mu-r-dash 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 ∪ 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 ∩ Text Equivalent Intersection Meaning And Formula For example: (A ∩ B) is happening of both event A and event B Link to Glossary (if appropriate)