statistics symbols cheat sheet, Cheat Sheet of Statistics

Download statistics symbols cheat sheet and more Cheat Sheet Statistics in PDF only on Docsity! 100+ online courses in statistics Alphabetical Statistical Symbols: Symbol Text Equivalent Meaning Formula Link to Glossary (if appropriate) a Y- intercept of least square regression line a = xby  , for line y = a + bx Regression: y on x b Slope of least squares regression line b =     )( 2 ))(( xx yyxx for line y = a + bx Regression: y on x B (n, p) 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 B (n, p) then, P (X = r) = rnr r n ppC  )1( , Where, 0 < p <1, r = 0,1,2, ...n Binomial Distribution c Confidence level ))1,0(( cc zNormalzPc  Confidence interval C r n n-c-r Combinations (number of combinations of n objects taken r at a time) )!(! ! rnr n Cr n   , where n  r C rn, n-c-r Combinations (number of combinations of n objects taken r at a time) )!(! ! , rnr n C rn  , where n  r Cov (X, Y) Covariance between X and Y Covariance between X & Y Cov (X) =E [(X-E (X))(Y- E (Y)] 100+ online courses in statistics Symbol Text Equivalent Meaning Formula Link to Glossary (if appropriate) CV Coefficient of variation CV= meanArithmatic DeviationdardS tan . df Degree(s) of freedom E Maximal error tolerance n zE c   for large samples. E (f (x)) Expected value of f (x) E (f (x)) =  )()( xPxf f Frequency f = number of times score. F F-distribution variable F= n n 2 2 2 1 2 1   where n1 and n2 are the corresponding degrees of freedom. F-distribution, Hypothesis testing for equality of 2 variances. F (x) or F x Distribution function    x xx dxfF f (x) or f x Probability mass function Depends on the distribution. f x  0 &  x dx xf = 1. 0H H-naught Null hypothesis. The null hypothesis is the hypothesis about the population parameter. Testing of hypothesis 1H 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 IQR = Q 3 - Q 1 Measures of central tendency. 100+ online courses in statistics Symbol Text Equivalent Meaning Formula Link to Glossary (if appropriate) SD Sample standard deviation 1 )( 2     n xx s for ungrouped data.   1 )( 2      f xxf s for grouped data. skb Bowley’s coefficient of skewness skb = )( )() 13 1223( QQ QQQQ   Measures of skew ness skp Pearson’s coefficient of skewness skp = DeviationdardS ModeMean tan  Measures of skew ness SS x Sum of Squares SS 2)(  xxx for ungrouped data. SS 2)(  xxfx for grouped data. t Student’s t variable. n Normal t n 2 )1,0(  t-distribution ct t critical The critical value for a confidence level c. ct =Number such that the area under the t distribution for a given number of degrees of freedom falling between ct and ct is equal to c. Testing of hypothesis Var (X) Variance of X Variance of X Var (X) = E (X-  ) 2 X Independent variable or explanatory variable in regression analysis Eg. In the study of, yield obtained & the irrigation level, independent variable is, X= Irrigation level. 100+ online courses in statistics Symbol Text Equivalent Meaning Formula Link to Glossary (if appropriate) x x-bar Arithmetic mean or Average of X scores. n x x  for ungrouped data.    f fx x 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, Y= Yield obtained. Z Z-score Standard normal variable (Normal variable with mean = 0 & SD = 1)    x z , where X follows Normal ( , ). Standard normal distribution cz z critical The critical value for a confidence level c. cz = Number such that the area under the standard normal curve falling between cz and cz 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.  = P [Rejecting the null hypothesis | Null hypothesis is true]. Hypothesis Testing 100+ online courses in statistics Symbol Text Equivalent Meaning Formula Link to Glossary (if appropriate)  Beta Type II error or Power of the test.  = P [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 y = 0+ 1 *x +  Regression 2 Chi-square Chi-square distribution 2 = Sum of n independent Standard normal variables Chi-square distribution. 2 Chi-square Chi-square distribution    E EO 22 )( where O is the observed frequency and E is the expected frequency. Or 2 2 2 )1(   sn   (?) Goodness of fit test )(n Gamma-n Gamma function )(n = (n-1) !  Lambda Parameter used for Poisson distribution  = Mean of Poisson distribution Poisson distribution  Mu Arithmetic mean or Average of the population. N x   = E (x) =  )(xxP  r Mu-r r th central moment  r = E [(X-  )r] Measures of central tendency.  ' r Mu-r-dash r th Raw moment  'r = E (X r) Measures of central tendency.  Rho Population correlation coefficient )(*)( ),(Covariance YSDXSD YX 