CONTINUOUS DATA |
LOCATION |
AVERAGE |
Calculate the average (arithmetic mean) of a dataset. † |
AVERAGE_q |
Calculate the average (arithmetic mean) of a dataset. † |
COUNT |
Calculate the count of numeric rows in a dataset. † |
COUNT_q |
Calculate the count of numeric rows in a dataset. † |
GEOMEAN |
Calculate the geometric mean of a dataset. |
GEOMEAN_q |
Calculate the geometric mean of a dataset. † |
HARMEAN |
Calculate the harmonic mean of a dataset. |
HARMEAN_q |
Calculate the harmonic mean of a dataset. † |
MEDIAN |
Calculate the median value in a dataset. |
MEDIAN_q |
Calculate the median value in a dataset. † |
MODE |
Calculate the mode (most frequent value) of a dataset. |
MODE_q |
Calculate the mode (most frequent value) of a dataset. † |
TRIMMEAN |
Calculate the mean of the interior of a dataset. |
TRIMMEAN_q |
Calculate the mean of the interior of a dataset. † |
|
DISPERSION |
AVEDEV |
Calculate average deviation. |
AVEDEV_q |
Calculate average deviation. † |
COVAR |
Calculate covariance. |
COVAR_q |
Calculate covariance. † |
COVARIANCE_P |
Calculate population covariance. |
COVARIANCE_S |
Calculate sample covariance. |
DEVSQ |
Calculate deviation squared. |
DEVSQ_q |
Calculate deviation squared. † |
IPR |
Calculate inter-percentile range. Available in XLeratorDB/statistics 2008 only |
IQR |
Calculate inter-quartile range. Available in XLeratorDB/statistics 2008 only |
KURTOSIS_P |
Calculate population kurtosis. |
KURTOSIS_S |
Calculate sample kurtosis. |
LARGE |
Calculate the kth largest value in a dataset. |
LARGE_q |
Calculate the kth largest value in a dataset. † |
PERCENTILE |
Calculate percentile. |
PERCENTILE_q |
Calculate percentile. † |
PERCENTILE_EXC |
Calculate percentile. Available in XLeratorDB/statistics 2008 only |
PERCENTILES |
Calculate any number of percentiles from a set of values . (table-valued function) |
PERCENTRANK |
Calculate the rank of a value in a dataset as a percentage of the dataset. |
PERCENTRANK_q |
Calculate the rank of a value in a dataset as a percentage of the dataset. † |
PERCENTRANKS |
Calculate the relative standing of values within a dataset . (table-valued function) |
PERCENTRANK_EXC |
Calculate the rank of a value in dataset Available in XLeratorDB/statistics 2008 only |
QUARTILE |
Calculate the specified quartile of a dataset. |
QUARTILE_q |
Calculate the specified quartile of a dataset. † |
QUARTILE_EXC |
Return the specified quartile of a dataset Available in XLeratorDB/statistics 2008 only |
RANGE |
Calculate the difference between the minimum and maximum values in a dataset. Available in XLeratorDB/statistics 2008 only |
RANK |
Return the rank of a number in a list of numbers. |
RANK_q |
Return the rank of a number in a list of numbers. † |
RANKAVG |
Return the average rank of a number in a list of numbers. Available in XLeratorDB/statistics 2008 only |
SKEWNESS_P |
Calculate the skewness for an entire population. |
SKEWNESS_S |
Calculate the sample skewness. |
SMALL |
Calculate the kth smallest value in a dataset. |
SMALL_q |
Calculate the kth smallest value in a dataset. † |
STDEV |
Return the estimated standard deviation based on a sample. |
STDEV_q |
Return the estimated standard deviation based on a sample. † |
STDEVP |
Return the standard deviation for an entire population. |
STDEVP_q |
Return the standard deviation for an entire population. † |
STDEV_P |
Calculate the standard deviation for an entire population. |
STDEV_S |
Return the estimated standard deviation based on a sample. |
VAR_P |
Calculate the variance for an entire population. |
VAR_S |
Estimate variance based on a sample, or use VAR_S to estimate the population variance from a sample of N elements with an unknown mean (the mean being calculated from the sample itself). |
|
SHAPE |
KURT |
Calculate the kurtosis of a dataset. |
KURT_q |
Calculate the kurtosis of a dataset. † |
SKEW |
Return the degree of asymmetry of a distribution. |
SKEW_q |
Return the degree of asymmetry of a distribution. † |
VAR |
Estimate variance based on a sample, or use VAR to estimate the population variance from a sample of N elements with an unknown mean (the mean being calculated from the sample itself). |
VAR_q |
Estimate variance based on a sample. † |
VARP |
Return the variance for an entire population. |
VARP_q |
Calculate population variance. † |
|
STATISTICAL INFERENCE |
SPECIFIC TESTS |
CHISQ |
Calculate the chi-square (?2) statistic. † |
CHISQ_q |
Calculate the chi-square (?2) statistic. † |
CHISQ2 |
Calculate the chi-square (?2) statistic. † |
CHISQ2_q |
Calculate the chi-square (?2) statistic. † |
CHISQN |
Calculate the chi-square (?2) statistic for data in third-normal form. |
CHISQN_q |
Calculate the chi-square (?2) statistic for data in third-normal form. † |
CHISQN2 |
Calculate the chi-square (?2) statistic for data in third-normal form. |
CHISQN2_q |
Calculate the chi-square (?2) statistic for data in third-normal form. † |
CHITEST |
Calculate the Pearson chi-square test for independence. † |
CHITEST_q |
Calculate the Pearson chi-square test for independence. † |
CHITEST2 |
Calculate the Pearson chi-square test for independence. † |
CHITEST2_q |
Calculate the Pearson chi-square test for independence. † |
CHITESTN |
Calculate the Pearson chi-square test for independence on data in third-normal form. |
CHITESTN_q |
Calculate the Pearson chi-square test for independence on data in third-normal form. † |
CHITESTN2 |
Calculate the Pearson chi-square test for independence on data in third-normal form. |
CHITESTN2_q |
Calculate the Pearson chi-square test for independence on data in third-normal form. † |
FTEST |
Return the result of an F-test. |
FTEST_q |
Return the result of an F-test. † |
KSTEST |
Compare a sample with a reference probability distribution. |
KSTEST_q |
Compare a sample with a reference probability distribution. † |
KSTEST2 |
Perform the two-sample Kolmogorov-Smirnov test to compare the distributions of the values in two samples. |
KSTEST2_q |
Perform the two-sample Kolmogorov-Smirnov test to compare the distributions of the values in two samples. † |
SFTEST |
Perform the Shapiro-Francia test for the composite hypothesis of normality. |
SFTEST_q |
Perform the Shapiro-Francia test for the composite hypothesis of normality. † |
SWTEST |
Compute Shapiro and Wilk’s W statistic and its p-value. |
SWTEST_q |
Compute Shapiro and Wilk’s W statistic and its p-value. † |
TTEST |
Calculate the probability associated with Student’s t-test. |
TTEST_q |
Calculate the probability associated with Student’s t-test. † |
TTEST_INDEP |
Perform a t-test on data in two samples assuming equal variance. |
TTEST_INDEPU |
Perform a t-test on data in two samples assuming unequal variance. |
TTEST_PAIRED |
Perform a t-test on data in two samples assuming unequal variance. |
ZTEST |
Calculate the one-tailed probability of a Z-test. |
ZTEST_q |
Calculate the one-tailed probability of a Z-test. † |
|
CORRELATION AND REGRESSION ANALYSIS |
CORRELATIONS |
CORREL |
Calculate the correlation coefficient between two datasets. |
CORREL_q |
Calculate the correlation coefficient between two datasets. † |
PEARSON |
Return the Pearson product-moment coefficient between two datasets. |
PEARSON_q |
Return the Pearson product-moment coefficient between two datasets. † |
PROB |
Calculate the probability that values in a range are between two limits. |
PROB_q |
Calculate the probability that values in a range are between two limits. † |
RSQ |
Return the Pearson product moment correlation coefficient through data points in known-y’s and known-x’s. |
RSQ_q |
Return the Pearson product moment correlation coefficient through data points in known-y’s and known-x’s. † |
|
LINEAR REGRESSIONS |
EXPPRED |
Calculate the predicted value for a dependent variable using the coeffiecients from a previously run mutlivariate exponential regression. Available in XLeratorDB/statistics 2008 only |
FORECAST |
Calculate a future value by using existing values. |
FORECAST_q |
Calculate a future value by using existing values. † |
GROWTH |
Calculate predicted exponential growth by using existing data. |
GROWTH_q |
Calculate predicted exponential growth by using existing data. † |
GROWTHMX |
Calculate values along an exponential trend. † |
GROWTHMX_q |
Calculate values along an exponential trend. † |
INTERCEPT |
Calculate the point at which a line will intersect the y-axis by using existing x-values and y-values. |
INTERCEPT_q |
Calculate the point at which a line will intersect the y-axis by using existing x-values and y-values. † |
LINEST |
Calculate an ordinary least squares (OLS) solution for a series of x- and y-values. † |
LINEST_q |
Calculate an ordinary least squares (OLS) solution for a series of x- and y-values. † |
LMPRED |
Calculate the predicted value for a dependent variable using the coefficients from a previously run multivariate linear regression. Available in XLeratorDB/statistics 2008 only |
LOGEST |
Calculate an exponential curve that best fits a series of x- and y-values. † |
LOGEST_q |
Calculate an exponential curve that best fits a series of x- and y-values. † |
SLOPE |
Calculate the slope of the linear regression through the data points in the known x-values and y-values. |
SLOPE_q |
Calculate the slope of the linear regression through the data points in the known x-values and y-values. † |
TREND |
Calculate the values along a linear trend. |
TREND_q |
Calculate the values along a linear trend. † |
TRENDMX |
Calculate values along a linear trend. † |
TRENDMX_q |
Calculate values along a linear trend. † |
WLS *!* |
Calculate a weighted least squares (WLS) solution for a series of x- and y-values and their associated weights. (table-valued function) Available in XLeratorDB/statistics 2008 only |
WLS_q *!* |
Calculate a weighted least squares (WLS) solution for a series of x- and y-values and their associated weights. (table-valued function) Available in XLeratorDB/statistics 2008 only |
|
LOGISTIC REGRESSIONS |
LOGIT |
Calculate the binary logistic regression coefficients from a table of x-values (the independent variables) and dichotomous y-values (the dependent variable). (table-valued function) |
LOGITPRED |
Calculate the probability that Y = 1 given a set of coefficients from a logistic regression and a set of x-values. |
LOGITPROB |
Calculate the probability that Y = 1 given a set of coefficients from a logistic regression Available in XLeratorDB/statistics 2008 only |
LOGITSUM |
Calculate the binary logistic regression coefficients from a table of grouped x-values (the independent variables) with counts of the successes and failures for each group. (table-valued function) |
ROCTable |
Show the calculation of the area under the ROC curve. (table-valued function) |
VIF |
Calculate the R-squared, tolerance, and the variance inflation factor for a set of independent variables. (table-valued function) |
|
DATA COLLECTION |
SAMPLING |
KMEANS |
Perform k-means clustering in N-dimensions. Available in XLeratorDB/statistics 2008 only (table-valued function) |
STEYX |
Return the standard error of the predicted y-value for each x in a regression. |
STEYX_q |
Return the standard error of the predicted y-value for each x in a regression. † |
|
INTEROBSERVER AGREEMENT |
ICC |
Calculate the intra-class coefficient. † |
ICC_TV |
Calculate the intra-class coefficient. (table-valued function) |
KAPPA_COHEN |
Calculate Cohen’s kappa (?) or weighted kappa as an index of inter-rater agreement between 2 raters. † |
KAPPA_COHEN_TV |
Calculate Cohen’s kappa (?) or weighted kappa as an index of inter-rater agreement between 2 raters. (table-valued function) |
KAPPA_FLEISS |
Calculate Fleiss’ kappa (?) as an index of inter-rater agreement between m raters on categorical data. † |
KAPPA_FLEISS_TV |
Calculate Fleiss’ kappa (?) as an index of inter-rater agreement between m raters on categorical data. (table-valued function) |
KENDALLT |
Calculate Kendall’s tau (t), a non-parametric measure of association based on the number of concordances and discordances in paired observations. † |
KENDALLT_TV |
Calculate Kendall’s tau (t), a non-parametric measure of association based on the number of concordances and discordances in paired observations. (table-valued function) |
KENDALLW |
Calculate Kendall’s coefficient of concordance (w) as an index of inter-rater reliability for ordinal data. † |
KENDALLW_TV |
Calculate Kendall’s coefficient of concordance (w) as an index of inter-rater reliability for ordinal data. (table-valued function) |
MCNEMAR |
Perform McNemar’s chi-squared test for symmetry of rows and columns in a two-dimensional contingency table. † |
MCNEMAR_TV |
Perform McNemar’s chi-squared test for symmetry of rows and columns in a two-dimensional contingency table. (table-valued function) |
PSIGNRANK |
Calculate the distribution function of the Wilcoxon Signed Rank statistic. |
RANK_AVG |
Calculate the ranks for a collection of x- and y-values. (table-valued function) |
SPEARMAN |
Calculate Spearman’s rank correlation coefficient (?). † |
SPEARMAN_TV |
Calculate Spearman’s rank correlation coefficient (?). (table-valued function) |
WMPSR |
Calculate the Wilcoxon matched-pair signed-rank test. † |
WMPSR_TV |
Calculate the Wilcoxon matched-pair signed-rank test. (table-valued function) |
|
DISTRIBUTIONS |
BETA_DIST |
Calculate the probability density function or cumulative distribution function of a beta distribution for x with shape parameters a and ß. |
BETADIST |
Calculate the beta cumulative probability density function. |
BETAINV |
Calculate the quartiles of the beta cumulative distribution function. |
BETAPDF |
Calculate the probability density function for the beta distribution. |
BINOM_DIST_RANGE |
Calculate the probability of a trial result using a binomial distribution. |
BINOMDIST |
Calculate the binomial distribution. |
BINOMINV |
Calculate the value of number of success in the binomial distribution given the cumulative distribution function. |
BIVAR |
Calculate bivariate normal probabilities. |
CAUCHY |
Calculate the probability density function or the lower cumulative distribution function of the Cauchy distribution. |
CAUCHYINV |
Calculate the inverse lower cumulative distribution of the Cauchy distribution. |
CHI2NC |
Calculate the lower cumulative distribution function of the non-central chi-square distribution. |
CHI2NCINV |
Calculate the inverse of the lower cumulative distribution function of the non-central chi-square distribution. |
CHIDIST |
Calculate the one-tailed probability of the chi-square distribution. |
CHIINV |
Calculate the inverse of the one-tailed probability of the chi-square distribution. |
CHISQ_DIST |
Calculate the probability density or the lower cumulative probability of a chi-squared distribution for x and a number of degrees of freedom. |
CHISQ_DIST_RT |
Calculate the upper distribution of a chi-squared distribution for x and a number of degrees of freedom. |
CHISQ_INV |
Calculate the inverse of the left-tailed probability of a chi-squared distribution. |
CHISQ_INV_RT |
Calculate the inverse of the right-tailed probability of a chi-squared distribution. |
CHISQPDF |
Calculate the probability density function of the chi square distribution. |
CONFIDENCE |
Calculate a value that you can use to construct a confidence interval for a population mean. |
CONFIDENCE_NORM |
Calculate the confidence interval for a population mean, using a normal distribution. |
CONFIDENCE_T |
Calculate a confidence interval when you don't know the population standard deviation and are using the sample standard deviation instead. |
CRITBINOM |
Calculate the smallest value for the cumulative binomial distribution that is greater than or equal to a criterion value. |
DIGAMMA |
Calculate digamma(z), the logarithmic derivative of the gamma function. Available in XLeratorDB/statistics 2008 only |
EXPDIST |
Calculate the probability density function or the upper cumulative distribution function of the Exponential distribution. |
EXPONDIST |
Calculate an exponential distribution that is equivalent to the function used in EXCEL. |
EXPINV |
Calculate the inverse of the cumulative distribution function of the exponential distribution. |
FDIST |
Calculate the F probability distribution. |
F_DIST |
Calculate the probability density or the lower cumulative probability of an F-distribution for x and degrees of freedom for 2 independent random variables. |
F_DIST_RT |
Calculate upper cumulative probability of an F-distribution for x and degrees of freedom for 2 independent random variables. |
FINV |
Calculate the inverse of the F probability distribution. |
F_INV |
Calculate the inverse of the F lower probability distribution. |
F_INV_RT |
Calculate the inverse of the F upper probability distribution. |
FPDF |
Calculate the probability density function of the F distribution. |
FISHER |
Calculate the Fisher transformation at x. |
FISHERINV |
Calculate the inverse of the Fisher transformation. |
GAMMADIST |
Calculate the gamma distribution. |
GAMMAINV |
Calculate the inverse of the cumulative gamma distribution. of the cumulative gamma distribution |
GAMMAP |
Calculate the regularized gamma function P(a, x). |
GAMMAQ |
Calculate the regularized gamma function Q(a, x). |
GEOMETRIC |
Calculate the probability mass function of the geometric distribution. |
GEOMETRICP |
Calculate the cumulative distribution function of the geometric distribution. |
GEOMETRICINV |
Calculate the inverse of the cumulative distribution function of the geometric distribution. |
HYPGEOM_DIST |
Calculate the pmf or the cdf of the hypergeometric distribution. |
HYPGEOM_INV |
Calculate the quantiles of the hypergeometric distribution. |
HYPGEOMDIST |
Calculate the hypergeometric distribution. |
HYPGEOMDISTP |
Calculate the lower cumulative distribution of the hypergeometric function. |
HYPGEOMDISTPINV |
Calculate the inverse of the cumulative distribution function of the hypergeometric distribution. |
HYPGEOMDISTQ |
Calculate the upper cumulative distribution of the hypergeometric function. |
INVGAMMAP |
Calculate the inverse of the incomplete gamma function P(a,x). |
KScdf |
Compute the cumulative probability P[Dn >= x] of the Kolmogorov-Smirnov distribution with sample size n at x. |
KSccdf |
Compute the complementary cumulative probability P[Dn >= x] of the Kolmogorov-Smirnov distribution with sample size n at x. |
KSP |
Calculate the Kolmogorov-Smirnov (KS) cumulative distribution function. |
KSPINV |
Calculate the inverse of the Kolmogorov-Smirnov (KS) cumulative distribution function. |
KSQ |
Calculate the complementary Kolmogorov-Smirnov (KS) cumulative distribution function, Qks = 1 - Pks. |
KSQINV |
Calculate the inverse of the complementary Kolmogorov-Smirnov (KS) cumulative distribution function, Qks = 1 - Pks. |
LAPLACE |
Calculate the probability density function or the lower cumulative distribution function of the Laplace distribution. |
LAPLACEINV |
Calculate the inverse lower cumulative distribution of the Laplace distribution. |
LOGINV |
Calculate the inverse of the lognormal cumulative distribution function of x where ln(x) is normally distributed within the parameters mean and standard deviation. |
LOGISTIC |
Calculate the probability density function or the lower cumulative distribution function of the logistic distribution. |
LOGISTICINV |
Calculate the inverse lower cumulative distribution of the logistic distribution. |
LOGNORM_DIST |
Calculate the probability density function or the cumulative distributive function of the normal distribution of x, when ln(x) is normally distributed with parameters µ and s. |
LOGNORM_INV |
Calculate the inverse of the lognormal distribution function of x, when ln(x) is normally distributed with parameters µ and s. |
LOGNORMDIST |
Calculate the lognormal cumulative distribution function of x where ln(x) is normally distributed within the parameters mean and standard deviation. |
LOGNORMPDF |
Calculate the probability density function of the lognormal distribution. |
NCFCDF |
Calculate the lower cumulative distribution function of the non-central F distribution. |
NCFINV |
Calculate the inverse of the lower cumulative distribution function of the non-central F distribution. |
NCFPDF |
Calculate the probability density function of the non-central F distribution. |
NCHISQPDF |
Calculate the probability density function of the non-central chi square distribution. |
NCTCDF |
Calculate the lower cumulative distribution function of the non-central T distribution. |
NCTINV |
Calculate the inverse of the lower cumulative distribution function of the non-central T distribution. |
NCTPDF |
Calculate the probability density function of the non-central T distribution. |
NEGBINOM_DIST |
Calculate the probability mass function or the cumulative distributive function of the negative binomial distribution. |
NEGBINOMDIST |
Calculate the negative binomial distribution. |
NEGBINOMDISTP |
Calculate the cumulative distribution function of the negative binomial distribution. |
NEGBINOMINV |
Calculate the smallest value of x such that NEGBINOMDISTP(x, number of successes, probability of success) >= p. |
NEGHYPGEOM_DIST |
Calculate the probability mass function or the cumulative distributive function of the negative hypergeometric distribution. |
NEGHYPGEOM_INV |
Calculate the quantiles of the negative hypergeometric distribution. |
NORMAL |
Calculate the probability density function for the standard normal distribution. |
NORM_S_DIST |
Calculate the probability density function or the lower cumulative distribution function of the standard normal distribution in SQL Server. |
NORMDIST |
Calculate the normal distribution for the specified mean and standard deviation. |
NORMINV |
Calculate the inverse of the normal cumulative distribution function (cdf). |
NORMSDIST |
Calculate the standard normal cumulative distribution function. |
NORMSINV |
Calculate the inverse of the standard normal distribution in SQL Server. |
POISSON |
Calculate the Poisson distribution. |
POISSON_DIST |
Calculate the probability mass function or the lower cumulative probability of a Poisson distribution for a given number of events occurring in a fixed interval given the rate. |
POISSONINV |
Calculate the inverse of the cumulative distribution function of the Poisson distribution. |
STANDARDIZE |
Calculate a normalized value from a distribution characterized by a mean and standard deviation. |
STUDENTST |
Calculate Student’s t-distribution. |
TDIST |
Calculate the probability for the Student t-distribution where a numeric value (x) is a calculated value of t for which the probability is to be computed. |
T_DIST |
Calculate the probability density function and the left-tailed cumulative probability distribution of Student's t-distribution. |
T_DIST_2T |
Calculate the two-tailed cumulative probability distribution of Student's t-distribution. |
T_DIST_RT |
Calculate the right-tailed cumulative probability distribution of Student's t-distribution. |
TINV |
Calculate the t-value of the Student's t-distribution as a function of the probability and the degrees of freedom. |
T_INV |
Calculate the inverse of the left-tailed cumulative probability distribution of Student's t-distribution. |
T_INV_2T |
Calculate the inverse of the two-tailed distribution of Student's t-distribution. |
TPDF |
Calculate the probability density function of the T distribution. |
TRIGAMMA |
Calculate trigamma(z) the second derviative of the natural log of the gamma function. Available in XLeratorDB/statistics 2008 only |
UNIFORM |
Calculate the probability density function or the lower cumulative distribution function of the uniform distribution. |
UNIFORMINV |
Calculate the inverse of the lower cumulative distribution of the uniform distribution. |
WEIBULL |
Calculate the Weibull distribution. |
WEIBULLINV |
Calculate the inverse of the cumulative distribution function of the Weibull distribution. |
|
COMBINATORICS |
BETA |
Calculate the beta function, also known as the Euler integral. |
BETAI |
Calculate the incomplete beta function. |
BICO |
Calculate the binomial coefficient. |
FACTLN |
Calculate the natural logarithm of a factorial. |
FACTORIALPOWER |
Calculate rising or falling factorials. |
GAMMA |
Invoke the (complete) gamma function G(x). |
GAMMAINC |
Calculate the incomplete gamma function. |
GAMMALN |
Calculate the natural logarithm of the (complete) gamma function G(x). |
LCHOOSE |
Calculate the natural logarithm of the binomial coefficient. |
LPERMUT |
Calculate the natural logarithm of the PERMUT function. |
LPERMUTA |
calculate the natural logarithm of the PERMUTATIONA function. |
MULTINOM |
calculate the probability distribution of the outcomes of a multinomial experiment. |
PERMUT |
Calculate the number of permutations for a given number objects that can be selected from a number of objects. |
PERMUTATIONA |
Calculate the number of permutations with replacement. |
STIRLING1 |
Calculate a Stirling Number of the first kind. Available in XLeratorDB/statistics 2008 only |
STIRLING2 |
Calculate a Stirling Number of the second kind. Available in XLeratorDB/statistics 2008 only |
|
XLDB_STATISTICS_VERSION |
Displays package Version and Licensing Information |
|
SAMPLE DATA |
Sample data for certain XLeratorDB/statistics functions documentation |