Tau calculator

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Kendall's Tau; Kendall's W; Intra-Class-Correlation; Kendall's Tau Calculator Medical example data. If you want to calculate Kendall's tau, just copy your data into the upper table and select two ordinal variables. Then the Kendall's Tau will be calculated automatically. Afterwards you will get the results of the Kendall's Tau in the following Download Tau Love Calculator latest version for Windows free. Tau Love Calculator latest update: Ma

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Kendall's Tau-aOverviewKendall's Tau-a is a nonparametric measure of association used to assess the strength and direction of the relationship between two ordinal variables. It evaluates the concordance between paired observations, providing a coefficient that ranges from -1 to +1. Values close to +1 indicate a strong positive association, values close to -1 indicate a strong negative association, and values near 0 suggest little or no association.Kendall's Tau-a FormulaThe formula for Kendall's Tau-a is given by:\tau_a = \dfrac{P - Q}{0.5 * N * (N - 1)}Where:P is the number of concordant pairs.Q is the number of discordant pairs.N is the total number of observations.Kendall's Tau-a measures the association between two variables based on the difference between concordant and discordant pairs, normalized by the number of observations.Constructing Kendall's Tau-aTo calculate Kendall's Tau-a, we need two ordinal variables. In this example, we use the mtcars dataset, comparing the variables cyl (number of cylinders) and gear (number of gears).# R Code for Kendall's Tau-a Example# Calculate Kendall's Tau-a for two ordinal variables (e.g., 'cyl' and 'gear' in 'mtcars' dataset)library(DescTools)contingency_table Steps in Model Construction:Select two ordinal variables for comparison.Calculate the number of concordant and discordant pairs between the variables.Apply the Kendall's Tau-a formula to determine the association between the variables.Model InterpretationAfter calculating Kendall's Tau-a, the output provides a single value that indicates the strength and direction of the association between the two ordinal variables.Key metrics from Kendall's Tau-a include:Kendall's Tau-a (\tau_a): The calculated value is -0.3327. This negative value suggests a moderate negative association between the two variables, meaning that higher values of one variable are somewhat associated with lower values of the other. A Tau-a value close to -1 would indicate a stronger negative association, while values near 0 imply little or no association.This result is helpful for understanding the ordinal relationship between two variables, with Kendall's Tau-a providing an interpretable measure of association that is resistant to outliers.ConclusionKendall's Tau-a is a valuable tool for analyzing ordinal associations between two variables, offering a straightforward interpretation of the strength and direction of their relationship.Key Takeaways:Nonparametric Measure: Kendall's Tau-a does not assume a specific distribution, making it suitable for ordinal data.Interpretation: The coefficient provides an interpretable measure of association between two ordinal variables.Concordance and Discordance: The calculation relies on comparing pairs of observations, making it sensitive to their ordering.Explore our AI-Powered Statistical Tool or Statistics Calculator to calculate Kendall's Tau-a on your own datasets. | 'ln' | 'log' | 'log2' | 'log10' | 'hypot' | 'sin' | 'asin' | 'sinh' | 'asinh' | 'sinc' | 'cos' | 'acos' | 'cosh' | 'acosh' | 'tan' | 'tanh' | 'atan' | 'atanh' | 'atan2' | 'sec' | 'asec' | 'sech' | 'asech' | 'csc' | 'acsc' | 'csch' | 'acsch' | 'cot' | 'acot' | 'coth' | 'acoth' | 'abs' | 'nabs' | 'sign' | 'min' | 'max' | 'avg' | 'gcd' | 'lcm' | 'combin' | 'permut' | 'hgd' | 'interp' ; argument-list: | expression | argument-list ',' expression ;primary-expression: | constant | '(' expression ')' ; constant: | named-constant | numeric-constant ; named-constant: | 'e' | 'π' | 'pi' | 'τ' | 'tau' ; numeric-constant: | integer-part [ fraction-part ] [ exponent-part ] | fraction-part [ exponent-part ] ; integer-part: | digit { digit } ; digit: | '0' | '1' | '2' | '3' | '4' | '5' | '6' | '7' | '8' | '9' ; fraction-part: | '.' integer-part ; exponent-part: | exponent-char [ exponent-sign ] integer-part ; exponent-char: | 'E' | 'e' ; exponent-sign: | '+' | '-' ;uses AcknowledgementsWe would like to thank MathJS for inspiring this calculator and some of the source code.

sphNG-tau-calculator/README.md at master dh4gan/sphNG-tau-calculator

Last updated: Oct 01, 2024 On this page On this page Introduction Imagine a calculator that is not constrained to under 16 significant digits. Dream no longer, for this calculator will perform most scientific functions to hundreds of significant digits. This was too good to keep to ourselves, so please enjoy.Constants▼Named Constants▼The following named constants are available: Name(s) Approximate value e 2.718281828459045… π pi 3.141592653589793… τ tau 6.283185307179586… Numeric Constants▼A numeric constant can have an integer part, a fractional part, or both, optionally followed by an exponent part: an integer part consists of one or more decimal digits a fractional part consists of a radix point . followed by one or more decimal digits an exponent part consists of E or e, optionally followed by + or -, followed by one or more decimal digits Examples 1 .5 1.5 1e2 .5e2 1.5e2 1E2 .5E2 1.5E2 1e+2 .5e+2 1.5e+2 1E+2 .5E+2 1.5E+2 1e-2 .5e-2 1.5e-2 1E-2 .5E-2 1.5E-2 Operators▼The following operators are available for use in expressions: Category Precedence Associativity Operator Description Example Primary highest none () Subexpression (1 + e) Postfix 2nd highest left to right () Function lcm(3, 4) ! Factorial 4! Power 3rd highest right to left ^ Exponentiation 2^6 Prefix 4th highest right to left + Unary plus +3 - Negation -7 √ Square Root √2 Multiplicative 5th highest left to right Implicit multiplication 2pi * Explicit multiplication 2 * pi / Division pi / 2 % Remainder 12 % 5 Additive lowest left to right +. Kendall's Tau; Kendall's W; Intra-Class-Correlation; Kendall's Tau Calculator Medical example data. If you want to calculate Kendall's tau, just copy your data into the upper table and select two ordinal variables. Then the Kendall's Tau will be calculated automatically. Afterwards you will get the results of the Kendall's Tau in the following

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Correlation Coefficients > Kendall’s Tau (Kendall Rank Correlation Coefficient) Contents:What is Kendall’s Tau?When to use Kendall’s TauTypes of Kendall’s TauExample ProblemPerfect AgreementCalculating Statistical SignificanceWhat is Kendall’s Tau?Kendall’s Tau is a non-parametric measure of relationships between columns of ranked data. The Tau correlation coefficient returns a value of 0 to 1, where:0 is no relationship,1 is a perfect relationship.A quirk of this test is that it can also produce negative values (from -1 to 0). Unlike a linear graph, a negative relationship doesn’t mean much with ranked columns (other than you perhaps switched the columns around), so just remove the negative sign when you’re interpreting Tau. Several version’s of Tau exist.Tau-A and Tau-B are usually used for square tables (with equal columns and rows). Tau-B will adjust for tied ranks.Tau-C is usually used for rectangular tables. For square tables, Tau-B and Tau-C are essentially the same.Most statistical packages have Tau-B built in, but you can use the following formula to calculate it by hand: Kendall’s Tau = (C – D / C + D) Where C is the number of concordant pairs and D is the number of discordant pairs.When to use Kendall’s TauThree popular indices included in most statistical software packages are the Pearson product moment correlation, Spearman’s rank-order correlation and Kendall’s tau correlation. Nonparametric methods such as Kendall’s tau and Spearman’s rank-order correlation coefficients are recommended for non-normal data while the Pearson product moment correlation coefficient is commonly used for normally distributed data.Several guidelines exist to determine when to use each of these correlation coefficients. One guideline is based on the type of data being analyzed. PPMC is suitable only for interval data, whereas Spearman’s and Kendall’s correlation coefficients can be used for either ordinal or interval data [1].Other guidelines suggest which correlation coefficient is more appropriate for data involving different types of variables. Kendall’s tau is more suitable for data with at least one ordinal variable [2]. Other researchers have suggested using Spearman’s correlation coefficients in similar scenarios [3, 4, 5]. However, all of these correlation coefficients can also be computed for interval data (e.g., continuous data) [1].Kendall [6] claims that for many practical purposes, tau is preferable partly because when estimating a correlation, the population parameter being estimated has a simpler interpretation. Kendall’s tau is less sensitive to outliers than Spearman’s Rho and is often preferred due to its simplicity and ease of interpretation.Types of Kendall’s TauThere are various versions of Kendall’s Tau available. Tau-A is the most basic form. It isn’t commonly used because Tau-B and Tau-C are easier to interpret and are more robust to tied ranks. Tau-B, which adjusts for tied ranks, is commonly used for square tables, where the number of columns and Rows are equal. Tau-C is primarily used for rectangular tables. For square tables, Tau-B and Tau-C are essentially the same. Most statistical packages include Tau-B as a built-in feature, but you can also calculate it manually using the formula:Kendall’s Tau = (C – D / C + D),where C represents the number of concordant pairs and D represents the number of discordant pairs.TypeDescriptionTied ranks adjustment?Suitable for…Tau-AThe basic version of Kendall’s tau.NoSquare tablesTau-BAdjusts for tied ranks by dividing the number of concordant pairs and discordant pairs by the total number of possible pairs.YesSquare tablesTau-CAdjusts for tied ranks by using a different tied ranks formula to accommodate rectangular tables.YesRectangular tablesKendall’s tau-C adjusts for tied ranks by using a different definition of concordant and discordant pairs. In the basic definition of concordant and discordant pairs used in Tau-A, two pairs are considered in agreement if they match in order, and in disagreement if they differ in order. However, this definition doesn’t consider the presence of tied ranks.For instance, let’s consider the following two rankings of 3 items:Ranking 1: A B CRanking 2: A C BAccording to the original definition, these two rankings would be regarded as discordant because they differ in order. However, A and B are tied in both rankings with A B C in both ranking 1 and 2.Tau-C takes into account the number of tied ranks by considering the number of concordant and discordant pairs that would occur if there were no tied ranks. In the example above, there would be 1 concordant pair and 0 discordant pairs if no ties were present. Therefore, Tau-C would consider these two rankings to be concordant.The formula for Tau-C is as follows:τc = (C – D) / (T – t)where:C = the number of concordant pairsD = number of discordant pairsT = total number of possible pairst = number of tied ranksTau-C provides a more accurate measure of the association between two rankings than Tau-A or Tau-B when there are tied ranks. However, it is also computationally more intensive.Example ProblemExample Question: Two interviewers ranked 12 candidates (A through L) for a position. The results from most preferred to least preferred are:Interviewer 1: ABCDEFGHIJKL.Interviewer 2: ABDCFEHGJILK.Calculate the Kendall Tau correlation. Step 1: Make a table of rankings. The first column, “Candidate” is optional and for reference only. The rankings for Interviewer 1 should be in ascending order (from least to greatest). Step 2: Count the number of concordant pairs, using the second column. Concordant pairs are how many larger ranks are below a certain rank. For example, the first rank in the second interviewer’s column is a “1”, so all 11 ranks below it are larger. However, going down the list to the third

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Loss of generality, we reformulate problem (50) as$$ \begin{gathered} \{ {\overline{\mathbf{F}}}_{R} ,{\overline{\mathbf{W}}}_{R} \} = \mathop {\arg \max }\limits_{{\{ {\mathbf{F}}_{R} ,{\mathbf{W}}_{R} \} }} { \tilde{\mathcal{R}}}{(}{\mathbf{F}}_{R} ,{\mathbf{W}}_{R} {)}{,} \hfill \\ {s}{.t}{. }{\mathbf{f}}_{O} (\overline{\theta }_{\tau } ) \in {\mathcal{C}}_{BO} ,\tau = 1 \cdots M_{T} , \hfill \\ {\mathbf{f}}(\overline{\gamma }_{\tau } ) = {\mathbf{f}}_{I} (\varphi_{{p_{0} }} ) \odot {\mathbf{f}}_{O} (\overline{\theta }_{\tau } ),\overline{\gamma }_{\tau } = \varphi_{{q_{0} }} + \overline{\theta }_{\tau } , \hfill \\ {\mathbf{w}}_{O} (\overline{\phi }_{\varepsilon } ) \in {\mathcal{C}}_{MO} ,\varepsilon = 1 \cdots M_{R} , \hfill \\ {\mathbf{w}}(\overline{\eta }_{\tau } ) = {\mathbf{w}}_{I} (\vartheta_{{p_{0} }} ) \odot {\mathbf{w}}_{O} (\overline{\phi }_{\tau } ),\overline{\eta }_{\varepsilon } = \vartheta_{{p_{0} }} + \overline{\phi }_{\varepsilon } , \hfill \\ \end{gathered} $$ (51) where \({\mathbf{F}}_{R} = [{\mathbf{f}}(\overline{\gamma }_{1} ), \cdots ,{\mathbf{f}}(\overline{\gamma }_{{M_{T} }} )]\) and \({\mathbf{W}}_{R} = [{\mathbf{w}}(\overline{\eta }_{1} ), \cdots ,{\mathbf{w}}(\overline{\eta }_{{M_{R} }} )]\). The above optimization problem is essentially the same as (35). Therefore problem (51) can be solved by the proposed AWCEO algorithm with some parameters adjustment.When applying the AWCEO algorithm to the problem (51), it becomes necessary to redefine certain variables. The probability matrix associated with the transmitter is redefined as \({\mathbf{P}} \triangleq \{ p_{\mu \tau } \} \in {\mathbb{R}}^{{N_{B} \times M_{T} }}\), where \(p_{\mu \tau }\) represents the probability of selecting the μ-th column vector in \({\mathbf{C}}_{B}^{{(q_{0} )}}\) as \({\mathbf{f}}(\overline{\gamma }_{\tau } ),1 \le \tau \le M_{T}\). Similarly, the probability matrix corresponding to the receiver is redefined as \({\mathbf{Q}} \triangleq \{ q_{\upsilon \varepsilon } \} \in {\mathbb{R}}^{{N_{A} \times M_{R} }}\), where \(q_{\upsilon \varepsilon }\) signifies the probability of choosing the υ-th column vector in \({\mathbf{C}}_{M}^{{(p_{0} )}}\) as \({\mathbf{w}}(\overline{\eta }_{\varepsilon } ),1 \le \varepsilon \le M_{R}\). These redefinitions allow for a more precise and targeted application of the AWCEO algorithm to the specific problem under consideration, enabling a more efficient and effective solution to be obtained. The initial probability matrices are calculated by$$ p_{\mu \tau } = t_{\mu } /\sum\nolimits_{\mu = 1}^{{N_{B} }} {t_{\mu } } ,t_{\mu } = \mathop {\max }\limits_{k} \left| {{\mathbf{H}}_{{p_{0} ,q_{0} }}^{a} (k,\mu )} \right|{ ,} $$ (52) $$ q_{\upsilon \varepsilon } = r_{\upsilon } /\sum\limits_{\upsilon = 1}^{{N_{A} }} {r_{\upsilon } } ,r_{\upsilon } = \mathop {\max }\limits_{k} \left| {{\mathbf{H}}_{{p_{0} ,q_{0} }}^{a} (\upsilon ,k)} \right|{.} $$ (53) The input codebook matrices \({\mathbf{C}}_{B}\) and \({\mathbf{C}}_{M}\) in Algorithm 1 should be replaced by \({\mathbf{C}}_{B}^{{(q_{0} )}}\) and \({\mathbf{C}}_{M}^{{(p_{0} )}}\), respectively. Combined the MGH-v method and the AWCEO algorithm, both the inner beamformers

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Gamma, Sigma Phi, Sigma Phi Delta, Sigma Phi Epsilon, Sigma Chi, Sigma Alpha, Sigma Alpha Iota, Sigma Gamma Rho, Sigma Delta Tau, Sigma Iota Alpha, Sigma Kappa, Sigma Lambda Gamma, Sigma Lambda Upsilon, Sigma Iota Rho, Sigma Phi Rho, Sigma Sigma Sigma Tau Sub-Forums: Tau Delta Phi, Tau Epsilon Phi, Tau Kappa Epsilon, Tau Beta Sigma Upsilon Phi Sub-Forums: Phi Beta Sigma, Phi Gamma Delta, Phi Delta Theta, Phi Iota Alpha, Phi Kappa Theta, Phi Kappa Sigma, Phi Kappa Tau, Phi Kappa Psi, Phi Lambda Chi, Phi Mu Alpha Sinfonia, Phi Mu Delta, Phi Sigma Kappa, Phi Sigma Phi, Phi Beta Chi, Phi Mu, Phi Sigma Sigma, Phi Alpha Delta, Phi Gamma Nu, Phi Delta Phi, Phi Lambda Upsilon, Phi Sigma Pi, Phi Beta, Phi Eta Psi Chi Sub-Forums: Chi Phi, Chi Psi, Chi Omega, Chi Upsilon Sigma, Chi Alpha Omega Psi Sub-Forums: Psi Upsilon Omega Sub-Forums: Omega Delta Phi, Omega Psi Phi, Omega Phi Beta, Omega Phi Chi, Omega Phi Alpha Non Greek Letter (NGL) Sub-Forums: Acacia, Farmhouse, Triangle, Groove Phi Groove, Swing Phi Swing All times are GMT -4. The time now is 06:24 PM.. Kendall's Tau; Kendall's W; Intra-Class-Correlation; Kendall's Tau Calculator Medical example data. If you want to calculate Kendall's tau, just copy your data into the upper table and select two ordinal variables. Then the Kendall's Tau will be calculated automatically. Afterwards you will get the results of the Kendall's Tau in the following

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Specificity of a gene. In other words, tau can assign a gene to a single tissue, not multiple tissues. Since the definition of tissue-specific genes is considered to be “specifically expressed in one or several tissues”, tau method needs to be improved by additional statistical procedures to assign genes to multiple tissues for specific expression. In this study, estimation of statistically significant interval from maximum expression was calculated to assign a gene to second and/or more tissues for the genes having high tau scores. Therefore, this study makes a major contribution to research on determining tissue-specificity by extending the already effective tau method allowing one-to-many mappings between genes and tissues. Throughout this paper, the term extended tau will refer to our novel and rigorous approach for assigning genes to multiple tissues for specific expression. More detailed and accurate tissue specificity of gene expression will enhance understanding evolution of tissues [36,37,38,39], relationship between expressions and main functions of genes [20, 40]; and others [41] in various organisms such as mouse [42], Drosophila [40] and Arabidopsis thaliana [43].MethodsData retrievalRNA-seq data for gene expression profiles of 27 human tissues from Fagerberg et. al (EMTAB-1733) [44], 32 human tissues from Uhlen Lab (EMTAB-2836) [45], 53 human tissues from GTEx Project (EMTAB-5214) [28], 56 human tissues from FANTOM5 Project (EMTAB-3358) [46] and 13 human tissues from ENCODE Project (EMTAB-4344) [47, 48] were downloaded via Expression Atlas [49] and ArrayExpress [50]. Detailed information about the raw expression data, number of genes, and tissues are explained in Supplementary Tables 1 and 2, respectively. All calculations were performed using protein-coding genes and tissue types not cell types from the datasets. All tissue types were investigated and grouped according to localization determined via Brenda Tissue Ontology (BTO) [51].Categorization of genes based on expression levelGenes were categorized according to their expression level patterns and tau scores. Genes expressed \(\le\) 1.0 FPKM or TPM in all tissues were designated as “Null expression” and were excluded from subsequent analysis. Then, expression levels were transformed based on log(2), and the tau score, ranging from 0 to 1, was calculated for each gene [19] using the formula below where \(x_{i}\) is expression of a gene in tissue i and n is number of tissues.$$\begin{aligned} \tau =\frac{ \sum _{i= 1}^{n}\left( 1-\hat{x}_{i} \right) }{n-1} \end{aligned}$$$$\begin{aligned} \hat{x}_{i}= \frac{x_{i}}{\max _{1 \le i\le n} x_{i}} \end{aligned}$$If tau score is \((\tau )\ge 0.85\) for a given gene, that gene is marked to have Specific expression. The genes having \(\tau were classified as Wide-spread expression. Genes which have expression values \( in all tissues was denoted as Weak expression [8]. Tau score was calculated for weakly expressed genes but their scores were ignored during tissue specificity assessment. Log transformation was used only during tau calculation; after that, all other calculations were performed using raw expression values. Rigorous tissue-specificity classification was proceeded with the genes with \(\tau \ge 0.85\) and expression value \(> 10\) in all tissues.Estimation of statistically significant intervalF-test [52] was used to verify the equality of variance between datasets.