Welch's t Test
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High Quality Content by WIKIPEDIA articles! In statistics, Welch's t test is an adaptation of Student's t-test intended for use with two samples having possibly unequal variances. As such, it is an approximate solution to the Behrens Fisher problem. Welch's t-test defines the statistic t by the following formula: t = {overline{X}1 - overline{X}2 over sqrt{ {s1^2 over N1} + {s2^2 over N2} }}, where overline{X}{i}, s{i}^{2} and Ni are the ith sample mean, sample variance and sample size, respectively. Unlike in Student's t-test, the denominator is not based on a pooled variance estimate. The degrees of freedom associated with this variance estimate is approximated using the Welch-Satterthwaite equation: nu = {{left( {s1^2 over N1} + {s2^2 over N2}right)^2 } over {{s1^4 over N1^2 cdot nu1}+{s2^4 over N2^2 cdot nu2}}}={{left( {s1^2 over N1} + {s2^2 over N2}right)^2 } over {{s1^4 over N1^2 cdot left({N1-1}right)}+{s2^4 over N2^2 cdot left({N2-1}right)}}} ., Here i = Ni 1, the degrees of freedom associated with the ith variance estimate.
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GarantieWeitere Informationen
- Allgemeine Informationen
- GTIN 09786131184031
- Editor Lambert M. Surhone, Miriam T. Timpledon, Susan F. Marseken
- EAN 9786131184031
- Format Fachbuch
- Titel Welch's t Test
- Herausgeber Betascript Publishing
- Anzahl Seiten 76
- Genre Mathematik
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