{"id":4484,"date":"2026-07-29T17:01:13","date_gmt":"2026-07-29T15:01:13","guid":{"rendered":"https:\/\/ellistat.com\/?post_type=guide-dutilisateur&p=4484"},"modified":"2026-07-30T10:32:38","modified_gmt":"2026-07-30T08:32:38","slug":"hotellings-t%c2%b2-statistic","status":"publish","type":"guide-dutilisateur","link":"https:\/\/ellistat.com\/en\/guide-dutilisateur\/statistique-t%c2%b2-de-hotelling\/","title":{"rendered":"Hotelling's T\u00b2 statistic"},"content":{"rendered":"

T\u00b2 addresses a control issue: Is this part compliant, considering all its characteristics as a whole?<\/strong>A part may fall within the tolerance range for each dimension and still be nonconforming due to the combination of those dimensions\u2014and that is precisely what dimension-by-dimension inspection fails to detect.<\/p>\n\n\n\n

The T\u00b2 measures the distance of each individual from the center of the cloud, taking into account the correlations between characteristics (Mahalanobis distance). The graph resembles a control chart: one value, one limit.<\/p>\n\n\n\n

Zone 1<\/strong> : Options.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

\u21d2 Learning about \/ from<\/strong> : the lines used to establish the reference (mean and covariance matrix). The others are compared to this reference; ;<\/p>\n\n\n\n

\u21d2 Type T2<\/strong> : the method used to calculate the limit\u2014Sullivan, Classical, or Chi-squared; ;<\/p>\n\n\n\n

\u21d2 alpha risk<\/strong> : the risk of a false alarm; ;<\/p>\n\n\n\n

\u21d2 Fixed Limit<\/strong> : sets a limit rather than recalculating it; ;<\/p>\n\n\n\n

\u21d2 Remove outliers<\/strong> and Remove outliers from T\u00b2<\/strong> : clean the training sample so that the reference is not based on outliers; ;<\/p>\n\n\n\n

\u21d2 Search for groups<\/strong> : identifies outliers that are close to one another and colors them by group. Outliers that deviate in the same way indicate a common cause; ;<\/p>\n\n\n\n

\u21d2 Logarithmic Scale<\/strong> : legible when one point stands out from all the others.<\/p>\n\n\n\n

Zone 2<\/strong> : the associated cloud.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

\u21d2 With 2 variables<\/strong>, it displays the individuals and the\u2019confidence ellipse<\/strong> : the multivariate compliance boundary. This is the most illustrative representation; ;<\/p>\n\n\n\n

\u21d2 With 3 variables<\/strong>, the three-dimensional cloud; ;<\/p>\n\n\n\n

\u21d2 More than 3 variables<\/strong>, the individuals are plotted on the PCA factor plane, which is the only possible representation.<\/p>\n\n\n\n

\ud83d\udca1 A T\u00b2 that is generated without any characteristics falling outside the tolerance limits is an interesting case: the combination has changed. Switch to PCA to see which link has changed.<\/p>","protected":false},"featured_media":0,"menu_order":70,"template":"","meta":{"_acf_changed":true},"menu-guide-dutilisateur":[40],"class_list":["post-4484","guide-dutilisateur","type-guide-dutilisateur","status-publish","hentry","menu-guide-dutilisateur-6-statistiques-multivariees"],"acf":[],"yoast_head":"\nStatistique T\u00b2 de Hotelling - Ellistat<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/ellistat.com\/en\/users-guide\/hotellings-t\u00b2-statistic\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Statistique T\u00b2 de Hotelling - Ellistat\" \/>\n<meta property=\"og:description\" content=\"Le T\u00b2 r\u00e9pond \u00e0 une question de pilotage : cette pi\u00e8ce est-elle conforme, toutes caract\u00e9ristiques prises ensemble ?Une pi\u00e8ce peut \u00eatre dans la tol\u00e9rance sur chaque cote et rester atypique par leur combinaison \u2014 c’est pr\u00e9cis\u00e9ment ce que la surveillance cote par cote laisse passer. 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