Generalization of the Paired T-Test for the Missing Values Case

Sophie Desjardins , Alain Desgagné (1) , Pierre Lafaye de Micheaux (2, 3) , Benoit Liquet (4, 5, 6, 7)

1 DMS - Département de Mathématiques et de statistique [UdeM- Montréal]
2 SAGAG - Statistique Appliquée et de Géométrie Aléatoire de Grenoble
3 GIN - Grenoble Institut des Neurosciences
4 ISPED - Institut de Santé Publique, d'Epidémiologie et de Développement
5 LABSAD - Laboratoire de Statistiques et Analyse des Données
6 Biostatistique
7 Epidémiologie et Biostatistique [Bordeaux]

For the comparison of the means of two variables when the observations are paired, we usually use the paired t-test. However, sample data with missing values often occurs and the t-test is not designed to handle them. In this paper, we generalize the t-test to consider the case with missing values and paired observations. A statistic for the test is proposed and it is shown that its distribution is close to a Student-t distribution. The degrees of freedom are also given. Normality of variables is assumed. The power of our test is compared to the one of alternative methods. Applications to real examples are given to illustrate the simplicity of its use.

Mots clés: T-Test; Missing Values; Paired Data; Comparison of Means; Power

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Sophie Desjardins, Alain Desgagné, Pierre Lafaye de Micheaux, Benoit Liquet. Generalization of the Paired T-Test for the Missing Values Case. JSM 2007 - Joint Statistical Meetings 2007, Jul 2007, Salt Lake City, United States. pp.274. ⟨hal-00299467⟩