Generalized Least Squares F Test in Regression Analysis with Two-Stage Cluster Samples

Forest conditions and management under rapid legislation change in Romania

“…Glass et al (1972) used a series of examples to show that t and F tests are robust to the normality assumption. However, more recent studies have demonstrated that these tests only become robust to the normality assumption when specific procedures or adjustments are used (see Rao et al 1993, Keselman et al 1997, Cain et al 2000, Shoemaker 2003, Islam and Tiku 2004. Therefore, when we discovered that certain attribute data were not normally distributed, we performed comparisons using two non-parametric tests: Wilcoxon (Wilcoxon 1945) and Friedman (Friedman 1937).…”

Environmetric analysis in complex surveys

“…Part of the growing literature on the subject is based on the traditional sampling framework such as, for example, the works of Konijn (1962) and Kish and Frankel (1974). Others such as Scott and Holt (1982), Deaton and Irish (1983), King and Evans (1986), Christensen (1984Christensen ( , 1986Christensen ( , 1987a, Moulton (1986Moulton ( , 1990), Dorfman (1993), Rao et al (1993), and more recently, Bhatti (1995Bhatti ( , 1996Bhatti ( , 1997Bhatti ( , 1999 have focused on the model-based approach.…”

“…Recently, there has been an increasing use of regression techniques based on survey data in environmental, social, physical, and biological sciences. Examples of these awareness may be found in Wu et al (1988), Bhatti (1993), Rao et al (1993), Ghosh and Rao (1994), Wu and Bhatti (1994), and series of articles by Bhatti (1995Bhatti ( , 1996Bhatti ( , 1997Bhatti ( , 1999Bhatti ( , 2000, and Stukel and Rao (1997), among aothers. Often the data arising from these areas are naturally in blocks.…”

A new alternative to the standard F test for clustered data

“…The method rests on the assumption that the adjusted test statistic approximately follows central F distribution with the degrees of freedom same as those of the standard F statistic so that the usual F test can be applied using the adjusted F statistic. Rao et al (1993) proposed a two-stage generalized least square (GLS) test. The method involves making the observations uncorrelated, using a transformation previously proposed by Fuller and Battese (1973), and then applying the standard F test on the transformed observations.…”

“…Thus, in this paper we consider the other approach, which avoids the estimation of the intra-cluster correlation. In order to make the observations independent, we employ a transformation that is different from the Fuller-Battese transformation used by Rao et al (1993). Following Rao et al (1993), we then apply the standard F test.…”