Question

suppose that y1; y2; y3 is a sample of observations from a nðm; s2þ population butthat y1; y2; and y3 are not independent. in fact, suppose that

Answer 1

The question addresses the prerequisites for conducting one-way ANOVA, highlighting the need for samples from normal distributions with equal variances and independence.

Step-by-step explanation:

The question pertains to assumptions made during statistical testing and one-way ANOVA in particular. To perform a one-way ANOVA, certain assumptions must be met: samples must be drawn from normally distributed populations, samples must be independent and randomly selected, and all populations from which samples are drawn must have equal standard deviations.

From the given information, the problem arises when these assumptions are violated, as in the case where the samples have different standard deviations. This is critical because one-way ANOVA requires that the groups being compared have the same variance. Thus, additional statistical tests like Levene's test or Bartlett's test for homogeneity of variances may be required before conducting the ANOVA. Furthermore, if the assumption of normality is in doubt, data transformations or non-parametric tests may be considered.

Answer 2

The question addresses the prerequisites for conducting one-way ANOVA, highlighting the need for samples from normal distributions with equal variances and independence.

Step-by-step explanation:

The question pertains to assumptions made during statistical testing and one-way ANOVA in particular. To perform a one-way ANOVA, certain assumptions must be met: samples must be drawn from normally distributed populations, samples must be independent and randomly selected, and all populations from which samples are drawn must have equal standard deviations.

From the given information, the problem arises when these assumptions are violated, as in the case where the samples have different standard deviations. This is critical because one-way ANOVA requires that the groups being compared have the same variance. Thus, additional statistical tests like Levene's test or Bartlett's test for homogeneity of variances may be required before conducting the ANOVA. Furthermore, if the assumption of normality is in doubt, data transformations or non-parametric tests may be considered.