Exam 15: Analysis of Variance

In a two-way ANOVA, the degrees of freedom for treatment is calculated in the same way as that for a one-way ANOVA.

The method of analysis of variance is not applicable for data in which sample sizes are not all equal.

A complete-block design is being used to test the null hypothesis that mean responses are identical under four treatments, with three levels used for the blocking factor. The following data are obtained: $S S(T r)=60, S S B=90, S S T=200$ . a. Construct the ANOVA table. b. Should the null hypothesis of identical population means be rejected at the $\alpha=0.05$ significance level.

Table 15.1 -A complete-block experiment is used to test the null hypothesis that three teaching methods produce no difference in mean achievement score. The blocking variable consists of four ability levels. Use the data in Table 15.1. a. Construct the ANOVA table. b. The null hypothesis of equal population means is tested at $\alpha=0.05$ . Should it be rejected?

A two-way analysis of variance applied to an experiment in which we want to test both factors is called a __________.

The __________ sum of squares measures the variation within samples.

In an $F$ ratio for a one-way ANOVA, the numerator degrees of freedom is __________.

A two-way ANOVA in which only one variable is of material concern, consists of one treatment factor and one __________.

In a two-factor ANOVA, in terms of squares, $S S T=$ __________.

If the null hypothesis in a one-way analysis of variance is false, then the variance among the sample means is larger than the variation within samples.

When each kind of treatment appears together with each other kind of treatment once within the same block, the design is referred to as __________.

In a complete-block design

An experimental design in which the number of rows must equal the number of columns is provided by the

In a one-factor ANOVA having three treatment levels with five observations in each sample, the between samples degrees of freedom is equal to

A job performance evaluator is concerned with how workers' performance ratings are affected by their skill level and their attitude. He obtained the following data: a. Construct the ANOVA table. b. Test the two hypotheses at $\alpha=0.05$ .

In a Latin Square experiment, it is impossible for one factor to have three levels and another to have four levels.

Analysis of variance is a method by which we can decide whether or not observed differences among more than two sample variances can be attributed to chance.

A blocking factor is

Find $F_{0.01}$ if the degrees of freedom for treatments is 4 the degrees of freedom for error is 12.

The treatment sum of squares is symbolized by SST.