chapter 13

NOVA competing hypothesis

H0:μ1=μ2=μ3=μ4 HA:HA: Not all population means are equal -Note that HA does not require that all means must differ from one another. In principle, the sample data may support the rejection of H0 in favor of HA even if only two means differ

means

When conducting the equality of __ test, you might be tempted to set up a series of hypothesis tests, comparing μ1 and μ2, then μ1 and μ3, and so on, and then use the two-sample t test with equal variances

studentized range distribution

a distribution used in a tukey's HSD method that has broader, flatter and thicker trails than the t distribution

randomized block design

allowing the variation in the means to be explained by two factors

two way nova test

extends the analysis by measuring the effects of two factors simultaneously

between treatments variance

in NOVA, a measure of the variability b/w sample means -The other estimate of σ2 can be attributed to the variability of the data within each sample; that is, the variability due to chance

treatments

used to identify the c populations being examined

(x¯i − x¯¯)2

Each squared difference of a sample mean from the grand mean (x¯i−x¯¯)2 is multiplied by the respective sample size for each treatment ni

NOVA test

a generalization of the two-sample t test with equal but unknown variances -test is based on the F(df1,df2) distribution

error sum of squares (SSE)

a measure of the degree of variability that exists even if all population means are the same. in regression analysis, it measure the unexplained variation in the response variable

fishers least significant difference (LSD) method

a test that determines which means significantly differ by computing all pairwise differences of the means

sum of squares due to treatments (SSTR)

a weighted sum of squared differences b/w the sample means and the overall mean of the data -we divide SSTR by its degrees of freedom c−1, we obtain the mean square for treatments; or equivalently, the between-treatments estimate of σ2,σ2, which we denote by MSTR

one way NOVA test

compares population means based on one categorical variable or factor

within treatment variances

in NOVA, a measure of the variability within each sample -If the two independent estimates of σ2 are relatively close together, then it is likely that the variability of the sample means can be explained by chance and the null hypothesis of equal population means is not rejected

grand mean

in NOVA, the sum of all observations in a data set divided by the total number of observations and denoted as x¯ -We compute the grand mean by summing all observations in the data set and dividing by the total number of observations

1. The populations are normally distributed. 2. The population standard deviations are unknown but assumed equal 3. The samples are selected independently

one way NOVA test it is used for testing c population means under the following assumptions

analysis of variance (ANOVA)

test to determine if differences exist between the means of three or more populations under independent sampling

mean square error (MSE)

the average of the error (residual) sum of squares, where the residual is the difference b/w the observed and the predicted value of a variable