Chapter 12

In one-way ANOVA, the ______ is calculated by summing the squared difference between each observed value and its corresponding group mean, over all of the observations. SSE SST MST MSE

SSE

In one-way ANOVA, the ______ measures the amount of variability within treatment groups. MSE SST SSTO SSE MST

SSE

In one-way ANOVA, the mean square error (MSE) is calculated as ______. SSTp−1SSTp-1 SSEp−1SSEp-1 SSTn−pSSTn-p SSEn−p

SSE/n−p

In one-way ANOVA, the ______ is calculated as a weighted sum of squared differences between the sample means and the overall mean. SSTO Reason: SST = ∑i=1pni(xi-x)2 MSE Reason: SST = ∑pi=1nixi-x2 MST Reason: SST = ∑pi=1nixi-x2 SSE Reason: SST = ∑pi=1nixi-x2 SST

SST

In one-way ANOVA, the ______ measures the amount of variability between treatment groups. SST SSE Reason: SST = treatment sum of squares SSTO Reason: SST = treatment sum of squares MST Reason: SST = treatment sum of squares MSE Reason: SST = treatment sum of squares

SST

In one-way ANOVA, the treatment mean square (MST) is calculated as ______. SSEp−1SSEp-1 Reason: MST uses SST in the numerator. SSTp−1SSTp-1 SSEn−pSSEn-p Reason: This is the mean square error (MSE). SSTn−pSSTn-p Reason: Use p-1 in the denominator.

SST/p−1

In one-way ANOVA, the ______ is calculated as the between-treatment variability plus the within-treatment variability. SST MST SSTO MSE SSE

SSTO

In a one-way ANOVA test, when can we reject the null hypothesis? p-value < α F > Fα p-value > α F < Fα

p-value < α F > Fα

In one-way ANOVA, if SST = 137.2, SSE = 190.8, MST = 68.6, and MSE = 15.9, then SSTO =

328

The competing hypotheses for a one-way ANOVA test that compares the means of three populations are defined as ______ H0: μ1 = μ2 = μ3 Ha: At least one pair of means differ H0: μ1 ≠ μ2 ≠ μ3 Ha: μ1 = μ2 = μ3 H0: μ1 = μ2 = μ3 Ha: μ1 ≠ μ2 ≠ μ3

: μ1 = μ2 = μ3 Ha: At least one pair of means differ

True or false: In one-way ANOVA we are investigating whether or not all group means are different. True False

False We are investigating whether or not at least one group has a different mean.

In one-way ANOVA, the ______ measures the total amount of variability in the observed response values. SSE Reason: SSTO = total sum of squares MSE Reason: SSTO = total sum of squares MST Reason: SSTO = total sum of squares SST Reason: SSTO = total sum of squares SSTO

SSTO

ANOVA is a statistical technique used to determine ______ if differences exist between the proportions of populations. if differences exist between the means of populations. the strength of the relationship between two random variables. whether or not a random variable follows a normal distribution.

if differences exist between the means of populations.

Researchers are often interested in how a factor influences the responses given by participants. In this instance, the factor is called the ______ variable. dependent independent

independent

In one-way ANOVA, we consider ___ factor(s) having __ levels and try to determine if differences exist between the means response to the various treatment levels. one; p one; two two; three

one; p

The degrees of freedom in a one-way ANOVA test are ______. n - p (numerator) and p - 1 (denominator) p - 1 (numerator) and n - 1 (denominator) n - 1 (numerator) and p - 1 (denominator) p - 1 (numerator) and n - p (denominator)

p - 1 (numerator) and n - p (denominator)