QuestionWhich of the following is true regarding ANOVA?
It reaches a conclusion regarding differences among the variances of each group.
Analysis begins with the sum of squares error (SSE) as the starting point.
Equality of variances is tested using the Tukey-Kramer Procedure
It uses the promciple of partitioning to subdivide the sources of variation
Studdy Solution
STEP 1
1. ANOVA (Analysis of Variance) is a statistical method used to test differences between two or more group means.
2. The primary purpose of ANOVA is to determine if there are any statistically significant differences between the means of independent groups.
STEP 2
1. Understand the purpose of ANOVA.
2. Evaluate each statement regarding ANOVA.
3. Identify the true statement.
STEP 3
Understand that ANOVA is used to analyze differences among group means, not variances. It tests the null hypothesis that all group means are equal.
STEP 4
Evaluate the first statement: "It reaches a conclusion regarding differences among the variances of each group."
- ANOVA tests differences in means, not variances. This statement is false.
STEP 5
Evaluate the second statement: "Analysis begins with the sum of squares error (SSE) as the starting point."
- ANOVA begins with the total sum of squares (SST), which is partitioned into sum of squares between groups (SSB) and sum of squares within groups (SSE). This statement is misleading as SSE is not the starting point.
STEP 6
Evaluate the third statement: "Equality of variances is tested using the Tukey-Kramer Procedure."
- The Tukey-Kramer Procedure is a post-hoc test used after ANOVA to find which specific group means are different. It does not test equality of variances. This statement is false.
STEP 7
Evaluate the fourth statement: "It uses the principle of partitioning to subdivide the sources of variation."
- ANOVA uses the principle of partitioning to divide the total variation into components: between-group variation and within-group variation. This statement is true.
STEP 8
Identify the true statement:
- The true statement regarding ANOVA is: "It uses the principle of partitioning to subdivide the sources of variation."
The correct statement is:
"It uses the principle of partitioning to subdivide the sources of variation."
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