Asked by Shailee Woods on Jun 26, 2024
Verified
For a set of data with the number of groups = 3 and the total N = 196, the degrees of freedom are equal to ______.
A) 1
B) 2
C) 3
D) 195
Degrees Of Freedom
The number of independent pieces of information on which a statistical estimate is based, minus the number of parameters estimated.
Groups
Collections of individuals or items classified together based on common characteristics or for the purpose of analysis.
Total N
The total number of observations or participants in a study or dataset.
- Acquire an understanding of degrees of freedom as it pertains to the analysis of statistical information.
Verified Answer
SC
Stephanie CandioJun 29, 2024
Final Answer :
B
Explanation :
The formula to calculate degrees of freedom for a one-way ANOVA is:
df = N - k
where:
N = total number of observations
k = number of groups
Substituting the values given in the question, we get:
df = 196 - 3
df = 193
However, we need to remember that in a one-way ANOVA, one degree of freedom is lost due to estimating the grand mean, and another degree of freedom is lost due to estimating the variance within each group. Therefore, the correct degrees of freedom for this scenario would be:
df = k - 1
df = 3 - 1
df = 2
Hence, the answer is B.
df = N - k
where:
N = total number of observations
k = number of groups
Substituting the values given in the question, we get:
df = 196 - 3
df = 193
However, we need to remember that in a one-way ANOVA, one degree of freedom is lost due to estimating the grand mean, and another degree of freedom is lost due to estimating the variance within each group. Therefore, the correct degrees of freedom for this scenario would be:
df = k - 1
df = 3 - 1
df = 2
Hence, the answer is B.
Learning Objectives
- Acquire an understanding of degrees of freedom as it pertains to the analysis of statistical information.
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