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Elan Coil [88]
3 years ago
15

A researcher compares differences in positivity between participants in a low-, middle-, or upper-middle-class family. If she ob

serves 15 participants in each group, then what are the degrees of freedom for the one-way between-subjects ANOVA? (2, 12) (3, 43) (2, 42) (3, 12)
Mathematics
1 answer:
777dan777 [17]3 years ago
3 0

Answer:

(2, 12)

Step-by-step explanation:

Analysis of variance (ANOVA) "is used to analyze the differences among group means in a sample".  

The sum of squares "is the sum of the square of variation, where variation is defined as the spread between each individual value and the grand mean"  

If we assume that we have 3 groups and on each group from j=1,\dots,n_j we have n_j individuals on each group we can define the following formulas of variation:  

SS_{total}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x)^2  

SS_{between=Treatment}=SS_{model}=\sum_{j=1}^p n_j (\bar x_{j}-\bar x)^2  

SS_{within}=SS_{error}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x_j)^2  

And we have this property  

SST=SS_{between}+SS_{within}  

The degrees of freedom for the numerator on this case is given by df_{num}=k-1=3-1=2 where k =3 represent the number of groups.  

The degrees of freedom for the denominator on this case is given by df_{den}=df_{between}=N-K=15-3=12.  

And the total degrees of freedom would be df=N-1=15 -1 =14  

And the correct answer would be 2 degrees of freedom for the numerator and 12 for the denominator

(2, 12)

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