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Difficulty: HardInferential Statistical Tests

A randomized, double-blind clinical trial evaluates the efficacy of a novel Janus kinase (JAK) inhibitor for the treatment of moderate-to-severe atopic dermatitis. A total of 428428 patients are randomized into one of four treatment arms: JAK inhibitor 15 mg, JAK inhibitor 30 mg, an active comparator (dupilumab), and placebo. The primary outcome is the absolute reduction in the Eczema Area and Severity Index (EASI) score from baseline to week 16. The data for this continuous variable are determined to be normally distributed, and Levene's test confirms homogeneity of variances across the groups.

Researchers perform a one-way analysis of variance (ANOVA) to evaluate whether there is a statistically significant difference in the mean EASI score reduction among the treatment groups. The FF-statistic is calculated by dividing the between-group mean square by the within-group mean square.

What is the within-group (denominator) degrees of freedom for this statistical test?

Answer: 424

Answer

424
Analysis of variance (ANOVA) is used to compare the means of three or more independent groups. The test statistic (FF) is the ratio of the between-group variance (mean square between) to the within-group variance (mean square within or error). The within-group variance measures the dispersion of individual data points around their specific group mean. The degrees of freedom for the within-group variance (the denominator of the FF-statistic) is calculated by subtracting the total number of groups (kk) from the total sample size (NN). In this study, N=428N = 428 and k=4k = 4, so the within-group degrees of freedom is 428−4=424428 - 4 = 424.

Step-by-Step Solution

1
Identify the total number of subjects and the number of treatment groups.
Total subjects (NN) = 428428. Number of groups (kk) = 44.
These variables are required to calculate the degrees of freedom for an ANOVA.
2
Determine the appropriate formula for the within-group degrees of freedom.
The within-group (denominator) degrees of freedom is calculated as N−kN - k.
In ANOVA, the total variance is partitioned into between-group and within-group variance. The within-group degrees of freedom accounts for the variance of individual observations around their respective group means.
3
Perform the calculation.
428−4=424428 - 4 = 424.
Subtracting the number of groups from the total sample size yields the correct degrees of freedom for the denominator of the FF-statistic.

Key Concept

In a one-way ANOVA, the within-group (denominator or error) degrees of freedom is calculated as the total sample size minus the number of groups (N−kN - k).
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Topics

Inferential Statistical Tests

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