Using the data in the table above, which of the following correctly reports the degrees of freedom that you would need to report a one-way ANOVA?

Question

BlackTom AI · Accepted Answer

To determine the correct degrees of freedom for a one-way ANOVA, we use the standard formulas: df_between = k − 1, where k is the number of groups, and df_within = N − k, where N is the total number of observations across all groups.

Option A: dfbetween = 3, dfwithin = 30
This would imply k − 1 = 3, so k = 4 groups, and N − k = 30, so N = 34 total observations. Unless the data table actually reflects 4 groups and 34 observations in total, this combination does not align with the typical one-way ANOVA structure given a fixed k. If the table shows 3 groups or a different N, this option would be inconsistent.

Option B: dfbetween = 2, dfwithin = 27
This would imply k − 1 = 2, so k = 3 groups, and N − k = 27, so N = 30 total observations. If the data table reports 3 groups with a total of 30 observations, this set of degrees of freedom is consistent with the definitions for a one-way ANOVA.

Option C: dfbetween = 27, dfwithin = 2
Here, df_between = 27 would require k − 1 = 27, so k = 28 groups, which is exceedingly unlikely in a typical table scenario and would imply a very large number of groups. df_within = 2 would require N − k = 2, i.e., N = k + 2, which would be incompatible with k = 28 since that would yield N = 30, but the combination would still be unusual and inconsistently paired with the high between-group degrees of freedom. Overall, this pairing does not represent a standard, plausible configuration for a one-way ANOVA unless the table explicitly supports it.

Option D: dfbetween = 3, dfwithin = 27
This would imply k − 1 = 3, so k = 4 groups, and N − k = 27, so N = 31 total observations. If the table shows 4 groups and 31 observations, this would be consistent with the formulas. However, if the data display a different number of groups or total observations, this option would be incorrect.

In summary, evaluating each option against the core formulas df_between = k − 1 and df_within = N − k helps check internal consistency with the table’s reported group count (k) and total sample size (N). The option that aligns with the actual k and N in the provided table is the one that yields degrees of freedom matching those counts. When options present plausible but mismatched combinations, they can be ruled out by verifying whether the implied k and N correspond to what the table specifies. If the table indeed reflects 3 groups and 30 observations in total, the combination of df_between = 2 and df_within = 27 would be the coherent pairing under these definitions. Conversely, any option implying a different number of groups or total observations would be inconsistent with the data described by the table.

Using the data in the table above, which of the following correctly reports the degrees of freedom that you would need to report a one-way ANOVA?单项选择题

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