Question

1. a researcher uses an anova to compare six treatment conditions with a sample of ( n = 12 ) in each treatment. for this analysis, find ( d f_{\text {total }}, d f_{\text {between }} ), and ( d f_{\text {within }} ).

Explanation:

Step1: Calculate \(df_{between}\)

\(df_{between}=k - 1\), where \(k\) is the number of treatment conditions. Here \(k = 6\), so \(df_{between}=6 - 1=5\)

Step2: Calculate \(df_{within}\)

\(df_{within}=N - k\), where \(N\) is the total number of observations. Since \(n = 12\) per treatment and \(k = 6\), \(N=12\times6 = 72\). Then \(df_{within}=72 - 6=66\)

Step3: Calculate \(df_{total}\)

\(df_{total}=N - 1\). With \(N = 72\), \(df_{total}=72 - 1=71\)

Answer:

\(df_{between}=5\), \(df_{within}=66\), \(df_{total}=71\)