8. a researcher uses an anova to compare six treatment conditions with a sample of ( n = 12 ) in each…

8. 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 }} ).

8. 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 }} ).

Answer

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)