A survey with 51 persons was conducted to analyze the
design of an advertising campaign. Each respondent was asked to
evaluate the overall impression of the advertisement on an
eleven-point scale from 0 (bad) to 10 (good). The evaluations are
summarized separately with respect to type of occupation of the
respondents in the following figure.
To analyze the influence of occupation on the evaluation of the advertisement an analysis of variance was performed:
Res.Df RSS Df Sum of Sq F Pr(>F)
1 50 53.549
2 47 34.018 3 19.531 8.995 8.1265e-05
Which of the following statements are correct?
In order to be able to answer the questions the fraction of explained variance has to be determined. The residual sum of squares when using only a single overall mean value ($\mathit{RSS}_0$) as well as the residual sum of squares when allowing different mean values given occupation ($\mathit{RSS}_1$) are required. Both are given in the RSS column of the ANOVA table. The fraction of explained variance is given by $1 - \mathit{RSS}_1/\mathit{RSS}_0 = 1 - 34.018/53.549 = 0.365$.
The statements above can now be evaluated as right or wrong.