Skip to main content
Cross Validated

Return to Answer

replaced http://stats.stackexchange.com/ with https://stats.stackexchange.com/
Source Link
Community Bot
Community Bot
  • 1

When you hear "more than 70% variability is explained by ...", the speaker is referring to the sums of squares (SS), not the mean squares (MS). I should note that exactly what they mean is not certain; they could be referring to either eta-squared or partial eta-squared:
\begin{align} \eta^2&=\frac{SS~IV_j}{SS~Total} \\ ~\\ ~\\ \eta^2_\text{partial}&=\frac{SS~IV_j}{SS~IV_j+ SS~Residuals} \end{align} Part of the reason why is that the SS can be partitioned (at least if you are using type I SS, see herehere), but the MS cannot.

You raise a good point that there is more opportunity for a given factor to contribute to the variability in the response when there are more groups in that factor (this assumes, of course, that there is real variability in the levels of the factor). Many people forget, or are ignorant of, this fact. Unfortunately, it is not possible to get around this issue. The implication of this is that the question 'which factor is most important' may not be answerable in an absolute sense, but only relative to something else.

When you hear "more than 70% variability is explained by ...", the speaker is referring to the sums of squares (SS), not the mean squares (MS). I should note that exactly what they mean is not certain; they could be referring to either eta-squared or partial eta-squared:
\begin{align} \eta^2&=\frac{SS~IV_j}{SS~Total} \\ ~\\ ~\\ \eta^2_\text{partial}&=\frac{SS~IV_j}{SS~IV_j+ SS~Residuals} \end{align} Part of the reason why is that the SS can be partitioned (at least if you are using type I SS, see here), but the MS cannot.

You raise a good point that there is more opportunity for a given factor to contribute to the variability in the response when there are more groups in that factor (this assumes, of course, that there is real variability in the levels of the factor). Many people forget, or are ignorant of, this fact. Unfortunately, it is not possible to get around this issue. The implication of this is that the question 'which factor is most important' may not be answerable in an absolute sense, but only relative to something else.

When you hear "more than 70% variability is explained by ...", the speaker is referring to the sums of squares (SS), not the mean squares (MS). I should note that exactly what they mean is not certain; they could be referring to either eta-squared or partial eta-squared:
\begin{align} \eta^2&=\frac{SS~IV_j}{SS~Total} \\ ~\\ ~\\ \eta^2_\text{partial}&=\frac{SS~IV_j}{SS~IV_j+ SS~Residuals} \end{align} Part of the reason why is that the SS can be partitioned (at least if you are using type I SS, see here), but the MS cannot.

You raise a good point that there is more opportunity for a given factor to contribute to the variability in the response when there are more groups in that factor (this assumes, of course, that there is real variability in the levels of the factor). Many people forget, or are ignorant of, this fact. Unfortunately, it is not possible to get around this issue. The implication of this is that the question 'which factor is most important' may not be answerable in an absolute sense, but only relative to something else.

Source Link
gung - Reinstate Monica
gung - Reinstate Monica
  • 147.5k
  • 89
  • 406
  • 717

When you hear "more than 70% variability is explained by ...", the speaker is referring to the sums of squares (SS), not the mean squares (MS). I should note that exactly what they mean is not certain; they could be referring to either eta-squared or partial eta-squared:
\begin{align} \eta^2&=\frac{SS~IV_j}{SS~Total} \\ ~\\ ~\\ \eta^2_\text{partial}&=\frac{SS~IV_j}{SS~IV_j+ SS~Residuals} \end{align} Part of the reason why is that the SS can be partitioned (at least if you are using type I SS, see here), but the MS cannot.

You raise a good point that there is more opportunity for a given factor to contribute to the variability in the response when there are more groups in that factor (this assumes, of course, that there is real variability in the levels of the factor). Many people forget, or are ignorant of, this fact. Unfortunately, it is not possible to get around this issue. The implication of this is that the question 'which factor is most important' may not be answerable in an absolute sense, but only relative to something else.