## Arbitrary (and unjustified) cut-off of r² [RSABE / ABEL]

Dear Detlew & AB!

Yes! Explained variance (sloppy: information) in regression (strongly!) depends on the sample size. See here and a rather lengthy thread of 2002 at David Bourne’s PKPD-list.

Critical values of \(\small{r}\) according to Odeh (1982)

n & r & r^2\\\hline

3 & 0.9877 & 0.9755\\

4 & 0.9000 & 0.8100\\

5 & 0.805\phantom{0} & 0.6486\\

6 & 0.729\phantom{0} & 0.5319\\

7 & 0.669\phantom{0} & 0.4481\\

8 & 0.621\phantom{0} & 0.3863\\

9 & 0.582\phantom{0} & 0.3390\\

10 & 0.549\phantom{0} & 0.3018\\

11 & 0.521\phantom{0} & 0.2719\\

12 & 0.497\phantom{0} & 0.2473\\

13 & 0.476\phantom{0} & 0.2267\\

14 & 0.457\phantom{0} & 0.2093\\

15 & 0.441\phantom{0} & 0.1944\\\hline

\end{array}}$$ In other words, an \(\small{r^2}\) of 0.6486 from five data points denotes the same ‘quality of fit’ than an \(\small{r^2}\) of 0.9755 from three. Searching the forum I get the impression that you (AB) are not alone with a cut-off of 0.80. Justification: nil. Maybe there is some copypasting going on? If you really want to use a cut-off (which I don’t recommend and is not required in any GL) take the number of data points into account. I strongly suggest to revise your SOP.

BTW, visual inspection of fits is mandatory (see there with references). Don’t trust in numbers alone. A classical example is Anscombe’s quartet.

All data sets: \(\small{\bar{x}=9.0,\,s_x^2=11,\,\bar{y}=7.5,\,s_x^2=4.1\rightarrow\widehat{y}=3+0.5\cdot x,\,R_{yx}^2=0.82\ldots}\)

❝ Not to calculate the AUC(0-inf) values if the fit of the terminal part of the concentration-time curves had an r^{2} value less than 80% is at least statistically not very sound, not to say *nonsense* IMHO .

Yes! Explained variance (sloppy: information) in regression (strongly!) depends on the sample size. See here and a rather lengthy thread of 2002 at David Bourne’s PKPD-list.

Critical values of \(\small{r}\) according to Odeh (1982)

^{1}(and modified for \(\small{r^2}\)); one sided, 5%:$$\small{\begin{array}{rcc}n & r & r^2\\\hline

3 & 0.9877 & 0.9755\\

4 & 0.9000 & 0.8100\\

5 & 0.805\phantom{0} & 0.6486\\

6 & 0.729\phantom{0} & 0.5319\\

7 & 0.669\phantom{0} & 0.4481\\

8 & 0.621\phantom{0} & 0.3863\\

9 & 0.582\phantom{0} & 0.3390\\

10 & 0.549\phantom{0} & 0.3018\\

11 & 0.521\phantom{0} & 0.2719\\

12 & 0.497\phantom{0} & 0.2473\\

13 & 0.476\phantom{0} & 0.2267\\

14 & 0.457\phantom{0} & 0.2093\\

15 & 0.441\phantom{0} & 0.1944\\\hline

\end{array}}$$ In other words, an \(\small{r^2}\) of 0.6486 from five data points denotes the same ‘quality of fit’ than an \(\small{r^2}\) of 0.9755 from three. Searching the forum I get the impression that you (AB) are not alone with a cut-off of 0.80. Justification: nil. Maybe there is some copypasting going on? If you really want to use a cut-off (which I don’t recommend and is not required in any GL) take the number of data points into account. I strongly suggest to revise your SOP.

BTW, visual inspection of fits is mandatory (see there with references). Don’t trust in numbers alone. A classical example is Anscombe’s quartet.

^{2}All data sets: \(\small{\bar{x}=9.0,\,s_x^2=11,\,\bar{y}=7.5,\,s_x^2=4.1\rightarrow\widehat{y}=3+0.5\cdot x,\,R_{yx}^2=0.82\ldots}\)

- Odeh RE.
*Critical values of the sample product-moment correlation coefficient in the bivariate distribution.*Commun Statist–Simula Computa. 1982; 11(1): 1–26. doi:10.1080/03610918208812243.

- Anscombe FJ.
*Graphs in statistical analysis.*Am Stat. 1973; 27: 17–21. doi:10.2307/2682899.

—

Helmut Schütz

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*Dif-tor heh smusma*🖖🏼 Довге життя Україна!_{}Helmut Schütz

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### Complete thread:

- SAS error in 3 way ref replicate study AB 2012-05-04 15:13 [RSABE / ABEL]
- SAS error in 3 way ref replicate study jag009 2012-05-04 15:36
- SAS error in 3 way ref replicate study AB 2012-05-05 06:45

- FDA's ABE code and partial replicate design d_labes 2012-05-06 10:10
- Arbitrary (and unjustified) cut-off of r²Helmut 2012-05-06 13:29
- Anscombe quartet d_labes 2012-05-07 08:48
- Anscombe quartet in R Helmut 2012-05-07 11:15
- Anscombe quartet in R AB 2012-05-07 12:07

- Anscombe quartet in R Helmut 2012-05-07 11:15
- Arbitrary (and unjustified) cut-off of r² FI 2012-10-08 10:39
- Predominant half life; exclusions Helmut 2012-10-08 13:45
- Excluding time points for lambdaZ d_labes 2012-10-09 09:33
- Analytical variability Helmut 2012-10-09 14:09
- Answer machine d_labes 2012-10-09 15:15
- Well done! Helmut 2012-10-09 19:43

- Answer machine d_labes 2012-10-09 15:15

- Analytical variability Helmut 2012-10-09 14:09

- Excluding time points for lambdaZ d_labes 2012-10-09 09:33

- Predominant half life; exclusions Helmut 2012-10-08 13:45

- Anscombe quartet d_labes 2012-05-07 08:48

- Arbitrary (and unjustified) cut-off of r²Helmut 2012-05-06 13:29

- SAS error in 3 way ref replicate study jag009 2012-05-04 15:36