My Math Forum Error bars on log-transformed plots?

 Algebra Pre-Algebra and Basic Algebra Math Forum

 April 21st, 2008, 05:45 AM #1 Newbie   Joined: Apr 2008 Posts: 3 Thanks: 0 Error bars on log-transformed plots? Hello - I am a genetics researcher. I have a series of data points with errors (standard errors), that I wish to plot as a column plot with error bars: GENE, AVG FOLD CHANGE, SE Gene1, 2193.10, 1200.74 Gene2, 96.28, 9.08 Gene3, 39.02, 22.51 Gene4, 5.88, 0.82 Gene5, -0.68, 0.33 Gene6, 1.14, 0.02 Gene7, -1.46, 0.16 Gene8, -1.56, 0.50 Gene9, -1.58, 0.10 Gene10, -1.88, 0.45 Gene11, -2.04, 0.45 Gene12, -6828.82, 975.41 Positive values are up-regulated genes; negative values are down-regulated genes (re: gene expression levels). I wish to plot this as a column plot on a log scale (y-axis) with negative values below the zero baseline, positive values above, and with the errors indicated. Something like: 1000 100 10 * 1 * 0------------------- -1 * -10 * -100 -1000 but with bars instead of the asterisks - you get the idea. I can do this easily enough using MS Excel, by taking the log of the absolute value, multiplying the result by +1 or -1 (to restore the original "directionality" - i.e. up- or down-regulated). A couple of questions: (Q1) Is it "better" to use log (base 10) or ln (natural) log transformations? (Q2) How would I present the error bars - would I log (or ln) -transform the standard errors, for example, and plot these [or the absolute values of these, since the log of numbers <1 are negative; e.g. log(0.5) = -0.301)]? I tried finding the answer to these questions in Google, but I wasn't very successful. ... I would very much appreciate any comments regarding the log-transformation of data and plots of log-transformed data, particularly regarding error bars! Thank you! Sincerely, Greg :-)
 April 22nd, 2008, 02:06 PM #2 Newbie   Joined: Apr 2008 Posts: 3 Thanks: 0 Hello - I think I have this right ... Referring to the sample data (below; this would be easier, if I could attach my Excel spreadsheet), I first log-transformed my data, x = log( |x| + 1) using the absolute values (to avoid taking the log of negative numbers) and adding 1 (to avoid taking the log of zero). Next, I multiplied these log-transformed values by +1 (to indicate up-regulated genes) or -1 (to indicate down-regulated genes). Last, I calculated the mean and standard error of these log-transformed data, and plotted the results. I think that this is correct - please comment, if I am mistaken. Thank you! Greg :-) =========== Test Data: ============ SE (= SD /(n^0.5) - i.e. SD / sqrt(number of data points) log ( | fold-change +1 | ) - i.e. log of (absolute value +1) "Correction:" Multiplier +1 (up-regulated) or -1 (down-regulated) ----------------------------------- Gene // Fold-change // Mean // SD // SE (= SD /(n^0.5) // log ( | fold-change +1 | ) // Up-reg: 1; Down-reg: -1 // "Corrected" log(fold-change) // Mean [corrected log(fold-change)] // SE [corrected log(fold-change)] Gene1 -36865.92 < Outlier - ignore Gene1 -8023.41 3.904 -1 -3.904 Gene1 -5634.22 -6828.815 1689.412 1194.595 3.751 -1 -3.751 -3.828 0.077 Gene2 1.04 0.310 1 0.310 Gene2 1.08 0.318 1 0.318 Gene2 -2.57 -0.150 2.096 1.210055095 0.196 -1 -0.196 0.144 0.170 Gene3 1.24 0.350 1 0.350 Gene3 -2.75 0.243 -1 -0.243 Gene3 -1.64 -1.050 2.059 1.188991169 -0.194 -1 0.194 0.100 0.178 Gene4 -1.09 -1.046 -1 1.046 Gene4 -1.16 -0.796 -1 0.796 Gene4 -1.16 -1.137 0.040 0.023333333 -0.796 -1 0.796 0.879 0.083 Gene5 6.06 0.849 1 0.849 Gene5 7.21 0.914 1 0.914 Gene5 4.38 5.883 1.423 0.821712304 0.731 1 0.731 0.831 0.054 Gene6 -1.64 -0.194 -1 0.194 Gene6 -1.60 -0.222 -1 0.222 Gene6 1.13 -0.703 1.588 0.916739391 0.328 1 0.328 0.248 0.041 Gene7 1438.15 3.158 1 3.158 Gene7 4544.80 3.658 1 3.658 Gene7 596.34 2193.097 2079.674 1200.700135 2.776 1 2.776 3.197 0.255 Gene8 83.29 1.926 1 1.926 Gene8 113.77 2.060 1 2.060 Gene8 91.77 96.277 15.732 9.082770013 1.967 1 1.967 1.984 0.040 Gene9 83.29 1.926 1 1.926 Gene9 9.85 1.035 1 1.035 Gene9 23.92 39.020 38.979 22.50456176 1.397 1 1.397 1.453 0.259 Gene10 -1.17 -0.770 -1 0.770 Gene10 0.80 0.255 1 0.255 Gene10 -0.06 -0.143 0.988 0.570214385 -0.027 -1 0.027 0.351 0.220 0.000 Gene11 -1.75 -0.125 -1 0.125 Gene11 -1.57 -0.244 -1 0.244 Gene11 -1.41 -1.577 0.170 0.098206132 -0.387 -1 0.387 0.252 0.076 Gene12 1.16 0.334 1 0.334 Gene12 -2.36 0.134 -1 -0.134 Gene12 -2.60 -1.267 2.105 1.215309746 0.204 -1 -0.204 -0.001 0.169 Summary - Log-transformed data: Gene Mean SE Gene7 3.197 0.255 Gene8 1.984 0.040 Gene9 1.453 0.259 Gene4 0.879 0.083 Gene5 0.831 0.054 Gene10 0.351 0.220 Gene11 0.252 0.076 Gene6 0.248 0.041 Gene2 0.144 0.170 Gene3 0.100 0.178 Gene12 -0.001 0.169 Gene1 -3.828 0.077
 April 22nd, 2008, 04:45 PM #3 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms Ah, fold changes? I work in a genotyping lab part time (in addition to my full-time job, naturally) so I have familiarity, though not expertise, in the subject. The log transform is standard; Knudsen uses the same, as I recall. (Q1) Is it "better" to use log (base 10) or ln (natural) log transformations? They will be visually identical. Any choice of logarithm will give the same shape, changing only the scale. For ease of use I would recommend common (base 10) or binary (base 2) depending on the size of the effect -- base 10 with your data, probably. (Q2) How would I present the error bars - would I log (or ln) -transform the standard errors, for example, and plot these [or the absolute values of these, since the log of numbers <1 are negative; e.g. log(0.5) = -0.301)]? If the value is 1000 and the standard error is 100, I would plot the error bars at log (|1000 + 100| + 1) and log (|1000 - 100| + 1). This puts them on the same scale as the data. Don't use the log of the error directly!
 April 24th, 2008, 12:33 PM #4 Newbie   Joined: Apr 2008 Posts: 3 Thanks: 0 Hello - When I didn't get an initial response here (after several days), I cross-posted this thread, to the URL / forum, below. I continued pursuing this topic (there), as I was able to upload a MS Excel file, that contained my test data, plus annotations. Please refer here for the resolution of this problem: http://www.talkstats.com/showthread.php ... #post10965 Thanks, once again, for your replies - appreciated. Sincerely, Greg :-)
 April 24th, 2008, 06:12 PM #5 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms Looks like the answers you got there were the same as what I posted. Well, I'm glad you got your answers!

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