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ASHS 2004 Annual Meeting picture 1000 words examining your dataGraphical Data Presentationoverview– stemleaf, hist, boxplot– scatter plots with annotation– counts using graphs as a formal statistical toolsBrian S. Yandell––––Horticulture & Statistics DepartmentsUniversity of Wisconsin-Madisonplot.pxg and t-testinteraction plot and anovaregression and ancovadiagnostics gene mapping– 1-D genome scan (LOD map)– 2-D scan (color vs. BW)– testing or estimation or model selection?www.stat.wisc.edu/ yandell microarray experiments– design for single spot (mRNA or cDNA or )– thinking across all spotssun 18 jul 2004ASHS 2004 Brian S. Yandell1sun 18 jul 2004picture 1000 words?Location (cM)sun 18 jul 20042counts: recombination(Tom Osborn’s B. napus linkage map)1. wg1h4c wg1g5c tg5e11b E35M47.262 tg6c3a E32M48.249 E33M50.252 E35M48.120ec5d5 wg1g10a E33M48.369 E33M50.451 tg1f8 wg7b6a isoACO ec4f12. ec2e5a E33M49.117 ec3b12 wg2d11b wg1g8a E32M49.73 wg3g11 ec3a8 wg7f3aE33M59.59 E35M62.117 wg6b10 wg8g1b wg5a5 tg6a12 Aca1 E38M50.133E35M59.117 ec2d1a wg1a10 tg2h10b tg2f123. E33M49.491 E38M62.229 wg1g10b ec4h7 wg4d10 E32M50.409 E38M50.159E33M47.338 ec2d8a E33M49.165 wg4f4c E35M48.148 wg6c6 ec4g7b wg7a11wg5b1a ec4e7a E32M61.218 wg4a4b E33M50.183 E33M62.140 wg9c7 wg6b2E33M49.211 wg2e12b isoIdh wg3f7c4. ec3b4 E33M62.206 wg5b2 E32M59.302 wg6a12 wg4d7c ec4c5b E32M61.166E32M47.136 E32M62.107 wg6f10 ec5e12c5. E38M62.358 E35M62.256 ec5a7b wg3c9 E33M47.154 E35M59.581 E32M47.460ec4g7a ec6b2 E35M62.111 wg1g6 E35M62.201 ec4c5a ec5a7a wg1h5 wg6a10E33M50.120 ec4e86. E33M48.191 E32M47.168 E35M62.225 E35M62.340 wg1g8c E32M62.75E32M49.473 E32M59.330 wg7e10 wg6h1b wg2c1 tg5h12 wg3b6 wg7d9a wg1g3b7. wg7h2 wg9d5 E32M59.359 E33M59.353 E32M61.137 ec3h4 wg8g3 wg2a11 tg2b4E35M47.367 ec2e4b E32M47.512 ec2h2a Lem tg5d9a wg7f5a wg5a1a ec3e12a8. wg4b6b wg6g9 E33M59.147 eru1 ec4h3 E33M62.99 E38M50.157 wg6d99. E33M60.50 wg4h5a wg3h8 ec3d3a ec2c7 wg4d11 tg1h12 ec2e5b10. E38M62.461 wg3f7a E35M60.312 E38M62.189 tg3c1 ec3d3b E33M49.175E33M48.268 E35M62.80 E35M48.143 wg1g4a E33M47.182b E38M50.119 wg7b3E33M59.64 ec3g3c ec2h2b E32M48.21211. wg1g5b tg6c3b ec5a1 wg6f3 E32M62.115 E33M62.250 E32M62.186 wg2b7 wg8h5wg3h412. tg2h10a tg5e11a E32M50.90 ec2d1b E32M50.77 wg1g4c wg8g1a wg2c3 wg7f3bwg4h1 ec4e7b wg5a6 ec2c12 wg2d11a ec2e12a wg7a8a13. isoLap E33M62.176 E35M48.84 E33M49.293 E35M62.136 eru2 E38M50.186 ec4f11E32M50.252 E32M59.107 wg1g8b wg2g9 E33M50.282 E35M48.123 wg1e3 wg6d6wg4f4a ec5c4 E35M48.198 E35M62.135 wg1a4 ec2e12b wg3h6 wg4d5a wg5b1bE33M61.54 ec3d2 E32M48.191 E33M59.333 wg6e3b ec4d11 E32M59.88 ec4g4wg1g4b ec3g12 ec3g3a14. wg9f2 E35M62.222 wg4a4a E33M59.234 E33M61.84 wg4d7b ec5e12b ec4c11wg6e3a E32M48.69 ec3b2b E32M47.186 ec4d9 wg4d5c E33M48.67 E35M60.329wg1h4b15. E38M62.188 E32M50.261 E33M50.118 wg1g3a E35M60.230 wg6a11 wg6h1aE32M62.241 E32M47.288 E33M48.316 E33M59.225 ec2e4c16. ec3e12b wg5a1b wg2a3c ec5e12a wg7f5b E32M47.159 tg5d9b slg6 E35M59.8517. ec2d8b E35M62.132 E35M47.337 E35M47.257 wg9e9 ec2b3 E33M60.229E32M50.325 wg6c1 ec3b2a E35M47.170 wg2d5a E33M60.120 E33M47.115wg1g10c18. E33M62.130 E32M47.344 E32M50.255 wg3g9 E32M50.424 pr2 tg5b2 E33M59.165E35M60.125 E33M62.19619. ec2h2c wg3f7b ec3f1 E35M60.107 wg1g2 E33M48.346 E33M50.371 E33M47.138tg4d2b E32M62.394 E33M47.189 E32M49.409 wg7b6bASHS 2004 Brian S. YandellGenetic map0Stellar on marker 1Major on marker 1SMMM50Major onmarker 2Stellar onmarker 2100SSMS150pie chart: are the markers linked?N1 N2 N3 N4 N5 N6 N7 N8 N9 N10N11N12N13N14N15N16N17N18N19ChromosomeASHS 2004 Brian S. Yandell3sun 18 jul 2004counts: recombinationASHS 2004 Brian S. Yandell4counts: nts252015105SM0MSMMrecombinantsMSsun 18 jul 2004ASHS 2004 Brian S. YandellrecombinantsS1SMpie chart: are the markers linked?SS5sun 18 jul 2004ASHS 2004 Brian S. Yandell61

counts: recombinationcounts: recombinationPairwise recombination fractions and LOD scoresec2d1aE33M59.59 M SM 24 17S 34 29353025Markers2015r 51/104 0.494LOD 55101520Markerssun 18 jul 2004ASHS 2004 Brian S. Yandell7sun 18 jul 2004counts:recombination&LODscoresN1N2N3N4 N5 N6 N7 N8N9N10N11N12N13N14N15N16N17N18N19(Ferreira et al. 1995)N19N18N17N16N152508-week4-week0 90 9991 01122333441 1111 556668888888889999991 6677999999992 00001111112222233333342 000011111122333444442 55579992 55556667788993 33 0002333 73 584 4 144 54 5 5 flowering time (days) for Major type plants6 (based on marker E33M59.59 on chr2)6 6under 4- or 8-week N6N5N4N350N2N1501001502002508flowering time: stem-leaf plotsPairwise recombination fractions and LOD scores300ASHS 2004 Brian S. Yandell300never flowered10 0Markerssun 18 jul 2004ASHS 2004 Brian S. Yandell9sun 18 jul 2004(colors, background, grid lines, group order)m4s4m8s8251061588-week flowering time542021500Stellar (biennial)0204060801000204-week flowering time4060801008-week flowering time55510101515202010000Major (annual)10side-by-side histogramshistogram summaries4-week flowering timeASHS 2004 Brian S. Yandell0sun 18 jul 2004204060801002.50ASHS 2004 Brian S. Yandell204060807.512.5 17.5 22.5 27.5 32.5 37.5 42.5 47.5 52.5 57.5 62.5 67.5 72.5 77.5 82.5 87.5 92.5 97.510011sun 18 jul 2004ASHS 2004 Brian S. Yandell122

3-D histograms3-D histograms(another view angle)(group order, grid lines, view angle)2520251520m4s410m415s4m8s85m810s85sun 18 jul 2004ASHS 2004 Brian S. Yandell13sun 18 jul 20043-D ribbon 562.572.542.5s852.522.532.52.512.50ASHS 2004 Brian S. Yandell14polygon histograms(group order, view angle)(colors, background, grid .572.542.502.5157.5 12.5 17.5 22.5 27.5 32.5 37.5 42.5 47.5 52.5 57.5 62.5 67.5 72.5 77.5 82.5 87.5 92.5 97.5sun 18 jul 2004ASHS 2004 Brian S. Yandell168-week Stellarboxplot vs. all data6810histogram024histogram showsmost of the dataand broad shape,but takes up a lotof spacem4ASHS 2004 Brian S. Yandell12sun 18 jul 2004s852.522.532.52.512.501020whisker10sun 18 jul 20043040medianboxplot shows keyfeatures(summaries) ofshape, hiding mostof the databoxplotquartiles1520ASHS 2004 Brian S. Yandellwhisker2530outliers3540451710sun 18 jul 200415202530ASHS 2004 Brian S. Yandell354045183

box plots show skew in daysboxplot for n 5!100but hide details (gap to no flowering)2040days6080no flowering141618202224StellarMajorStellarno vernsun 18 jul 2004ASHS 2004 Brian S. Yandell19StellarMajor8-weekASHS 2004 Brian S. Yandell20box plots on log scalejittered plot of data by groupshow symmetric, but still hide details100(add small noise to x axis; lines for medians)100Major4-weeksun 18 jul 2004no flowering10202040daysdays605080no floweringStellarMajorStellarno vernMajorStellar4-weeksun 18 jul 2004MajorStellar8-week21sun 18 jul 2004StellarMajorStellar4-weekMajor8-weekASHS 2004 Brian S. Yandell22phenotype by locus genotypejittered plots of log days100Majorno vernASHS 2004 Brian S. YandellchN2:50.7cME33M59.59503040no flowering20daysphenotype20mean /- SE1010red circles forimputed genotypesStellarMajorno vernsun 18 jul 2004StellarMajor4-weekASHS 2004 Brian S. 3sun 18 jul 2004ASHS 2004 Brian S. Yandell244

phenotype by two loci genotypesBBA-200totcarotenoids30includes SE spreadphenotype201501002 very significant QTL (p 0.0001)modest evidence for epistasis (p 0.03)AAAAStellarAAStellarABStellarABMajorsun 18 jul 200450genotypeMajorAAStellarABMajorABMajorAAASHS 2004 Brian S. Yandell25sun 18 jul 2004Interaction plot for ACCCAC112Q and Y2markinteraction plotASHS 2004 Brian S. Yandellchem 23004005050020060050070010050AAAB2BB0.000Y2marksun 18 jul 2004ASHS 2004 Brian S. Yandell001001202005total carotenoidslogtot26(plot on log scale; add half the min; axis in units)BBA-more equal SEssimilar interactionpatternBBhighly skewed data with em 210 2010ACCCAC112Q250shows phenotype vs.two factors(genetic teraction plot for ACCCAC112Q and Y2markinteraction plot270.0020.004sun 18 jul 20040.006 0.008chem 10.0100.0120.01401e-045e-04chem 10.002ASHS 2004 Brian S. Yandell0.00528annotated scatter plotscan show relationshipsplot pairssun 18 jul 2004ASHS 2004 Brian S. Yandell29sun 18 jul 2004ASHS 2004 Brian S. Yandell305

Residuals vs Fittedlarge residsind 2,61,801.351.401020504-week vern flower timesun 18 jul 20041020504-week vern flower time31sun 18 jul 2004design: what’s going on?day 0bio 1tech 1day 1bio 2tech 2tech 1bio 1tech 2tech 1tech 2tech 1tech 2bio 1tech 1210-2Cook's distance plot261810.30.2Cook's distance0.11.023610.00.5Standardized residuals11.351.401.45010203040Obs. numberASHS 2004 Brian S. Yandell32design: repeated measuresday 2bio 20Scale-Location plotFitted valuesASHS 2004 Brian S. Yandell-1Theoretical Quantiles80 21.3010080-2Fitted values1.510021.450.0SS genotype-1Standardized residuals0.05-0.05Residuals0.158-week vern flower time2030MM genotype6180 21.30hi influenceind 23,61,81Normal Q-Q plot61-0.1540regressiondiagnosticsfor MMs10108-week vern flower time203040regression linesbio 2tech 2tech 1 repeated measures oneach biological rep measurements may becorrelated over daysbio 1day 0day 1day 2techtech 1 2 biological reps (whole plant tissue)tech 2– 2 bioreps per day? (6 bioreps) or 2 bioreps total?bio 2– independent samples or repeated measurementsday 0tech 1 3 days (0,1,2) 2 technical reps on each daytech 2tech 1tech 2.– also known as sub-samples or pseudo-replicatessun 18 jul 2004ASHS 2004 Brian S. Yandell33design: pseudo-replication repeated measures oneach technical rep does NOT doublereplicates over time!day 2tech 2bio 2day 0tech 1tech 2sun 18 jul 2004 2 biological reps(whole plant tissue) independentsamples from eachbiorep over 3 days 2 technical reps(subsamples orpseudoreps) oneach daytech 1day 1day 1ASHS 2004 Brian S. Yandellbio 1day 0tech 1tech 2day 1tech 1day 2tech 2day 2tech 1tech 2bio 2.ASHS 2004 Brian S. Yandell34design: independent samplesbio 1day 0sun 18 jul 200435sun 18 jul 2004ASHS 2004 Brian S. Yandell366

one trait (gene expression)microarray studies experimental design & analysis per entrycolor/symbol bioreptechnical repsaligned vertically– spot reference vs. general design concepts– field plots on a smaller scale– multiple measurements for same experimentlog2( mRNA )0.5smooth parallel linesshow average day trend 1000s rather than 10s combining information across entries (variance estimation) multiple testing takes on new meaning finding key results0.0– shades of gray (grey?)– p-value and q-value ideas– what is your goal? follow-up studies?p-value for days is smallp 0.00001 confirmation: true positives biochemical pathway studies (KOs, genetics, etc.)-0.501234Daysun 18 jul 200438QTL studies40005000many p-valuesASHS 2004 Brian S. Yandell map informationfrequency3000– linkage map (shown earlier)– missing data and genotypes phenotype information– histograms (shown earlier)– phenotype x genotype plots (shown earlier)– LOD plots: 1D and 2D0flat histogramif null truefalse discoveryrate 3720001500 genesp-values forday effectsmall p largeday effectASHS 2004 Brian S. Yandell1000sun 18 jul 20040.0sun 18 jul 20040.20.40.6p-values for Day0.81.0ASHS 2004 Brian S. Yandell39missing genotype datablack missinggray dominantwhite codominant3456788black missinggray dominantwhite codominant150detailed view of chr 8,individuals un 18 jul 200440Missing genotypes9150Individualsnote many dominantmarkers but no patternto missing data2ASHS 2004 Brian S. Yandellmissing genotype dataMissing genotypes1sun 18 jul 2004ASHS 2004 Brian S. Yandell41sun 18 jul 2004ASHS 2004 Brian S. Yandell10Markers15427

1-QTL scan1-QTL scan(tall is good; small may still be interesting)(model is too simple: misses multiple QTL)6lod424200N2N3N4N5N6sun 18 jul 2004N7 N8N10N12N13N14N15N17N18N19ASHS 2004 Brian S. YandellN243sun 18 jul 20042-QTLs and flowering timeupper trianglefor epistasis(no evidence)lower trianglefor joint effects(strong evidence)ASHS 2004 Brian S. Yandell442-QTLs and flowering time101.5model allows 2 QTLat a timeN38N3upper trianglefor epistasis(no evidence)8N3164lower trianglefor joint effects(strong evidence)LOD score usinggray scale1640.5LOD score usingcolor scale0.5N2N2220N200N2N3Chromosomesun 18 jul 2004ASHS 2004 Brian S. Yandell45sun 18 jul 2004ReferencesASHS 2004 Brian S. Yandell46Thanks– How to Lie with Statistics (1993 WW Norton & Co) Karl Broman, Johns Hopkins U Biostat– How to display data badly (1984 Amer Statist 38:137) my hort & agron colleagues– The Visual Display of Quantitative Information(1983)– Envisioning Information (1990)– Visual Explanation (1997) Funding H Wainer– notes & ideas– Bob Stupar/Jiming Jiang– Brian Just/Phil Simon– Tom Osborn/Marcio Ferreira/C Kole ER Tufte (Graphics Press)– USDA/CSREES Hatch grants– NIH/NIDDK grants– ASHS WS Cleveland– Visualizing Data (1993 Hobart Press)– The Elements of Graphing Data (1994 CRC Press)ASHS 2004 Brian S. Yandell0N3Chromosome D Huffsun 18 jul 2004101.5ChromosomeN1Chromosomelod647sun 18 jul 2004ASHS 2004 Brian S. Yandell488

6 sun 18 jul 2004 ASHS 2004 Brian S. Yandell 31 regression lines 10 20 50 100 10 20 30 40 4-week vern flower time 8-week vern flower time MM genotype

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