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Previous Lecture : Exploring Data

Previous Lecture : Exploring Data. This Lecture. Introduction to Biostatistics and Bioinformatics Descriptive Statistics. Process of Statistical Analysis. Population. Random Sample. Make Inferences. Describe. Sample Statistics. Distributions. Normal. Skewed. Long tails. Complex.

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Previous Lecture : Exploring Data

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  1. Previous Lecture: Exploring Data

  2. This Lecture Introduction to Biostatistics and Bioinformatics Descriptive Statistics

  3. Process of Statistical Analysis Population Random Sample Make Inferences Describe Sample Statistics

  4. Distributions • Normal • Skewed • Long tails • Complex

  5. Randomly Sample from any Distribution Generate a pair of random numbers within the range. Assign them to x and y Keep x if the point (x,y) is within the distribution. Repeat 1-3 until the desired sample size is obtained. The values x obtained in this was will be distributed according to the original distribution.

  6. Mean Sample Mean

  7. Mean • Normal • Skewed • Long tails • Complex • 1 • -1 • 0.2 • -0.2 • 100 Sample Size

  8. Median, Quartiles and Percentiles Sample Quartiles for 25% of the sample for 50% of the sample (median) for 75% of the sample Inter Quartile Range Percentiles for m% of the sample

  9. Median and Mean • Normal • Skewed • Long tails • Complex • 1 Median - Gray • -1 • 0.2 • -0.2 • 100 Sample Size

  10. Quartiles and Mean • Normal • Skewed • Long tails • Complex • 1 Q3 - Purple Q1 – Gray • -1 • 0.2 • -0.2 • 100 Sample Size

  11. Central Limit Theorem • The sum of a large number of values drawn from many distributions converge normal if: • The values are drawn independently; • The values are from the one distribution; and • The distribution has to have a finite mean and variance.

  12. Variance Sample Mean Variance

  13. Variance • Normal • Skewed • Long tails • Complex • 0.6 • 0 • 0.1 • 0 • 100 Sample Size

  14. Inter Quartile Range and Standard Deviation • Normal • Skewed • Long tails • Complex • 1.0 IRQ/1.349 - Gray • 0 • 0.4 • 0 • 100 Sample Size

  15. Uncertainty in Determining the Mean • Normal • Skewed • Long tails • Complex • n=3 • n=3 • n=3 • n=10 • n=100 • n=10 • n=10 • n=10 • n=1000 • n=100 • n=100 • n=100 Average

  16. Standard Error of the Mean Sample Mean Variance Standard Error of the Mean

  17. Error bars In 2012, error bars appeared in Nature Methods in about two-thirds of the figure panels in which they could be expected (scatter and bar plots). The type of error bars was nearly evenly split between s.d. and s.e.m. bars (45% versus 49%, respectively). In 5% of cases the error bar type was not specified in the legend. Only one figure used bars based on the 95% CI. None of the error bar types is intuitive. An alternative is to select a value of CI% for which the bars touch at a desired P value (e.g., 83% CI bars touch at P = 0.05). M. Krzywinski & N. Altman, Error Bars, Nature Methods 10 (2013) 921

  18. Box Plot M. Krzywinski & N. Altman, Visualizing samples with box plots, Nature Methods 11 (2014) 119

  19. Box Plots • Normal • Skewed • Long tails • Complex • n=5 • n=5 • n=5 • n=5 • n=10 • n=10 • n=10 • n=10 • n=100 • n=100 • n=100 • n=100

  20. Box Plots with All the Data Points • Normal • Skewed • Long tails • Complex • n=5 • n=5 • n=5 • n=5 • n=10 • n=10 • n=10 • n=10 • n=100 • n=100 • n=100 • n=100

  21. Box Plots, Scatter Plots and Bar Graphs • Normal Distribution • error bars: standard deviation • Error bars: standard deviation • error bars: standard error • error bars: standard error

  22. Box Plots, Scatter Plots and Bar Graphs • Skewed Distribution • error bars: standard deviation • Error bars: standard deviation • error bars: standard error • error bars: standard error

  23. Box Plots, Scatter Plots and Bar Graphs • Distribution with Fat Tail • error bars: standard deviation • Error bars: standard deviation • error bars: standard error • error bars: standard error

  24. Application: Analytical Measurements Measured Concentration Theoretical Concentration

  25. A Few Characteristics of Analytical Measurements Accuracy: Closeness of agreement between a test result and an accepted reference value. Precision: Closeness of agreement between independent test results. Robustness:Test precision given small, deliberate changes in test conditions (preanalytic delays, variations in storage temperature). Lower limit of detection: The lowest amount of analyte that is statistically distinguishable from background or a negative control. Limit of quantification: Lowest and highest concentrations of analyte that can be quantitatively determined with suitable precision and accuracy. Linearity: The ability of the test to return values that are directly proportional to the concentration of the analyte in the sample.

  26. Measuring Blanks

  27. Coefficient of Variation Sample Mean Variance Coefficient of Variation (CV)

  28. Lower Limit of Detection The lowest amount of analyte that is statistically distinguishable from background or a negative control. Two methods to determine lower limit of detection: Lowest concentration of the analyte where CV is less than for example 20%. Determine level of blank by taking 95th percentile of the blank measurements and add a constant times the standard deviation of the lowest concentration. K. Linnet and M. Kondratovich, Partly Nonparametric Approach for Determining the Limit of Detection, Clinical Chemistry 50 (2004) 732–740.

  29. Limit of Detection and Linearity Measured Concentration Measured Concentration Theoretical Concentration Theoretical Concentration

  30. Precision and Accuracy Measured Concentration Measured Concentration Theoretical Concentration Theoretical Concentration

  31. Descriptive Statistics - Summary • Example distribution: • Normal distribution • Skewed distribution • Distribution with long tails • Complex distribution with several peaks • Mean, median, quartiles, percentiles • Variance, Standard deviation, Inter Quartile Range (IQR), error bars • Box plots, bar graphs, and scatter plots • Application: Analytical measurements: • Accuracy and precision • Limit of detection and quantitation • Linearity • Robustness

  32. Descriptive Statistics – Recommended Reading http://blogs.nature.com/methagora/2013/08/giving_statistics_the_attention_it_deserves.html

  33. Descriptive Statistics – Recommended Reading http://greenteapress.com/thinkstats/

  34. Next Lecture: Data types and representations in Molecular Biology GFF3 FASTA ##gff-version 3 #!gff-spec-version 1.20 ##species_http://www.ncbi.nlm.nih.gov/Taxonomy/Browser/wwwtax.cgi?id=7425 NC_015867.2 RefSeqcDNA_match 66086 66146 .- . ID=aln0;Target=XM_008204328.1 1 61 +; for_remapping=2;gap_count=1;num_ident=8766;num_mismatch=0;pct_coverage=100;pct_coverage_hiqual=100;pct_identity_gap=99.9886;pct_identity_ungap=100;rank=1 NC_015867.2RefSeqcDNA_match 65959 66007 .- . ID=aln0;Target=XM_008204328.1 62 110 +;for_remapping=2;gap_count=1;num_ident=8766;num_mismatch=0;pct_coverage=100;pct_coverage_hiqual=100;pct_identity_gap=99.9886;pct_identity_ungap=100;rank=1 NC_015867.2RefSeqcDNA_match 65799 65825 .- . ID=aln0;Target=XM_008204328.1 111 137 +;for_remapping=2;gap_count=1;num_ident=8766;num_mismatch=0;pct_coverage=100;pct_coverage_hiqual=100;pct_identity_gap=99.9886;pct_identity_ungap=100;rank=1 >URO1 uro1.seq Length: 2018 November 9, 2000 11:50 Type: N Check: 3854 .. CGCAGAAAGAGGAGGCGCTTGCCTTCAGCTTGTGGGAAATCCCGAAGATGGCCAAAGACAACTCAACTGTTCGTTGCTTCCAGGGCCTGCTGATTTTTGGAAATGTGATTATTGGTTGTTGCGGCATTGCCCTGACTGCGGAGTGCATCTTCTTTGTATCTGACCAACACAGCCTCTACCCACTGCTTGAAGCCACCGACAACGATGACATCTATGGGGCTGCCTGGATCGGCATATTTGTGGGCATCTGCCTCTTCTGCCTGTCTGTTCTAGGCATTGTAGGCATCATGAAGTCCAGCAGGAAAATTCTTCTGGCGTATTTCATTCTGATGTTTATAGTATATGCCTTTGAAGTGGCATCTTGTATCACAGCAGCAACACAACAAGACTTTTTCACACCCAACCTCTTCCTGAAGCAGATGCTAGAGAGGTACCAAAACAACAGCCCTCCAAACAATGATGACCAGTGGAAAAACAATG FASTQ @SRR350953.5 MENDEL_0047_FC62MN8AAXX:1:1:1646:938 length=152 NTCTTTTTCTTTCCTCTTTTGCCAACTTCAGCTAAATAGGAGCTACACTGATTAGGCAGAAACTTGATTAACAGGGCTTAAGGTAACCTTGTTGTAGGCCGTTTTGTAGCACTCAAAGCAATTGGTACCTCAACTGCAAAAGTCCTTGGCCC +SRR350953.5 MENDEL_0047_FC62MN8AAXX:1:1:1646:938 length=152 +50000222C@@@@@22::::8888898989::::::<<<:<<<<<<:<<<<::<<:::::<<<<<:<:<<<IIIIIGFEEGGGGGGGII@IGDGBGGGGGGDDIIGIIEGIGG>GGGGGGDGGGGGIIHIIBIIIGIIIHIIIIGII @SRR350953.7 MENDEL_0047_FC62MN8AAXX:1:1:1724:932 length=152 NTGTGATAGGCTTTGTCCATTCTGGAAACTCAATATTACTTGCGAGTCCTCAAAGGTAATTTTTGCTATTGCCAATATTCCTCAGAGGAAAAAAGATACAATACTATGTTTTATCTAAATTAGCATTAGAAAAAAAATCTTTCATTAGGTGT +SRR350953.7 MENDEL_0047_FC62MN8AAXX:1:1:1724:932 length=152 #.,')2/@@@@@@@@@@<:<<:778789979888889:::::99999<<::<:::::<<<<<@@@@@::::::IHIGIGGGGGGDGGDGGDDDIHIHIIIII8GGGGGIIHHIIIGIIGIBIGIIIIEIHGGFIHHIIIIIIIGIIFIG

  35. Next Tutorial: Python Programming Saturday 9/13 at 3 PM in TRB 120

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