# 1 statistical analysis

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Information about 1 statistical analysis

Published on February 17, 2014

Author: dgrapov

Source: slideshare.net

Biology Chemistry Informatics Evaluation of sample processing protocols for the analysis of pumpkin leaf metabolites Statistics Goals: Compare different extraction and drying protocols to identify the “optimal” sample processing approach Topics: 1. Data quality overview 2. Statistical comparisons 3. Power analysis

Data Quality Overview Biology Chemistry Informatics Goal: Calculate and visualize the summary statistics for each metabolite/treatment (Use DATA: Pumpkin data 1.csv) Calculate: 1. Mean and standard deviation (sd) 2. The percent relative standard deviation, %RSD, (sd/mean)*100 Statistics Visualize: 1. The relationship between mean vs. sd, mean and %RSD 2. Compare mean metabolite values for all treatments Exercises: 1. Describe the relationship between analyte mean and sd, mean and %RSD? 2. Describe what constitutes an “optimal” method? 3. Which extraction/treatment should be chosen to process further samples?

Summary statistics Biology Chemistry Statistics Informatics

Mean vs. SD Biology Chemistry Informatics Mean and sd are highly correlated Larger means have larger sd This effect is also called heteroscedasticity Statistics SD • • • Mean

Mean vs. %RSD Biology Chemistry Informatics Statistics %RSD • %RSD is minimally correlated with the mean Can be used as criteria for: • Comparing method reproducibility • Identifying data quality Mean

Qualities of %RSD Biology Chemistry Informatics • • • %RSD (also called the coefficient of variation or CV) is the sd (variation) scaled by the mean (magnitude). Removes the relationship between variation and magnitude Provides a single value which can be used to compare the variation of a measurement among different treatments/samples Statistics Showing the mean and sd of the %RSD for all metabolites for a given treatment

Data quality Biology Chemistry Informatics Below LOQ %RSD (sensitivity) Bad Statistics ~40% Moderate ~10,000 Mean Good

Selecting the “optimal” method Biology Chemistry Informatics Optimal can be: 1. Lowest average %RSD for all measurements 2. Lowest %RSD for measurements of interest 3. Largest number of metabolites passing %RSD cutoff 4. Lowest average %RSD for all measurements passing %RSD cutoff Using strategy #4 for metabolites %RSD ≤ 40 Statistics Count Method #2 (ACN/IPA/water 3:3:2) looks optimal… %RSD (mean sd)

Based on Method #2 Biology Chemistry Informatics Mean %RSD %RSD ≤ 40 Log Mean Statistics Analytes with high signal and high %RSD should be further interrogated for explanations of low reproducibility Log Mean

Biology Chemistry Statistical comparison of the effects of sample drying Informatics Goals: identify the effect of treatment (fresh/lyophylized) on Methods #3-4 performance? (Use DATA: Pumpkin data 2.csv) Count %RSD (mean sd) Statistics Steps: 1. Use t-Test to compare metabolite means for each treatment 2. Correct for the false discovery rate (FDR) adjusted p-value 3. Estimate FDR (q-value) Visualize: 1. Relationship between p-value and FDR adjusted p-value 2. Relationship between FDR adjusted p-value and q-value 3. Box plots for highest and lowest p-value metabolites Questions: 1. When should you use a one-sample, two-sample or paired t-test, ANOVA? *return to 0-introduction

Hypothesis Testing Strategies Biology Chemistry Statistics Informatics • One sample t-Test is used to compare single value to a population mean • Two sample t-Test is used to compare 2 independent populations • Paired t-Test is used to compare the same population (intervention, repeated measures) • One-way ANOVA (analysis of variance) is used to compare n populations for one factor • Two-way ANOVA is used to compare n populations for 2 factors • ANCOVA (analysis of covariance) is used to adjust n populations for covariate (typically continuous) prior to testing for n factors • Mixed effects models are versatile analogue to linear model or ANOVA/ANCOVA and typically used to adjust for covariates or variance due to repeated measures *All of the above are parametric tests, and some of which have non-parametric analogues

p-value vs. FDR adjusted p-value Biology Chemistry Informatics FDR adjusted p-value Benjamini & Hochberg (1995) (“BH”) • Accepted standard Statistics Bonferroni • Very conservative • adjusted p-value = pvalue*# of tests (e.g. 0.005 * 148 = 0.74 ) p-value

p-value vs. q-value Biology Chemistry Informatics Statistics FDR adjusted p-value • q-value can be used to select appropriate p-value cut off for an acceptable FDR for multiple hypotheses tested • q=0.05 nicely matches assumptions of p=0.05 for multiple hypotheses tested • q-value≤0.2 can be acceptable q-value

Biology Chemistry Change in metabolites due to treatment Informatics Statistics Effect size: small large

Effect of drying: is minimal Biology Chemistry Informatics - Log p-value FDR p-value= 0.05 Statistics 7 significantly different metabolites out of 148 (5%) - Log p-value Fold change (relative to fresh)

Power analysis Biology Chemistry Informatics Goals: Use power analysis to plan a follow up experiment to detect differences in metabolites due to treatment Steps: 1. Calculate effect size and power for three metabolites 2. Given the observed effect size calculate the number of samples needed to reach 80% power Statistics Questions: 1. How would you take FDR in to account?

Power analysis Biology Chemistry Informatics Statistics Scaled difference in means between treatments Ability to detect a difference when it exists (control false negative rate) Probability of being wrong when spotting a difference (control false positive rate)

Power analysis Biology Chemistry Informatics The minimum fold change (FC) in means observable by the study can be calculated using RSD and estimated effect size to reach 0.8 (80%) power given the population size Statistics RSD = 0.21 and effect size (EF) =1.2 We can observe a minimum of a 38% change in means at 0.8 power (p= 0.05).

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