StatisticsA scientific reportThe idea is to try and give all the information to helpothers to judge the value of your contributions, not justthe information that leads to judgment in one particulardirection or another. Richard P. Feynman
StatisticsDescription of observed datamean, median, mode (central tendency)standard deviation, range (dispersion)Presentation of uncertaintyp-value, statistical significance (hypothesis testing)confidence interval, SEM (interval estimation)
StatisticsWhat uncertainty?Generalization uncertainty, for example:- From one sample of rats to all rats (the uncertainty caused by biological variability)- From a single measurement on a single rat to all measurements of the same kind on the same rat (the uncertainty caused by using imperfect measurement instruments, i.e. reliability)
StatisticsWhat determines the degree of uncertainty?1. The number of observations2. The variability
StatisticsWhat is important when presenting results?1. The number of observations2. The variability
Reported mean concentration with ±SD (bar chart)
Estimated mean concentration with 95% confidence intervals
StatisticsWhy use CI instead of SEM?Because the CI is the better measure of uncertainty n SEM CI (for a mean value) 2 ±1 50% 3 ±1 58% 4 ±1 63% 6 ±1 64% 7 ±1 65% ∞ ±1 68%
StatisticsOther problems related to generalization uncertainty1. Independence of observations2. Gaussian probability distribution3. Multiplicity
Statistics1. Independent observations (2 treatments, 4 rats, n = ?) n=4 n=8 n = 96
StatisticsIndependent observationsDistinguish between:1. Biological variation2. Measurement reliabilityDescribe the sources of variation clearly in the manuscript!How many animals, repeated observations, technicalreplicates, etc. have been analyzed?
StatisticsAre your results empirically supported?Or do they rely on your assumptions?- Students t-test (Gaussian, identical variance)- Mann-Whitney U-test (identical shape and variance)
StatisticsDid you check if the assumptions were fulfilled?- How did you do it?- What was the result?Describe it in the manuscript!
Statistics3. MultiplicityWith more than one tested null hypothesis the realsignificance level will differ from the nominal
Statistics3. Multiplicity- Multiplicity corrections correct the type-1 error rate- Multiplicity corrections increase the type-2 error rate
Statistics3. Multiplicity- Bonferroni is not a good method, several better exist, for example the methods developed by Holm and Hochberg- P-value corrections within endpoints do not solve the problem of testing multiple endpoints
Statistics3. MultiplicityWhat is your strategy for dealing with multiplicity? AreBonferroni corrections necessary? Are all multiplicityissues addressed?Describe it in the manuscript!
StatisticsSummaryAs an author of a scientific report your task is toperform an adequate evaluation and presentation ofthe uncertainty and limitations of your findings.This involves more than just calculating a p-value.
StatisticsSummaryWhen a well-done trial or experiment or observationalstudy is fairly, honestly, and thoroughly reported, it willhave so many warts, footnotes, and exceptions that itmay be hard for the uninitiated to believe that the workwas of high quality. Frederick Mosteller