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lecture15

# lecture15 - 3.051J/20.340J Lecture 15 Statistical Analysis...

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1 3.051 J / 20 .340 J Lecture 15 Statistical Analysis in Biomaterials Research 1. Rationale: Why is statistical analysis needed in biomaterials research? ± Many error sources in measurements on living systems! Examples of Measured Values and Error in Biomaterials Data Graphs removed for copyright reasons.

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2 3.051 J / 20 .340 J Case Example: cell sedimentation assay of % of cells adhering to a biomaterial vs. control (the simplest cell assay) Sources of data variation: ¾ Contamination of surface cytotoxicity or modified surface chemistry ¾ Variations in the number of cells seeded on each surface ¾ Variations in biomaterial synthesis (reagent amounts, T, time, etc.) ¾ Variations in cells (different cell passages) ¾ Variations in media (e.g., different concentrations, proteins agglomerated) ¾ Variations in sterilization procedure ¾ Researcher error (e.g., sneezing on samples) ± Behavior is best characterized by a population or distibution of values Case Example: Titration of HCl solution with equimolar NaOH solution. Graphs removed for copyright reasons.
3 3.051 J / 20 .340 J Data converge to a population as N : Graph removed for copyright reasons. ± Our Goal: to make enough measurements to accurately characterize the distribution of behaviors, via ¾ The mean of the data distribution = <x> from N measurements N x i x = i = 1 N ¾ The width of the distribution, or standard deviation, S : N 2 ( x i −< x > ) Note that the standard deviation, S , is i = 1 divided by N -1 to avoid biasing, since S = we do not know the “true” mean, N 1 µ.. Τ he universal standard deviation, σ, is divided by N .

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−σ 4 3.051 J / 20 .340 J Equivalently the variance, S 2 , is defined by: N N x i 2 N
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lecture15 - 3.051J/20.340J Lecture 15 Statistical Analysis...

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