Exam 1 Cheat Sheet
Exam 1 Cheat Sheet BE 332
Popular in Engr Prop of Bio Materials
Popular in Biomedical Engineering
This 1 page Study Guide was uploaded by Rachel Streufert on Thursday October 1, 2015. The Study Guide belongs to BE 332 at Michigan State University taught by d. reinhold in Summer 2015. Since its upload, it has received 123 views. For similar materials see Engr Prop of Bio Materials in Biomedical Engineering at Michigan State University.
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Date Created: 10/01/15
ChaQter I Intro Biomaterial materials used in biological systems Biological material materials that are or once were living Biological properties interactions of matter and biological organisms bio activity biocompatibility biodegradability toxicity Chemical properties observed during chemical reactions reaction rates reactivity equilibrium constants Physical properties observed without a change in composition of material shape size density Intensive properties depend only on material independent of size specific surface area Extensive properties dependent on size surface area mass Accuracy close to true value Precision close to each other Variable properties in biomaterials heterogeneity and asymmetry ChaQter 2 Measuring Instrumental measurements Numerical amp continuous Continuous values that are measured only valid to certain sig fig Discrete values that are counted Interval scale zero is arbitrary redness of apple by spectrophotometer Ratio scale true zero highest level of data Ordinal data words or ranks where this is an order but no magnitude preference ranks consumer satisfaction ranks Nominal data words and names used to categorize or classify variety of pearlowest level of data Gross error mistakes in experiment values vary differently in data Experimental error experimenter and instrument error Systematic experimental error lowers accuracy of measurements effects every sample Random experimental error indeterminate results from variability in readings Sampling error sample does not represent entire population Sampling types probabilityor random simple randomindependent systematicno too close together stratifiedproportionally clusterall values may not be represented non probabilityconvenienceavailability quotasubrange quota snowballsurvey pass Normal Distribution mean amp standard deviation 6827 of values within one SD 9545 within two SD 1 mean 0 SD Ntotal number of values in pop Xbar sample average n1 degrees of freedom sstandard deviation Poisson distribution microbial analyses that use discrete integer values characterization only on mu Gates Gaudin Schuhman GGS function linear when plotted on logarithmic paper Weibull distribution describe population that have max and no neg values Rosin Rammler Sperling Bennet distribution ShapiroWilk assessment fewer than 30 data points 1 order smallest to largest 2 list data largestsmallest in next column 3 compute weighted sum of most extreme values 4 compare with given alpha normality rejected if WltWcrit Kurtosis leptokurticpeaky platykurtic at if zgtzcrit nonnormal standard error kurtosis sqrt24N Skewness standard error skew sqrt6N Cslt05 symmetrical 05ltCslt1 moderately skewed Csgt1 extremely skewed QQ plot data values against predicted values PERCENTRANK functions NORMDIST Standard error of mean quanti es uncertainty in an estimate of the mean standard deviationsqrtnumber of samples Con dence intervals measure of central tendency mean and uncertainty ChaQter 3 Analyzing Sig testing 1state objective 2state null amp alt hypo dir Hypo XgtY3set sig level 4 select test Type errors I rejecting a null hypo that is true 11 failing to reject incorrect null hypo Parametric tests use means amp SD provide more info more likely to detect real treatment effect when data ND Nonparametric tests nonND data based on frequencies ranks percentiles Ftest 1state objective 2 state nullalt hypo 3 set sig level 4 select test 5 calc test stat 6 assess sig Ttest computes pvalue probability of being wrong ANOVA F test to det if diff exist qstat to det where diff lie alpha risk of erroneously asserting diff for all comparisons combined denominatordegrees of freedom from F test num means being tested ChaQter 4 Predicting Regression estimation of how much one variable increasesdecreases on average with another variable quanti cation of association w correlation coefficient Best determined by sum of squared diff between observed values of dependent variable y and predicted values of y at all measured values for ind vari x Standard error of the estimate uncertainty associated w dep vari calculated by a regression Standard errors of regression coefficients uncertainty in the fitted parameters b amp m Correlation coef cient quantifies strength of the relationship between 2 variables without providing insight into the trend range from 1 to 1 highly correlated does not mean causation Pearson productmoment correlation coefficient normal dis data Spearman rank correlation coef cient ordinal scale data Simplify linearization of eq 1Identify dependentindependent variables 2Rearrange eq so all terms y on left all x on right 3Take log of both sides 4Rearrange eq into FymFxb Eq fitting in Excel 1Fitting eq on graph 2using embedded formulas or data analysis to do the same with linear or exponential eq 3using SOLVER to nd parameters 1pro fast con can t use to find eq for 3 parameter eq regression options limited little statistical info 2pro more statistical info regression tool quick con more work limited forms of eq linearexponential limited to 2 parameters 3pro gt2 parameters no linearization needed con no statistics may provide erroneous values LINESTregression tool High correlationRquot2 close to 1 low standard error lt10 statistically sig lt005 pvalue SOLVERtrendline compare predicted amp measured values determine if YX using LINEST correlation close to 1 pvalueltcrit ChaQter 5 Finding Sensitivity analysis in uence of dependent variables x on independent variable y Interpolating yy0xx0y1y0x1x0 Table 11 Selection of significance tests 4 Type of experiment Process Value Uncertainty m u L m m c39 35 2 3 3 5 E c 397 a r n E 7 u m a 5 u 3 E E m I g xlng r f2 r1f 2 x fl egg E EEE 5 15 eq u 34 Average X N 63 if Egg 3E3 E E E 3351 39 2quot gt mu aceInn sum 2 Levelof g3 33 e E g a 3 2 u 395 g E 3 a g Figure 210 tdlStl lbUth S measurement liiroE F g39s39inaEmisn39 a 3555 45gt gt quot 39 Y 2 q interval drawn Unpaired t Analysis of Paired ttest Re1peated Linear Addition 5 1 y 0 MILL72 Loy from normally test variance Confidence measures regression distributed Con dence intervals analysis of Pearson product populations intervals variance moment W I correlation Suhtmc ml Z Z T 7 0 2 Jl0w39quot 0y Bland artman analy515 Nominal Chiasquarre analysisajfi Mdlemar39s Cochran Q Contingency rg T ODntingency coef cients f 3 o f a Ordinal Mann Kruskale Willcouron Friedman Spear rank Mulhphmhnn Z 7 7 Whitney Wallis signed rank statistic correlation ranksum statistic I I rest I ff 7 6 2 MGXJ Survrvaltiime Logirankitest Dimsron I N J or Gehan39s test
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