Lecture 8 Confidence intervalMeasurement error= reading from an instrument - true valueAnswer :PowerPoint PresentationAnswerRationale behindChanging the confidence levelLecture 8 Confidence interval•Parameter and estimate•Standard error of the mean (SE)•95% confidence interval •Confidence level (coefficient) 1-•Using z score•Two sample problem; matched sample problem•Illustration with Computer simulation Which one? : population mean, sample meanStandard error refers to the standard deviation of an estimatorMeasurement error=reading from an instrument - true value One biotech company specializing microarray gene expression profiling claims they can measure the expression level of a gene with an error of size .1 (that is, after testing their method numerous times, they found the standard deviation of their measurement errors is 0.1) The distribution of errors follow normal distribution with mean 0 (unbiased).(a) Cells from a tumor tissue of a patient are sent to this company for Microarray assay. To assure consistency, the company repeat the assay4 times. The result of one gene, P53 (the most well-studied tumorsuppressor gene), is 1.1, 1.4, 1.5, 1.2.Estimate the true level of P53. What is the SE ? Find a 95% confidenceInterval.Answer :•The sample mean is (X1+X2+X3+X4)/4 = X•Standard deviation of each X random variable is .1•So SD(X) is .1/sqrt (4) = 0.05, this is the SE•Two SE is 0.05 times 2 = .1•So 95% confidence interval runs from 1.3-.1•To 1.3 + .1; that is 1.2 to 1.4•Another cell sample is prepared from a healthy person. The assay results are1.5 1.6 1.4 1.7.Question : Does the tumor cell have a lowerP53 level? Find a 95% confidence interval forThe difference.Answer•The estimator is the difference X - Y,•Where the Y bar is average of 4 random variables again, so it should have the same standard deviation as SD of X bar.Now SD(X-Y) = sqrt (var(X) + var (Y))= sqrt (.052 + .052) = 0.0707So SE is 2 times .0707 = 0.141495% confidence interval goes from (1.3-1.55)-.1414To (1.3-1.55) +.1414; that is from -.2914 to -0.0586Using 95% confidence interval, there is a statistically significant reduction in P53 expression.Rationale behind•Box A , true mean=1.35 SD=.1•Box B true mean= 1.50 SD=.1•Generate sample from box A•Generate sample from box B•Using computer•Find the difference of mean, check 2 SE interval to see if covering the true difference•Repeat it many times to see how often the interval covers the true differenceChanging the confidence level•For a 95% confidence interval, use 2SE rule•This is because of normal distribution - central area P{ -2<Z<2} is about .95•For 80% confidence interval, you look for•P{-c<Z<c}=.80; equivalently P {Z<c}=.80+.10=.90 so c must be
View Full Document
Unlocking...