BIOL 570 1nd Edition Lecture 4 Outline of Last Lecture I. Numerical data a. empirical ruleb. coefficient of variationc. interquartile range, box plots, outliersII. Categorical dataa. proportionsIII. Brief summary of variables, samples, and populationsIV. Properties of descriptive statisticsOutline of Current Lecture I. Estimation a. Point estimationII. Errora. Sampling errorIII. Sampling distribution IV. Standard error a. Definitionb. calculation V. 95% confidence interval a. Definitionb. calculation using the 2SE rulec. interpretationCurrent LectureEstimation- the process of inferring a population parameter from sample dataWhat is the mean dopamine concentration in the brains of rats? A sample of 7 individuals6.8 5.3 6.0 5.9 6.8 7.4 6.2 (nmol/g)Ȳ = 6.34 nmol/gPoint estimation- a single “best guess” of the value of a parameterError- the difference between our estimate and the population parameter value: Ȳ - µThese notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.50%µ = (.5)(0) + (.5)(2) = 1σ = 10(female) 2(male) Number of anther per individual n=6 n=60 20 Ȳ = (4/6) = 2/3 2 Ȳ = (6/6) = 10 00 02 02 2Sampling error- the error that is caused by the fact that our sample is finite*the larger the samples size, the more narrow the graph and less sampling errorFrequency 2/3 1Sampling distribution- the probability distribution of estimates that we might obtain when wesample the populationFun facts about the Sampling Distribution of Ȳ1) bell-shaped (normal distribution)2) mean is µa. Ȳ is an unbiased estimator; meaning it is right where it’s supposed to be which is at the population meanEmpirical rule- typically 95% of our observations are within 2SD of the meanThe standard error of an estimate- the standard deviation of the estimate’s sampling distribution: σȲ s ~σµ = 1 σ = 1n = 6σȲ = 1/ (sqrt 6) = 0.408n = 24σȲ = 1/ (sqrt 24) = 0.204Ȳ = 6.34 nmol/gs = .702SEȲ = 0.702/ (sqrt 7) = 0.265 nmol/gWe’d report: Ȳ = 6.34 ± 0.265 (SE) nmol/gSampling error- the larger the sample size, the closer to zeroApproximately 95% of the Ȳ estimates will be within 2SEȲ of µ…- so if we create an interval to include points within 2SEȲ of Ȳ, then approximately 95% of our intervals should contain µInterval estimate- range of points that are our best guessesConfidence interval- a range of values around our point estimate. The interval is likely to contain the value of the population parameter.- If we always report a 95% confidence interval, then the population parameter should be within the interval in 95% of our studies.We are 95% confident that… Ȳ - 2SEȲ < µ < Ȳ + 2SEȲ6.34 – 0.53 < µ < 6.34 + 0.535.81 nmol/g < µ < 6.87 nmol/g******HOMEWORK, Alexander #3Mean: height of the barStandard deviation: length of the