Error Calculations In Statistics
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How Do You Calculate The Standard Error
-- see below) is is the population standard deviation, n is the sample size, and z* is the appropriate z*-value for your desired level of confidence (which you can find in the following table). z*-Values for Selected (Percentage) Confidence Levels Percentage Confidence z*-Value 80 1.28 90 1.645 95 1.96 98 2.33 99 2.58 Note that these values are taken from the standard normal (Z-) distribution. The area between each z* value and the negative of that z* value is the confidence percentage (approximately). For example, the area between z*=1.28 and z=-1.28 is approximately 0.80. This chart can be expanded to other confidence percentages as well. The chart shows only the confidence percentages most commonly used. Here are the steps for calculating the margin of error for a sample mean: Find the population standard deviation and the sample size, n. The population standard deviation, will be given in the problem. Divide the population standard deviation by the square root of the sample size. gives you the standard error. Multiply by the appropriate z*-value (refer to the above table
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Systematic Error Calculation
calculators Book reviews Glossary AP practice exam Problems and solutions Formulas Notation Share with Friends random error calculation Important Statistics Formulas This web page presents statistics formulas described in the Stat Trek tutorials. Each formula links to a web page that explains how statistical error analysis to use the formula. Parameters Population mean = μ = ( Σ Xi ) / N Population standard deviation = σ = sqrt [ Σ ( Xi - μ )2 / N ] Population variance = σ2 = Σ ( http://www.dummies.com/education/math/statistics/how-to-calculate-the-margin-of-error-for-a-sample-mean/ Xi - μ )2 / N Variance of population proportion = σP2 = PQ / n Standardized score = Z = (X - μ) / σ Population correlation coefficient = ρ = [ 1 / N ] * Σ { [ (Xi - μX) / σx ] * [ (Yi - μY) / σy ] } Statistics Unless otherwise noted, these formulas assume simple random sampling. Sample mean = x = ( Σ xi ) / n Sample standard deviation = http://stattrek.com/statistics/formulas.aspx s = sqrt [ Σ ( xi - x )2 / ( n - 1 ) ] Sample variance = s2 = Σ ( xi - x )2 / ( n - 1 ) Variance of sample proportion = sp2 = pq / (n - 1) Pooled sample proportion = p = (p1 * n1 + p2 * n2) / (n1 + n2) Pooled sample standard deviation = sp = sqrt [ (n1 - 1) * s12 + (n2 - 1) * s22 ] / (n1 + n2 - 2) ] Sample correlation coefficient = r = [ 1 / (n - 1) ] * Σ { [ (xi - x) / sx ] * [ (yi - y) / sy ] } Correlation Pearson product-moment correlation = r = Σ (xy) / sqrt [ ( Σ x2 ) * ( Σ y2 ) ] Linear correlation (sample data) = r = [ 1 / (n - 1) ] * Σ { [ (xi - x) / sx ] * [ (yi - y) / sy ] } Linear correlation (population data) = ρ = [ 1 / N ] * Σ { [ (Xi - μX) / σx ] * [ (Yi - μY) / σy ] } Simple Linear Regression Simple linear regression line: ŷ = b0 + b1x Regression coefficient = b1 = Σ [ (xi - x) (yi - y) ] / Σ [ (xi - x)2] Regr
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Concepts Section Tests Pre-test Post-test Useful Materials Glossary Online Calculators Redox Calculator Kinetics Arrhenius Calculator Thermodynamics Calculator Nuclear Decay Calculator Linear Least Squares Regression Newton's Method Equation Solver Compressibility Calculator Units Conversion Calculator Nomenclature Calculator Related Information Links Texas Instruments Calculators Casio Calculators Sharp Calculators Hewlett Packard Calculators Credits Credits Contact Webmaster Simple Statistics There are a wide variety of useful statistical tools that you will encounter in your chemical studies, and we wish to introduce some of them to you here. Many of the more advanced calculators have excellent statistical capabilities built into them, but the statistics we'll do here requires only basic calculator competence and capabilities. Arithmetic Mean, Error, Percent Error, and Percent Deviation Standard Deviation Arithmetic Mean, Error, Percent Error, and Percent Deviation The statistical tools you'll either love or hate! These are the calculations that most chemistry professors use to determine your grade in lab experiments, specifically percent error. Of all of the terms below, you are probably most familiar with "arithmetic mean", otherwise known as an "average". Mean -- add all of the values and divide by the total number of data points Error -- subtract the theoretical value (usually the number the professor has as the target value) from your experimental data point. Percent error -- take the absolute value of the error divided by the theoretical value, then multiply by 100. Deviation -- subtract the mean from the experimental data point Percent deviation -- divide the deviation by the mean, then multiply by 100: Arithmetic mean = ∑ data pointsnumber of data points (n) Error = Experimental value - "true" or theoretical value Percent Error = Error Theoretical value ∗100 Deviation = Experimental value - arithmetic mean Percent Deviation = DeviationTheoretical value ∗100 A sample problem should make this all clear: in the lab, the boiling point of a liquid, which has a theoretical value of 54.0° C, was measured by a student four (4) times. Determine, for each measurement, the error, percent error, deviation, and percent deviation. Observed value Error Percent error Deviation Percent deviation 54.9 0.9 2.0% 0.5 0.9% 54.4 0.4 0.7% 0.0 0.0% 54.1 0