Statistics Study Guide for Chem 102 Dr. David L. Zellmer Department of Chemistry, CSUF Spring 2000 The following Study Guide is a list of the statistical topics covered in Chemistry 102. You are expected to know how to do all of these, unless some have been excluded by your instructor. When links are provided, click on them for more information. Note that some topics may not get detailed coverage until later in the course when they are needed in the laboratory. Mean and Median: the balance check exercise for instrument accuracy. Range and Standard Deviation: measures of precision. Getting the mean and standard deviation on your calculator. Directions for Statistics on Calculators. Absolute Errors and Relative Errors: a comparison table. Absolute vs. Relative Errors Relative Precision Errors and "Class A" Analytical Work. Absolute vs. Relative Errors Relative Accuracy Errors and Getting a Good Grade. Absolute vs. Relative Errors The t-table, degrees of freedom, and "s approaches sigma" for a proven analyst, automated instrument, or respected laboratory. t-table with definitions The 95% Confidence Limit of the mean. Statistics Formulas Propagated Error using the relative errors of Molarity runs and Unknown runs. A Survival Guide for Analytical Chemistry--Statistics. Also see Propagated Error Calculation Outliers: When can data be thrown out? The only sure way for small data sets: keep good notes in your notebook, and remove the one you said was swept up off the floor. The Q-test; when should you use it? The Q-test and credibility when removing outliers. (See your text for a discussion of the Q-test.) The t-test when the Truth is Known. t-calc > t-table vs. the Skoog C.L. way. (In the Skoog method, a confidence interval is computed from t-table, then compared to the distance between the mean value and the "true" value. See the text for examples.) Statistics Formulas Pooled standard deviation, improving s when several data sets have similar sigmas. Note that if "s approaches sigma," the pooled s is not needed, and t-critical is read from the bottom of the t-table. Statistics Formulas The F-test, to see if several data sets have similar sigmas. (See your text for details.) The t-test for two experimental mean values. The Skoog confidence limit t-test vs. the t-calc > t-table way. Statistics Formulas LLS, when can we use it? When should we NOT use it? A Survival Guide for Analytical Chemistry--Statistics Does your plot look strange? You may be a victim of the Dreaded Line Plot. Check the link to avoid making this embarrassing, but common, mistake. LLS, using the quick and dirty Excel Trendline. Calibration with standard solutions. Computing an unknown concentration from instrument response. A Survival Guide for Analytical Chemistry--Statistics Estimating errors in LLS by looking at your data plot. (The "eyeball" method.) A Survival Guide for Analytical Chemistry--Statistics For a quick-and-dirty error analysis using the STEYX() Excel formula, see A Tutorial on Gran's Plotting for End Point Detection using Potentials Table: Comparing the Skoog and West equations to their Excel spreadsheet equivalents. The LLS Formulas--S&W vs. Excel. The Model LLS analysis, featuring STEYX() and s-sub-c for error calculations. Note that errors increase as we move away from the center of our standard data. The Sp99 Model LLS Analysis The error of the X-axis intercept. This is needed for Grans Analysis and Standard Addition Analysis. A Tutorial on Gran's Plotting using pH. Includes Volume Intercept Error Analysis This is a full treatment using a variation on s-sub-c. See also The Standard Addition Method, which contains an additional example, as well as an animation of X-axis error. LLS fitting for non-linear data using the Excel Trendline wizard. How to make a Second Order Fit.