Stat-403/Stat-650 : Intermediate Sampling and Experimental Design ...
Stat-403/Stat-650 : Intermediate Sampling and Experimental Design ...
Stat-403/Stat-650 : Intermediate Sampling and Experimental Design ...
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The next example shows the help supplied for theconfidence interval function.Example: Excel 2000 Confidence Function“CONFIDENCEReturns the confidence interval for apopulation mean. The confidence interval is arange on either side of a sample mean. Forexample, if you order a product through themail, you can determine, with a particular levelof confidence, the earliest <strong>and</strong> latest theproduct will arrive.” [emphasis mine]The material emphasized, is, of course, a basicmisstatement of the meaning of a confidence interval.A last example displays the help given for thest<strong>and</strong>ard deviation function.Example: Excel 2000 STDEV Function“STDEVEstimates st<strong>and</strong>ard deviation based on asample. The st<strong>and</strong>ard deviation is a measureof how widely values are dispersed from theaverage value (the mean).(snip...)Remarks(snip...)The st<strong>and</strong>ard deviation is calculated using the"nonbiased" or "n-1" method.STDEV uses the following formula:∑∑n x 2 – x⎝⎛ ⎠⎞2------------------------------------------------nn ( – 1)This help item introduces a new term, nonbiased,but that is the least of the difficulties here. (And, ofcourse, the st<strong>and</strong>ard deviation given here is not unbiasedfor the population st<strong>and</strong>ard deviation under any set ofassumptions that I know of!) More importantly, theformula given, the so-called “computing formula,” iswell-known to be a very poor way to compute a st<strong>and</strong>arddeviation. We return to this below.Excel is especially deficient in its statisticalanalysis when some of the data are missing.✔Excel Makes Selecting Predictor Variables InRegression Especially Difficult When DataMissingAs an example, here is a simple paired dataset withsome of the data missing (NA= not available ormissing):PrePost1 1NA 23 34 NA5 56 67 78 89 9Here is the output of the paired data analysis of thesedata with the Excel Data Analysis Toolpack:t-Test: Paired Two Sample for MeansVariable 1 Variable 2Mean 5.375 5.125Variance 7.125 8.410714286Observations 8 8Pearson Correlation 1Hypothesized Mean Difference 0df 7t <strong>Stat</strong> -1P(T
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