Meas & Analy Eco Act
Meas & Analy Eco Act ECO 3410
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This 6 page Class Notes was uploaded by Stacey Bergstrom on Monday October 12, 2015. The Class Notes belongs to ECO 3410 at Florida International University taught by Staff in Fall. Since its upload, it has received 6 views. For similar materials see /class/221810/eco-3410-florida-international-university in Economcs at Florida International University.
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Date Created: 10/12/15
Excel and Statistics Jonathan Hill In this document we brie y explain how to use EXCEL to analyze data For all examples we use the following spreadsheet We discuss Page 1 Sample Statistics 2 2 Plotting and graphics 3 3 Probability Derivations normal I and chisquared F 4 4 Confidence Intervals 6 1 Sample Statistics For each EXCEL function type the command and press ENTER The following derives sample statistics for wages including the sample correlation for wages and education Note that EXCEL functions are denoted by an 11 sign Anything after EXCEL treats as a command and performs the command Sample Mean wages averageb2b6 The result is 128 Sample Variance wages varb2b6 The result is 2370 Sample Standard Deviation wages stdevb2 b6 The result is 4868 Sample Correlation wages and education c0rrela2a6b2b6 The result is 865 All Descriptive Statistics 151 Data Analysis Package Be sure the Data Analysis tool package is installed in your version of Excel Click on TOOLS if Data Analysis is not listed then clickon ADDIN S and checkoff Analysis Toolpak and Analysis Toolpak VBA then OK 151 Using the Data Analysis Package for Descriptive Statistics Clickon TOOLS DATA ANALYSIS thenDESCRIPTIVE STATISTCS In the area to the right of Input Range type in the cell range in which your data is stored Always include the row with the variable labels Clickon Labels in First Row Clickon Summary Statistics for standard sample statistics Clickon Con dence Level for Mean in order to generate the C1length Excel sends the output to another sheet which can be accessed by clickingon the sheet with the highest number at the bottom of the screen eg Sheet 4 Basic Plotting and Graphics 21 Scatter Plot For a simple scatter plot of wages and education highlight the data cells by clicking on cell A2 hold the mouse button and drag the mouse over all data cells Then in the EXCEL toolbar clickon INSERT CHART XY SCATTER Then NEXT NEXT You can now navigate around in order to remove gridlines remove the legend add a title Wages and Education Scatter Plaf and add axis titles Because EDUC is to the left of WAGE in the spreadsheet EXCEL automatically places education on the Xaxis The result is Wages and Education Scatter Plot 25 m 20 9 15 Q g 10 5 0 0 10 20 Education Inserting a Linear Function that Approximates Two Variables First create a scatter plot as above Next clickon the whitearea of the graph this highlights the graph Excel places small black boxes around the edges of the graph if this does not appear then the figure in not yet highlighted In Excel s main toolbar clickon CHART ADD TRENDLINE OPTIONS DISPLAY EQUATION Then OK The result is Wages and Education Scatter Plot 25 21y 15694x 79167 0 in 1 a g 0 o 5 0 0 5 10 15 20 Education We can edit the displated equation if we want in order to place the intercept term first as is traditionally done The equation y 79167 15694x approximates the relationship between education x and wages 1 Thus for every new year of education a person might expect to earn 15694hour more wage 3 Probability Derivations 30 Binomial Distribution For the pdfPX a for some variableXNBn 7r binomdista n a false For the cdfPX S a for some variableXNBn It binomdista n 1 true 31 Standard Normal Probability returns PZ S a Where Z N N011 normsdista Example For PZ 125 type normsdist125 Excel returns 89435 32 Inverse of Standard Normal Probability returns a Where PZ S a p normsinvp Example For a Where PZ a 975 type normsinv975 Excel returns 1959961 Roughly 196 33 Student s IProbability returns Pl Z a Where IN IV 2 tdista v 1 Example For Pl gt 125 Where IN 110 type tdist125101 Excel returns 11988 1 We must use lerr than 2 We must use greater than ChiSquared returns Px gt a x N 120 chidista v Inverse ChiSquared For some a such that Pxgtap xNZZv use chiinvp v F Distribution For Pxgta xNFvlvZ us fdista v For some a such that Pxgtap xNFvlvZ nvp v 4 Con dence Intervals 41 Confidence Recall the issue of l 00 confidence intervals for the true population mean We require some K such that PoliKSK yKlior where for example on 05 for a 95 confidence interval We can show that the value K is exactly 1 KZ 1 042 W where Z M is found by exploiting the standard normal distribution or PZ lt ZM17 3 Z N N01 Of course this requires knowledge of the true variance 03 If the true variance is not known we use 2 K t SK nagz E where lbw2 is found by exploiting the I distribution PtgttnrlaZ tNt n71 Excel unfortunately can only derive l as though the true variance were known However because the true variance is not own we must give Excel the sample variance Excel will then erroneously use 1 instead of 2 e Excel formula is con dence0c 039 n Suppose for example we want a 95 confidence interval for the mean of wages For a 95 CI of the mean of wage uw we have on 05 For the true standard deviation we can simply substitute in the sample standard deviation Finally we need the sample size n 5 We type confidence05 4868 5 The result is K 4267 Thus the interval forpw is 128 i 426D 8533 l7067 Notice because EXCEL assumes the variance is known and yet we use an estimated variance this confidence interval is only approximately correct For large sample sizes however the above formula will be very accurate 42 Descriptive Statistics Confidence interval lengths K are generated by the Descriptive Statistics application see topic 15
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