Introduction to Statistics with M&Ms

Sample and Measurements.  Each student will receive a bag containing about 20 M&Ms; they may be plain or peanut M&Ms.  Weigh the mass of each M&M in grams on the new Mettler-Toledo XS204 balances in the balance room.  In your notebook record the color and mass of each M&M.  Record all digits from the balance!   Be sure to make the M&Ms "disappear" after you have weighed them.

Analysis.  1 Descriptive Statistics:  Compute the "descriptive statistics" of your data.  This will usually include the average, the standard deviation, the standard deviation in the mean (aka the standard error), and the 95% confidence limits.  The minimum and maximum and other statistics are often useful.
    Excel.  Probably the easiest way to do this is to use the "Descriptive Statistics" function in the Data Analysis Tool Pak in Excel.  Place all your data in a column of a worksheet.  Then click on "Data Analysis ..." in the Tools menu of Excel, and select "Descriptive Statistics" from the alphabetical list.  The Descriptive Stats routine will want you to select a range for your data.  Check the box for "Summary Statistics".  The "New Worksheet Ply" means that the output will be placed on a brand new sheet in the workbook.  That probably isn't what you want to do, although go ahead and give it a try.  A better option is push the "Output Range" button which will cause the output to be placed on the current worksheet; however, you must select a 15 x 2 set of cells for the output.  Then click the OK button and the results will spill out on to the sheet.  There will a lot of results!  
    conf_limits.exe.  This program can be found in a subdirectory of the MOCOSIN computer network.   From "My Network Places" select "Chemistry (on Samba #.#.#)", and follow the subdirectory list thru Tools and Conf_limits, then click on the conf_limits.exe program. (The true location is Catwoman\chemistry\tools\conf_limits)  The program's icon looks like a calculator, pencil, and notepad.  The program is a bit funny in that the data entry requires that you mouse click on different cells to enter the numbers--the cursor keys and the return key are inactive!  But it does work.  After you enter the data click on the Calculate button and you'll see the statistics pop up.  You'll have to write down the statistics in your notebook.
                2 F tests and t tests:  The F test answers the question "Is my standard deviation significantly different from another?"  The t test answers the question "Is my mean value significantly different from another?"  You must compare the standard deviation and mean of your data with those of four other sets of data; two that are the same type of M&Ms as you own, and two that are the other type of M&M!
    Excel.  You will find that the F test is available in the Data Analysis Tool Pak.  You must have each set of data on the same spreadsheet to perform the F test.  A 3 x 10 set of cells is needed to contain the output.  Consult your Quant book to intrepret the results correctly, because it can be confusing.  The test will give you two F values, F and F critical.  If F is farther from 1.00 than F critical, then the standard deviations are different.  Try to arrange the test so that F comes out greater than 1.00, then F>F crit will tell you that the standard deviations are different.
The t test is also in the Data Analysis Tool Pak; however, you must select the t test based on the results of the F test!  Choose either  t Test: Two Sample Assuming Equal Variances or t Test: Two Sample Assuming Unequal Variances depending on whether the F test showed no difference or a difference.  You will need a 3 x 14 set of cells for the output.  Again, consult your Quant book to intrepret the results.  There will be three T values: T stat, T critical one-tail, and T critical two-tail.  Ignore the one-tail value.  If the absolute value of T stat is greater than T critical two-tail, then the means are significantly different.  
    Conf_limits.exe.  Enter two sets of data into two of the columns, and check both columns.  The F test and the t test are both straightforward.  The program will even intrepret the results for you and tell you whether the test says the difference is significant or not significant.  However, you haveto write down  the values and results of the test.
                3 Pooled Data:  All the M&M data should be pooled so that the mean and standard deviation for all plain M&Ms and for peanuts M&Ms can be computed for all the data.  Use the mean and standard deviation to construct Gausssian curves for each population.  Also, a box plot of each population would be nice as well.

Report.  From the MoCoSin network, you should also look at the lab report for this experiment.  Under Catwoman\chemistry\courses\ch220, look at the lab report called MandMs.doc.  It has already been written for you--to some extent.  There are places in the document file where you are allowed to entire data or conclusions.  Do not think that you can just cut and paste results from the descriptive statistics, the F test, or the t test directly from Excel into the lab report document.  You must edit the results--remove any numbers that are irrelevant to the reader, such as skewness or T critical one-tail.