STA 3024 Data Analysis 2 Due: February 27 D. Meeter, Spring, '01

The data: http://stat.fsu.edu/~meeter ç 3024 ç Data Analyses ç Data for Assignment 2

This should start a download. Pick the location where you want the file saved by changing the Save in blank. Open Minitab, ç File ç Open Worksheet; in Look in put the location of the file you downloaded. Change Files of Type to Excel [*.xls]; click on your file name, e.g. milk.xls, click open, and you should have the data.

Four random samples of evaporated milk were taken from each of ten lots, treated in four different ways, and assayed for the content of Vitamin B₆. The purpose of this experiment was to see whether sterilization reduced the amount of B₆, and whether the estimate depended on which organism was used in the test. Hodson, A. Z.; Vitamin B₆ in sterilized milk and other milk products, J. Agr. Food Chemists 4, 876-881, 1956.

The treatments were: Saccharomyces carlsbergensis before sterilization (SCbef)

" " " " after sterilization (SCaft)

Neurospora sitophilus before sterilization (NSbef)

" " " after sterilization (Nsaft)

Perform an analysis of variance:

Stat>ANOVA>Two-way Response: mgB6/l Row Factor: Treatmnt Ö Display Means Column Factor: Lot Ö Display Means Ö Store residuals (produces a column RESI1)

Graphs Ö Normal plot of residuals, Residuals vs. fits, Residuals vs. order OK OK

Don't discuss the ANOVA at this point; interpret the plots. Examine them for evidence of the need for a transformation (discuss), outliers (discuss), correlated errors (discuss). (The order of the data is Lot 1 to Lot 10 for SCbef, then Lot 1 to Lot 10 for SCaft, etc.)

Bliss, Statistics in Biology, v.1, decided to replace one of the observations with 0.341, using a simple estimate which is beyond the scope of this course. Look at the column of residuals RESI1 for a clue to find which valued he changed. Justify your choice.

Manip>Copy Columns Copy from columns: mgB6/l To columns: (specify an empty column) Change one number in this column to 0.341 (don't delete the number first or all of the data below it will move up one row!) Label this revised column mgB6/lrv.

Perform the ANOVA again using mgB6/lrv as the response. Examine the plots in the same way, and discuss the changes.

Bliss did a log transformation. Discuss whether this seems to be needed.

Now interpret the new ANOVA table for the corrected data. Calculate the ERE of a RBD to a CRD, discuss what this says about the need for blocking on milk lots.

Did sterilization have an effect on the amount of B₆ available to S. carlsbergensis? (Use a confidence interval for the difference of two means. Use the square root of the MSE to estimate s . If you don't know how, ask.) Repeat for N. sitophilus. Interpret.

Anything else. For example, you could make an interaction plot (read ahead) and discuss whether there is an interaction between organism type and sterilization.