Name

Student Number:

Class days and time:

Please include this on what you hand in!

Graded Assignment 4

The data set is part of a problem due to Groebner et. al..

14 Testers were sent out to 3 branches of a Mexican fast-food chain (Store 1-3). Though the order of the visits was random, each tester visited each store once. They rated the restaurant on a number of characteristics and their ratings were totaled and shown. Only neat and legible papers with written answers in complete sentences will be read! Make sure that you have access to a copy of Excel with statistical functions enabled. To enable statistical functions, enter Excel and use the Tools pull-down menu. Select Add-Ins and check Analysis Tool Pack and MegaStat. This is available in Anderson.

Tester / Str 1 / Str 2 / Str 3
1 / 830 / 647 / 630
2 / 743 / 840 / 786
3 / 652 / 747 / 730
4 / 885 / 639 / 617
5 / 814 / 943 / 632
6 / 733 / 916 / 410
7 / 770 / 923 / 727
8 / 829 / 903 / 726
9 / 847 / 760 / 648
10 / 878 / 856 / 668
11 / 728 / 878 / 670
12 / 693 / 990 / 825
13 / 807 / 871 / 564
14 / 901 / 980 / 719

Do this problem in Excel as follows.

Use columns A, B, C, D, and E on the Excel spreadsheet for data

In the first row of Columns B, C, and D put in Str1, Str2, and Str3. Head column A with the word ‘Tester.’ Starting in Cell A2 Put in the letters 1 through 14 to identify the testers – unless, of course, you want to suggest some names.

Now put in the data in columns B, C, and E, skipping column D

If you bring this document into Word, the data can be moved into the Excel worksheet by highlighting the cells you want and copying and pasting.

To fill column D in cell D2 write =E2. After your 'enter' this cell should read '630'

Use the 'edit' pull-down menu and 'copy' cell D2

Use the 'edit' pull-down menu and ‘paste’ in cells E3 through E14 or use handle on lit-up cell.

Now column D will be identical to E except for the heading. This can also be done as a simple copy and paste. Save your data as rating1.xls

Version A – One-way ANOVA

Use the 'tools' pull-down menu and pick ‘data analysis.' (If you cannot find this, use Tools and Add-Ins to put in the analysis packs.)

Pick 'ANOVA: Single Factor. Set input range to $B$1:$D$15. Select 'New worksheet ply' and ‘columns’, check 'labels in first row' hit 'OK' and save your results as rreslt1.xls.

Version B – Two-way ANOVA

In order to check for the effect of the fact that the data is blocked by employees, repeat the analysis using ‘ANOVA: Two-Factor without replication. Set input range to $A$1:$D$14, check ‘labels,’ and save your results as rreslt2.xls

Answer the following: Is there a significant difference between the store ratings? How is this conclusion affected by blocking by testers? Cite p-values and /or F-tests

Version C – One way ANOVA

Take the last digit of your student number (if it's zero, use 10). Go back to your original data or use the 'file' pull-down menu to open rating1.xls.

To fill column D this time in cell D2 write =E2+x, replacing x with the last digit of your student number.

Use the 'edit' pull down menu and 'copy' cell D2

Use the 'edit' pull down menu and ‘paste’ in cells D3 through D14. Now column D will be more than the original D by the amount of your value of x. Save your data as rating3.xls. Relabel the column as Str 3yy, where yy is 01 – 10, depending on what you added to the column.

Run the one-way ANOVA again and save your results as rreslt3.xls

Submit the data and results with your Student number. The most effective way to do this is to paste the results into a Word document and then add neat hand or typed notes. Indicate what hypotheses were tested, what the p-value was and whether, using the p-value, you would reject the null if (i) the significance level was 5% and (ii) the significance level was 10%, explaining why. You will have two answers for each of your two problems.

For your Version C do a Scheffe confidence interval and a Tukey-Kramer interval or procedure for each of the possible differences between means and report which are different at the 5% level according to each of the 2 methods.

Extra Credit: 1) Show that you learned something from computer problem 2 by doing part B on Minitab. There should be very little difference in your result.

The easiest way to do this is to copy the first five columns from the original Excel spreadsheet. Enter Minitab and use ‘editor’ to enable commands. Highlight the column labels and cells 1-14 of the first five columns. Remember that your column labels should be written in above the columns (Put row labels in column 1). Just to make sure that you are in the right place. Try the following Minitab commands.

print c1-c4

AOVO c2-c4;

Tukey 5;

Fisher 5.

You should get results equivalent to your first ANOVA but with individual and Tukey intervals done for you.

To set up for a 2-way ANOVA stack your data in columns 11 and 12.

Stack c2 c3 c4 c11;

Subscripts c12 ;

UseNames.

To move the row labels, copy the labels from column 1 to column 13. Label column 11-13 ‘Rating,’ ‘Store’ and ‘Tester1.’ Every number should now have a correct row label. Use the table commands from computer assignment 2 to check your data. I combined the ANOVA, and the table of means command by using the following.

Twoway c11 c13 c12;

Means c13 c12.

2) Take the data from your last ANOVA. Use the instructions in 1) above to copy it into the Minitab spreadsheet and perform Levene and Bartlett tests on it using the third example in 252mvarex as a pattern for your calculations using Minitab. Make sure that you explain what is being tested and what you conclude. There are two ways to do this. If you want to do it on the unstacked data use the following.

Vartest c2-c4;

Unstacked.

To do the tests on the stacked data use the following. Save and layout your graphs.

Vartest c11 c12.

You should also test the columns for Normality. The Lilliefors test for column 2 would be the following.

NormTest c2;

KSTest.

Now answer the following. What requirements must your individual columns meet for ANOVA to be valid? What evidence do you have that these requirements were met?

Extra Extra Credit: Do Bartlett and Levene tests ‘by hand’ using the examples in 252mvar as your pattern. This is an awful lot of work unless you cheat and use the computer. If you cover your tracks, I’ll never know. To do the Bartlett test you need logarithms of variances. Label Columns 10-12 ‘stdev,’ ‘var’ and ‘log.’ Use the data that you already have in four columns in Minitab c2-c5 (labels in c1) and get the variances as follows:

name k2 ‘stdv1’

name k3 ‘stdv2’

name k4 ‘stdv3’

stdev c2 k2

stdev c3 k3

stdev c4 k4

print k2-k5 #These are the standard deviations of the columns.

stack k2-k4 c6

let c7 = c6 * c6 #Now you have variances. Label c7 ‘Vars’

let c8 = logten(c7)

let k7= mean(c7) #This is the pooled variance when you have equal sized samples.

let k8 = logten(k7)

print k7 – k8

print c6 – c8.

Now you are on your own. The rest of this should be pretty easy because all your s are equal. Warning! Though I have used this procedure before, I haven’t had time to check these results out. Tune in tomorrow.

The Levene test looks longer, but should be much more familiar and perhaps easier to fake.

Copy columns 1 through 4 to c14-c17. You might want to label them as ‘Tester*,’ Str1*’ etc. Then find their medians and subtract them from the columns and convert the columns to absolute values.

name k15 ‘med1’

name k16 ‘med2’

name k17 ‘med3’

let k15 = median(c15)

let k16 = median(c16)

let k17 = median (c17)

let c15 = c15- k15

let c16 = c16- k16

let c17 = c24 – k17

describe c15 – c17 #All the columns should have zero medians now.

print c14 – c17

let c15 = absolute(c15)

let c16 = absolute(c16)

let c17 = absolute(c17)

#You are now ready for an ANOVA using:

AOVO c15-c17 #You should get the same p-value as you got for the first Levene test # that you did.

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