How many possible latin square designs are there, Applied Statistics

In an agricultural experiment, we wish to compare the yields of three different varieties of wheat. Call these varieties A, B and C. We have a ?eld that has been marked into a 3 * 3grid so that there are 9 plots available to plant the varieties. We randomly assign the varieties to the plots so that each variety appears 3 times in the grid.

a) How many different ways can the varieties be assigned to the plots?

b) The random assignment of varieties to plots is called a completely randomized design. A better design might be to randomly assign the varieties so that each variety appears once in every row of the grid. This is called a randomized block design. How many possible randomized block designs are there involving 3 varieties and a 3 * 3grid?

c) A third design would assign the varieties to the plots so that every variety appeared once in every row and once in every column of the grid. This is called a Latin square design. How many possible Latin square designs are there involving 3 varieties and a 3 * 3grid?

d) For r varieties and an r * r grid, how many designs of the ?rst two types are there? (The number of Latin Squares of a given oder is an open problem - solve it to become famous!!).

e) For the ?rst two designs (and the general case in d), what is the probability that at least one variety will appear in the same position in each row?

Posted Date: 3/30/2013 5:06:06 AM | Location : United States







Related Discussions:- How many possible latin square designs are there, Assignment Help, Ask Question on How many possible latin square designs are there, Get Answer, Expert's Help, How many possible latin square designs are there Discussions

Write discussion on How many possible latin square designs are there
Your posts are moderated
Related Questions
Pneumatic Actuator Design Matrix: The range of actuator design parameters have been provisionally assessed and are presented in Table. You are required to determine the following

Consider a Cournot duopoly with two firms (fi rm 1 and fi rm 2) operating in a market with linear inverse Demand P(Q) = x Q where Q is the sum of the quantities produced by both

MARKS IN LAW :10 11 10 11 11 14 12 12 13 10 MARKS IN STATISTICS :20 21 22 21 23 23 22 21 24 23 MARKS IN LAW:13 12 11 12 10 14 14 12 13 10 MARKS IN STATISTICS:24 23 22 23 22 22 24 2

First Moment of Dispersion or Mean Deviation Mean deviation or the average deviation is the measure if dispersion which   is based upon all the items in a variable .It is the a

I have 5 observations that i must plug into spss. I need an example of 1. I do not know if you are familiar with SPSS but I am going to ask anyway. Subject 1 is a Hispanic male who

Use the given information to find the P-value. The test statistic in a two-tailed test is z = 1.49 P-value = (round to four decimal places as needed)

The amounts of money won by the top ten finishers in a famous car race are listed below. $1,172,246    $163,659    $440,584    $350,634     $290,596 $186,731    $145,809     $143,2

Scenario: To fundraise for middle school camp the year 3 and 4 syndicate designed and produced chocolate treats to sell to the year 1 and 2, and year 5 and 6 students at morning te

The project of building a backyard swimming pool consists of eight major activities and has to be completed within 19 weeks. The activities and related data are given in the follow

Let X, Y, and Z refer to the three random variables. It is known that Var(X) = 4, Var(Y) = 9, and Var(Z) = 16. It is further known that E(X) = 1, E(Y) = 2, and E(Z) = 4. Furthermor