# barcode font reporting services Analysis of Variance in Software Generator QR-Code in Software Analysis of Variance

CHAPTER 9 Analysis of Variance
Using Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications.
Draw QR Code In None
Using Barcode maker for Software Control to generate, create QR-Code image in Software applications.
The F ratios in the last column of Table 9-6 can be used to test the null hypotheses H(1): All treatment (row) means are equal, i.e., aj 0 H(2): 0 All block (column) means are equal, i.e., bk 0 0 0
QR Code Decoder In None
Using Barcode recognizer for Software Control to read, scan read, scan image in Software applications.
Creating QR Code 2d Barcode In Visual C#
Using Barcode generation for VS .NET Control to generate, create QR Code image in Visual Studio .NET applications.
H(3): There are no interactions between treatments and blocks, i.e., gjk 0 H(3) 0
QR Code Creation In .NET Framework
Using Barcode drawer for ASP.NET Control to generate, create QR Code image in ASP.NET applications.
Painting QR-Code In .NET
Using Barcode creator for .NET framework Control to generate, create Denso QR Bar Code image in .NET applications.
From a practical point of view we should first decide whether or not can be rejected at an appropriate level of significance using the F ratio ^2 >s 2 of Table 9-6. Two possible cases then arise. s i ^e Case I H(3) Cannot Be Rejected: In this case we can conclude that the interactions are not too large. We can then 0 test H(1) and H(2) by using the F ratios ^2 >s 2 and ^2 >s 2, respectively, as shown in Table 9-6. Some stats r ^e s c ^e 0 0 isticians recommend pooling the variations in this case by taking the total vi ve and dividing it by the total corresponding degrees of freedom, (a 1)(b 1) ab(c 1), and using this value to replace se the denominator ^2 in the F test.
Encode QR Code In VB.NET
Using Barcode creator for Visual Studio .NET Control to generate, create QR-Code image in VS .NET applications.
Encode Code 39 In None
Using Barcode printer for Software Control to generate, create Code 39 Extended image in Software applications.
Case II H(3) Can Be Rejected: In this case we can conclude that the interactions are significantly large. Differ0 ences in factors would then be of importance only if they were large compared with such interactions. s r ^i For this reason many statisticians recommend that H(1) and H(2) be tested using the F ratios ^2 >s 2 and 0 0 ^2 ^2 s c >s i rather than those given in Table 9-6. We shall use this alternate procedure also. The analysis of variance with replication is most easily performed by first totaling replication values that correspond to particular treatments (rows) and blocks (columns). This produces a two-factor table with single entries, which can be analyzed as in Table 9-5. The procedure is illustrated in Problem 9.13.
Encode Bar Code In None
Using Barcode printer for Software Control to generate, create barcode image in Software applications.
Bar Code Drawer In None
Using Barcode printer for Software Control to generate, create bar code image in Software applications.
Experimental Design
UPC-A Supplement 2 Creator In None
Using Barcode generation for Software Control to generate, create UPC Code image in Software applications.
Generate Code-128 In None
Using Barcode creation for Software Control to generate, create Code-128 image in Software applications.
The techniques of analysis of variance discussed above are employed after the results of an experiment have been obtained. However, in order to gain as much information as possible, the details of an experiment must be carefully planned in advance. This is often referred to as the design of the experiment. In the following we give some important examples of experimental design. 1. COMPLETE RANDOMIZATION. Suppose that we have an agricultural experiment as in Example 9.1, page 314. To design such an experiment, we could divide the land into 4 4 16 plots (indicated in Fig. 9-1 by squares, although physically any shape can be used) and assign each treatment, indicated by A, B, C, D, to four blocks chosen completely at random. The purpose of the randomization is to eliminate various sources of error such as soil fertility.
USPS POSTal Numeric Encoding Technique Barcode Drawer In None
Using Barcode creator for Software Control to generate, create Postnet image in Software applications.
Bar Code Drawer In Java
Using Barcode generator for Java Control to generate, create barcode image in Java applications.
Fig. 9-1
UPC Code Generation In Java
Using Barcode generation for Android Control to generate, create UPC-A Supplement 2 image in Android applications.
Paint Data Matrix 2d Barcode In Java
Using Barcode printer for Java Control to generate, create Data Matrix image in Java applications.
Fig. 9-2
DataMatrix Maker In Java
Using Barcode drawer for Java Control to generate, create Data Matrix 2d barcode image in Java applications.
Data Matrix Encoder In Objective-C
Using Barcode creator for iPad Control to generate, create Data Matrix image in iPad applications.
Fig. 9-3
Bar Code Creator In .NET Framework
Using Barcode creation for ASP.NET Control to generate, create bar code image in ASP.NET applications.
ANSI/AIM Code 128 Scanner In VB.NET
Using Barcode scanner for Visual Studio .NET Control to read, scan read, scan image in .NET framework applications.
Fig. 9-4
2. RANDOMIZED BLOCKS. When, as in Example 9.2, it is necessary to have a complete set of treatments for each block, the treatments A, B, C, D are introduced in random order within each block I, I, III, IV (see Fig. 9-2) and for this reason the blocks are referred to as randomized blocks. This type of design is used when it is desired to control one source of error or variability, namely, the difference in blocks (rows in Fig. 9-2). 3. LATIN SQUARES. For some purposes it is necessary to control two sources of error or variability at the same time, such as the difference in rows and the difference in columns. In the experiment of Example 9.1, for instance, errors in different rows and columns could be due to changes in soil fertility in different parts of the land. In that case it is desirable that each treatment should occur once in each row and once in each column, as in Fig. 9-3. The arrangement is called a Latin square from the fact that Latin letters A, B, C, D are used.