Statistics and research methods for managerial decisions Essay Example

no interactions between the barricading variables or between the intervention variable and the blocking variable.

Facts ABOUT LATIN SQUARE DESIGN

• With the Latin Square design you are able to command fluctuation in two waies.
• Treatments are arranged in rows and columns
• Each row contains every intervention
• Each column contains every intervention.
• The most common sizes of LS are 5x5 to 8x8

Consequence of the Size of the Square on Error Degrees of Freedom

Where R = figure of rows, columns, and interventions.

• One manner to increase the Error df for little squares is to utilize more than one square in the experiment ( i.e. repeated squares ) .

EXAMPLE-1

Two 4x4 Latin squares.

*Additive across squares.

Where sq = figure of squares.

Examples of Uses of the Latin Square Design

1. Field tests in which the experimental mistake has two birthrate gradients running perpendicular each other or has a unidirectional birthrate gradient but besides has residuary effects from old tests.

Gradient 2

Gradient 1

2. Animal scientific discipline provender tests.
3. Insecticide field test where the insect migration has a predictable way that is perpendicular to the dominant birthrate gradient of the experimental field.
4. Greenhouse tests in which the experimental pots are arranged in a consecutive line perpendicular to the glass walls, such that the difference among rows of pots and distance from the glass wall are
   

expected to be the major beginnings of variableness.

Randomization Procedure

Depends on the type of Latin Square you use.

3x3 Latin Square

Start with the standard square and randomise all columns and all but the first row.

Randomize all but the first row

4x4 Latin Square

Randomly take a standard square.

Randomize all columns and all but the first row.

5x5 Latin Square

Randomly take a standard Square. Randomize all columns and rows.

STEP-1: Calculate intervention sums.

TreatmentTotal

1. 5.855
2. 5.885
3. 4.270
4. 5.355

STEP-2: Calculate the Correction Factor ( CF ) .

_Californium=^Yttrium..²

_R2

• 21.365²

4²

• 28.53

STEP-3: Calculate the Total SS

Sum= ?Yttrium_ij²?Californium

• ( 1.64²+1.210²+1.425²+ ... +0.66²) ?Californium

• 1.4139

STEP-4: Calculate the Row SS

Row=^?Row_R²?Californium

₌( 5.62²+5.35²+5.225²+5.17²)_?Californium4

= 0.0302

Measure 5: Calculate the Column SS.

Col.United states secret service=^?Col_R²?Californium

₌( 6.35²+4.395²+6.145²+4.475²)_?Californium4

= 0.8273

Measure 6: Calculate the Treatment SS

TrtSS=^?_R^Lolo.2?Californium

₌( 5.855²+5.885²+ 4.270²+5.355²)_?Californium4

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= 0.4268

Measure 7: Calculate the Error SS

Error SS = Total SS – Row SS – Column SS – Trt SS

= 0.129

Measure 8: Complete the ANOVA tabular array

STEP- 9: Calculate the LSD.

0.254

MANAGERIAL IMPLICATIONS

The advantage of fewer needed topics is accompanied by terrible disadvantages for usage of the Latin Square experiment design in marketing research. First, interaction effects between independent variables and independent variable values can non be investigated. Therefore, a Latin Square is limited to those state of affairss in which it is sensible to presume that no interaction effects occur, which in the world of a selling determination makes is really improbable.

Second, independent variable values ( i.e. , experimental interventions ) must be equal in figure to the figure of values for each immaterial variable explicitly controlled. Hence, the “square” name of this type of experiment is reflected in the corresponding “square” tabular array that represents its design. However, the existent universe of marketing determination shapers frequently involves state of affairss where the figure of independent variable values varies otherwise than the values of immaterial variables. For illustration, inquiries about gender might affect two values while inquiries about bundle design involve two, three, four, or more values.

Furthermore, these are serious tradeoffs when utilizing a Latin Square experiment for a selling research undertaking. While a positive facet is fewer needed topics, a negative facet is the legion restrictions finding when it can be used. First, it is practical merely with one independent variable. Second, there much ever be an

equal figure of independent variable values and immaterial variable values. Third, there is no trial of interaction effects. In selling, the world is that there is most ever an involvement in more than one independent variable and there are most ever interaction effects between variables. Therefore, despite the positive entreaty of less topics, which means less clip and money, the negative side is a serious restriction as to when this type of experiment can be used in marketing research.

FACTORIAL DESIGNS ( FD )

“A factorial design really consists of a set ofindividual-factor experiments.” That’s why it’s so of import to truly understand the single-factor design! Keppel illustrates the component nature of the factorial design in Table 9-1. Therefore, in the illustration he’s discussing, the length of the printed lines of text could be either 3, 5, or 7 inches. The difference in elation between the print and the paper could besides be manipulated ( low, medium, or high ) . The dependent variable is reading velocity.

3 in. 5 in. 7 in.

Low Contrast

Medium Contrast

High Contrast

We could analyze the simple consequence of line length under Low Contrast. We could besides analyze the simple consequence of line length under Medium Contrast. Finally, we could analyze the simple consequence of line length under High Contrast. In add-on, we could disregard ( norm over ) the assorted degrees of contrast and analyze the chief consequence of line length. Note the existent difference between simple effects and chief effects.

• Note that we could turn the experiment on terminal and think of the 3 simple effects of contrast at changing degrees of line length. We could besides see the chief consequence of contrast
  

( averaging over all degrees of line length ) .

• Aside from economic system, the existent advantage of factorial designs is the ability to analyze interactions. In kernel, an  interaction is present when the simple effects differ. Therefore, if the effects of line length were tantamount regardless of the degree of contrast, we would hold no grounds of an interaction. When an interaction is present, reading of a chief consequence becomes complicated.

The Concept of Interaction

• The chief effects of a factorial design are computed in a manner indistinguishable to the calculation of intervention effects in a individual factor design. ( See, I told you it was truly important to understand the single-factor ANOVA! ) Therefore, the lone new calculation is the interaction term

• Example of an result that illustrates no interaction:

Why is this result consistent with no interaction? Let’s focal point on the simple effects of line length. ( We could merely as easy have chosen to concentrate on the simple effects of contrast. ) For the Low Contrast status, note that the addition in reading velocity from the 3-inch status to the 5-inch status is 1.33, and the addition from the 5-inch status to the 7-inch status is.67. Although overall reading velocity additions when the contrast is medium, the addition in reading velocity from the 3-inch status to the 5-inch status remains 1.33, and the addition from the 5-inch status to the 7-inch status remains.67. Finally, when the contrast is high, reading velocities show farther betterment, but the addition in reading velocity from the 3-inch status to the 5-inch status remains 1.33, and the addition in

reading velocity from the 5-inch status to the 7-inch status remains.67. The fact that the alterations in reading velocity remain consistent for all the simple effects is declarative of a deficiency of interaction.

• You could besides take a graphical attack to interaction, which is to look for a deficiency of parallel lines in a graph of the status means. As you can seen in the graph below, the lines linking the agencies are parallel.

Contrast

• In the absence of a important interaction, you would concentrate your attending on the chief effects. That is, because the simple effects are all stating you fundamentally the same narrative, there’s small ground to analyze them individually.

• an illustration of an result that illustrates an interaction:

( Note that the fringy agencies remain the same as those in the illustration demoing no interaction. Therefore, the chief effects are indistinguishable. )

• In this illustration, you can rapidly see that the simple effects are non the same. This result is peculiarly apparent when looking at a figure of the information. ( Note the non-parallel lines. )

Like Figure 9-3

8

6

Contrast

• When an interaction is present, we are most frequently less interested in the chief effects. Alternatively, we typically focus on interpreting/understanding the interaction.
• It provides a figure of definitions of an interaction. In instance any one of them may assist you to understand the construct, I’ll merely copy them for you here:

An interaction is present when the effects of one independent variable on behavior alteration at the different degrees of the 2nd independent variable. ( To maintain in head that the

two independent variables do non act upon one another! )

An interaction is present when the form of differences associated with an independent variable alterations at the different degrees of the other independent variable.

An interaction is present when the simple effects of one independent variable are non the same at all degrees of the 2nd independent variable.

An interaction is present when the chief consequence of an independent variable is non representative of the simple effects of that variable.

An interaction is present when the differences between cell means stand foring the effects of Factor A at one degree of Factor B do non be the corresponding differences at another degree of Factor B.

An interaction is present when the effects of one of the independent variables are conditionally related to the degrees of the other independent variable.

An interaction is present when one of the independent variables does non hold a changeless consequence at all degrees of the other independent variable.

• Although the presence of an interaction may perplex the explication of the consequences of an experiment, you should recognize that many experiments really predict an interaction. Therefore, you may good be looking to happen an interaction in an experiment.

• It provides a figure of 2x2 results to exemplify the presence or absence of an interaction. You should be certain that you can easy find that an interaction appears to be present or absent in an experiment. Of class, the concluding supreme authority of the presence of an interaction is non a graph, but the statistical trial that you will happen in the beginning tabular array. Even though lines may look to be non-parallel, if the F for the
  

interaction is little ( i.e. , the P value is above.05 ) , so the lines are statistically parallel and there is no important interaction.

Mentions:

1. Books referred:
2. Designs and methods by Mr. C K Kothari.
3. Research Methodology by Mr. Paneersalvem
4. Business Research and Methodology by Mr. Srivastava and Mr. Rego.