Question

Project#2 - ANOVA - Outline

Project#2 is based on Exercise 9.32 (Page 522). The case scenario and data are from it. Feel free to use SPSS, SAS and/or Excel (or any other standard statistical software) for data analysis. The data set is available on Blackboard (under Projects). There are three questions in that exercise. Beyond those questions, your paper must address the following:

I. Introduction

1. Explain the case and issues in it in your own words. [Use not more than 250 words.]

2. Explain the goals of the study in your own words. [Not more than 150 words.]

II. Theory and concepts

1. What type of study is this? Observational or experimental study? Why? Explain. [Not more than          

      150 words.]

2. Identify the variables and explain their nature (such as qualitative or quantitative) and their

      relationships. [Not more than 150 words.]

3. Explain the factor/factors and factor levels, and also independent and dependent variables used in

     the study. [Not more than 150 words.]

4.   What are the major assumptions in your ANOVA analysis? [As many words as necessary.]

5.   How will you test the assumptions? [As many words as necessary.]

III. Hypothesis and Critical Value

1. State the null ad alternate hypothesis. Briefly explain the hypothesis. [Not more than 150 words.]

2. Find F_Critical. What is the meaning of it? Briefly explain how you found it. [Not more than 150 words.]

IV. Data Analysis

Using the software conduct the following analysis and explain the major findings:

1. Generate descriptive statistics of the variables. Explain the major findings. How do they relate to the

      ANOVA analysis. [Not more than 250 Words.]

2. Generate histograms, box Plots and Q-Q Plot for the variables. Explain the major findings. How do

      they relate to the ANOVA analysis? [Not more than 250 words.]

3. Conduct the ANOVA analysis. Explain the findings. [As many words as necessary.]

4. What are your conclusions from the analysis? Explain. [As many words as necessary.]

IV. Decisions

As a researcher what decision will you draw from this study? Why? Explain. [Not more than 200 words.]

Report on the Project

Write a report, following the steps given above. The report must include a simple title page. Also, include the software printouts. Submit your report on Blackboard (Project_2 Dropbox).

DATA:

Honey	DM	Control		Score	Treatment_Numeric Code		Code
12	4	5		12	1		Honey = 1
11	6	8		11	1		DM = 2
15	9	6		15	1		Control = 3
11	4	1		11	1
10	7	0		10	1
13	7	8		13	1
10	7	12		10	1
4	9	8		4	1
15	12	7		15	1
16	10	7		16	1
9	11	1		9	1
14	6	6		14	1
10	3	7		10	1
6	4	7		6	1
10	9	12		10	1
8	12	7		8	1
11	7	9		11	1
12	6	7		12	1
12	8	9		12	1
8	12	5		8	1
12	12	11		12	1
9	4	9		9	1
11	12	5		11	1
15	13	6		15	1
10	7	8		10	1
15	10	8		15	1
9	13	6		9	1
13	9	7		13	1
8	4	10		8	1
12	4	9		12	1
10	10	4		10	1
8	15	8		8	1
9	9	7		9	1
5		3		5	1
12		1		12	1
		4		4	2
		3		6	2
				9	2
				4	2
				7	2
				7	2
				7	2
				9	2
				12	2
				10	2
				11	2
				6	2
				3	2
				4	2
				9	2
				12	2
				7	2
				6	2
				8	2
				12	2
				12	2
				4	2
				12	2
				13	2
				7	2
				10	2
				13	2
				9	2
				4	2
				4	2
				10	2
				15	2
				9	2
				5	3
				8	3
				6	3
				1	3
				0	3
				8	3
				12	3
				8	3
				7	3
				7	3
				1	3
				6	3
				7	3
				7	3
				12	3
				7	3
				9	3
				7	3
				9	3
				5	3
				11	3
				9	3
				5	3
				6	3
				8	3
				8	3
				6	3
				7	3
				10	3
				9	3
				4	3
				8	3
				7	3
				3	3
				1	3
				4	3
				3	3

Answer 1

Introduction

1) Here we apply 3 types of treatment on different number of individuals and check the score of individuals.

2) Here goal of study is - to check these 3 treatments have exactly the same effect on score of individuals.

Theory And Concepts

1) These is experimental study becuse, An experimental study is a study where the researcher has control over most of the variables. Once the research problem has been formed, the researcher organizes a study that will allow him to find answers to the research problem. In this case, the researcher conducts the study in a specific setting where he can control the treatments(variables).

2) All these three variables are quantitative in nature because we apply these three tretments on individuals and record the score.

3) Here all 3 variables are Dependent variables , because in ANOVA test is conducted to assess whether means on a dependent variable are significantly different among the groups.

4) Assumption

The normal-model based ANOVA analysis assumes the independence, normality and homogeneity of the variances of the residuals. The randomization-based analysis assumes only the homogeneity of the variances of the residuals and uses the randomization procedure of the experiment.

Hypothesis And Critical Values

1) Null Hypothesis : there is no difference in means of 3 treatments. i.e.

Versus

Alternative Hypothesis : There is means are not all equal

2) F_critical is a standerized value of F statistic. And is use for comparision with F_calculated . And we found the value of F_critical using following table

And F_{(df1, df2)} = we get value corresponding to df1 column and df2 rows from above table.

Data Analysis

1) Descriptive Statistics - use excel syntax is as

Data Data Analysis Descriptive Statistic Inpute Range Grouped By (Column) output range Summary statistic Ok

2) Box - Plot

For these we first compute following terms

Box1 - hidden = Q!

Box2 - lower = Median - Q1

Box3 - upper = Q3 - Median

Top = Max - Q3

and Bottom = Q1 - Min

And then select data of Box1-hidden , Box2-lower and Box3-upper table and use syntax as

Insert Column Chart 2D chart ( Stacked column)

3) ANOVA - use syntax

Data Data Analysis ANOVA: for single factor Inpute Range Grouped By (Column) output range Alpha = 0.05 Ok

Excel result is as

here F_calculted > F_{critical .} So we reject null hypothesis

Conclusion

There is means are not all equal.