ANOVA Using Minitab

What is ANOVA

ANOVA stands for Analysis of Variance. It is a statistical method which is used to test the difference between two or more means. It is used to test the specific differences between the means. ANOVA assesses the importance of one or more factors by comparing the variable means at different factor levels. The null hypothesis of ANOVA states that all means are equal and the alternative hypothesis states that at least one is different. Though there are different methods like hypothesis testing, partitioning of sum of squares and others ANOVA is given the first preference these days. This is because it is easy to compute manually using simple algebra rather than complex calculations.

Uses of ANOVA

There are only two tests which can yield the same results – t-test and ANOVA. The t-test compares the means between two samples and is also easy to conduct. It is not reliable when there are more than two samples to be compared. In such cases ANOVA becomes more reliable and effective. ANOVA is the most preferred model in the field of pharmaceuticals and medical research because it helps to find out how effective are the two different types of treatment and how durable they are. In particular ANOVA helps to identify  how a particular treatment works and how long it lasts. Another main advantage of using ANOVA is that it can be used even if the number of observations in each group vary. Now a day’s ANOVA is also more commonly used in the field of Agriculture.

What is Minitab

Minitab is a statistical analysis package which will enable you to enter the data quickly and then perform different type of analysis on the data. You can enter data into Minitab in the same way like doing in an excel. Minitab can make the statistical computations on your data more easy and quick. Minitab provides a quick and effective solution for the level of analysis which is required in most of the Six Sigma projects. Minitab has four different types of ANOVA’s like One Way, Balanced and General Linear Model.

Why Use Minitab

Minitab is more widely used by students and others for statistical analysis than other statistical . Listed below are the five reasons why Minitab is so popular

• Minitab has a intuitive interface which makes it easy to use for students and instructors
• The commands and menus in Minitab are structured in a way that matches with the textbooks and provides easy guidance to get the output
• Minitab is more affordable as it offers discounts to students and academic institutions
• Minitab is a complete package with a lot of statistical tools so there is no need for special purchase of any add-ons or modules
• Minitab is a statistical which is used by many of the large companies. By learning Minitab the students are highly exposed to wide range of jobs in world class companies.
• Minitab serves as a reference for many textbooks and supplements. Minitab is a textbook example

Minitab Advantages

The advantages of Minitab are as follows

• The instructions can be written in English in Minitab
• It is user friendly
• Minitab has good help facilities
• It has a flexible and affordable licensing
• Easy to compute all the statistics problems
• It contains all the main techniques
• It offers a quick graphical output which will help the users to have a quick look at their analysis
• Minitab is easy to learn when compared with other statistical packages
• Minitab serves best for research as well as for teaching purposes

Minitab Disadvantages

The disadvantages of Minitab are listed as below

• The inbuilt routines in Minitab makes it unsuitable for applied research
• Minitab produces poor graphics. Though they have taken initiatives to improve the graphics in the recent versions
• The spreadsheet in Minitab cannot be easily manipulated like done in an Excel
• Minitab cannot read data easily from other ’s or packages
• The tabular output from Minitab is not that good as SPPS
• Minitab covers only few econometric methods
• It offers poor help to the users under few circumstances
• It is not easy to enable the command language in Minitab and as a result the users find the multiple windows very confusing

Course Objectives

After the completion of this course you will be able to

• Understand the context where ANOVA has to be used
• Determine which type of questions can be answered using ANOVA
• Know how to implement One way Anova
• Use the formulas used to compute basic values using ANOVA
• Understand the different models of ANOVA and how to use it
• Perform the ANOVA calculation

Pre Requisites for taking this course

To enrol in this course you should possess a basic knowledge of statistics and familiarity with concepts like averages, standard deviation and different sort of variants. Other than this basic knowledge of Minitab is considered as an added advantage.

Target audience for this course

Researchers, Statisticians, Students and Professionals can undertake this course. And anyone who is interested in learning ANOVA can also take up this course.

Course Description

Section 1: Introduction

Understanding and Implementation of ANOVA

ANOVA is a group of statistical models which is used to test the significance difference between means. It finds out whether the means of various groups are equal or not. Here the differences is found by comparing the variances. Before ANOVA the t test and z test was used. But then in 1918 ANOVA was developed by Ronald Fisher. ANOVA can be used to test various null hypothesis at the same time. ANOVA can be used for various purposes by various persons. Researchers use ANOVA in three ways – one way ANOVA, two way ANOVA and N way Multivariate ANOVA. This chapter explains you the basic of ANOVA and its implementation.

Pairwise Comparisons

Pairwise comparison is used to compare the entities in pairs to find out which of the entities are identical and which of the entities are not identical. This chapter will help you to learn how to test the differences among means. The other topics included in this section are

• Definition of Pairwise Comparison
• Problem in conducting t test among all pairs of means
• Fisher’s Protected LSD
• Bonferroni Correction
• Tuskey HSD test
• Scheffe’s test
• Confidence Intervals

Features of Chi – Test

The Chi square distribution was first used by Karl Pearson in the year 1900. The chi square distribution is the distribution of sum of squares of k independent standard normal random variables with k degree of freedom. The null hypothesis in Chi square test is that the distribution of the test statistics is a chi square distribution and it is true. The chi square test is used to find test the goodness of fit. Chi square test can be used on nominal data. It is easy to calculate and interpret. The detailed explanation of chi square test along with its examples are given in this chapter

Preference and Pulse Rate

Under this chapter a sample research problem is given to illustrate repeated measures ANOVA. In this example the researcher wants to examine the impact of dietary habit and exercise on the pulse rate of the sample. This example answers the following questions

• Does intensity influence pulse rate ?
• Does dietary preference influence pulse rate ?
• Does the exercise type on pulse rate depend on dietary preference ?
• Does the influence of diet on pulse rate depend on intensity ?

Difference between Growth Plan ad Dividend Plan in MF

When selecting a mutual fund an investor has n number of choices. The more tough decision is to choose between the fund with growth option and the fund with dividend reinvestment option. Each type of fund definitely has its own advantages and disadvantages. And deciding which type of fund to choose purely depends on the individual needs and purposes.

In the growth option the investor will have the same number of units in the end as it was in the beginning. The investor will not receive any dividends that will be paid out of the stocks. The growth option will not suit the investors who wants to receive regular profits from their investment. The growth option is the best way for the investors to increase their Net Asset Value (NAV).

The dividend reimbursement option is different from the growth option. In mutual funds some amount will be paid to the investors every year which is called dividend. This amount is paid to the investors to help them purchase more shares. The fund administrator purchases few more shares with that amount on behalf of the investor and will transfer them to the investor’s account.

The other differences between the growth option and dividend option in is explained in detail under this lesson

Checking NAV Price and Repurchase Price

Net Asset Value (NAV) is the actual value of single unit of a given scheme. The NAV is the liquidation value of the fund on that particular day. The NAV is calculated by deducting the liabilities from the value of all the assets. Then it is divided by the number of units which is outstanding.

A close ended fund has a fixed maturity period that varies between 2 and 14 years. Close ended funds sell only a fixed number of shares in the initial offering and the remaining shares are sold in the secondary market. The cost at which the shares are sold in the secondary market are totally based on the market and not on the NAV. Repurchase price is the price at which the investors sells back the units to the mutual fund. It is NAV related and can also include the exit load.

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