Question

Short Answer - (10pts)

1. Provide a personal or work related scenario on how an ANOVA (analysis of variance) can be used and give an example of how this statistical method will be beneficial in your current or future line of work.

Additional Information: ANOVA is a statistical method used to determine if differences exist between the means of three or more populations under independent sampling. For example, you may want to determine if the average miles per gallon of small hybrid cars vary by the brand or you may want to compare the effectiveness of different fertilizers on the average yield per acre.

Answer 1

Aim:

The aim of this assignment is to implement the Anova technique to analyze the number of tourists visiting India in different quarters of the year and weather they prefer a particular time in the year or not.

This assignment aims at collecting the data of the number of tourists visiting India in a particular span of time and different time in the year.

The Big Question:

Well, the question arises in our mind is

“Is there a preferred time when the tourists visit more or the number is just uniform over the year?”.

“If yes, then how much? Is the deviation really significant and worth caring?”.

So, let’s try to answer these questions by using some statistical methods that we know till now (Hopefully it should work!!!!).

Something About Data

We shall refer to the following data set which I obtained from tourism website of India

Year/Month**	1st Quarter Jan-April	2nd Quarter May-Aug	3rd Quarter Sept-Dec
2003	33.5	27.4	39.0
2004	34.3	27.0	38.7
2005	34.5	26.9	38.5

** Numbers in percentage

Now, we will use this data to implement Anova technique to check if there is a change in the number of visiting tourists

Assumption:

Following Gelman and Hill, the assumptions of the ANOVA, and more generally the general linear model, are, in decreasing order of importance:

1. the data points are relevant with respect to the scientific question under investigation;
2. the mean of the response variable is influenced additively (if not interaction term) and linearly by the factors;
3. the errors are independent;
4. the errors have the same variance;
5. the errors are normally distributed.

Hypothesis:

Null Hypothesis,                  H₀: means are equal

Alternate Hypothesis,         H₁: All other alternatives

Conclusion:

Our analysis finds enough evidence to reject our null Hypothesis.

So, We can’t say that there is equal probability of visiting tourists in any time in a year.

We can use these kind analysis to get an idea of when the tourist arrive more and what can be done to increase their experience!

Thanks