Allen G. Bluman, author of Elementary Statistics: A Step by Step Approach, describes the F- Test in detail. However, I had found other scholarly sources to explain the way the Levene’s Test can be used. While using Minitab both of the tests results are displayed when testing for significance. They both compute the same basic information but you will use the F-test when data is normally distributed and the Levene’s test when you do not have normal data.

The F-test is used to determine if variances of two different samples are the same or not. Otherwise you can use the Bartlett’s test for more than one set if the data are normally distributed. The variance or standard deviation can be used when dealing with discrete or continuous nominal data. The F-test takes all the means and tells if they are all equal or not. If they are then one can infer that the data can be from the same origin. In order for this to work it must be used with data that are normally distributed and independent of one another. The F-test can be used in determining any mean comparisons as long as these needs are met.  

                To perform the F-test you start by stating the null and the alternative hypothesis. Then you decide what the alpha is going to be and if you are using a Right-tailed, Left-tailed, or Two-tailed test. Then one will determine the degrees of freedom using a chart. After that you plug the variances into the formula. The formula is not difficult and can be stated as such: F equals S superscript 2, subscript 1, over, S superscript 2, subscript 2. The larger variance goes on the top. If standard deviations are given instead of variances then make sure that each one is squared. Finally you need to make a decision if the null hypothesis was rejected or accepted, and explain the answer. (Bluman)

                The Levene’s Test is not much different from the F-test in terms of what purpose we use it for. Its basically a “one-way analysis of variance on the absolute values of the differences between each observation and the of its group” (Glass). Usually it is paired with ANOVA since it does not need to have normally distributed data (Keyes). And because we can use it with ANOVA we can say that it works with quantitative data as well as nominal. There is still the process of creating a hypothesis and determining the alpha that one will base the p-value given against.

 Here you can compare more than one group together at one time it is sometimes more often compared to Bartlett’s test since a F-test usually deals with only two groups. Alan Heckert describes the different groups of Levene’s Test into 3 levels. He says, “The three choices for defining Z_ij determine the robustness and power of Levene’s test. By robustness, we mean the ability of the test to not falsely detect non-homogeneous groups when the underlying data is not normally distributed and the groups are in fact homogeneous.”  There are the hand calculations to do a Levene’s test would be extremely difficult so we use programs like Minitab to take care of that. Even though are four different syntax computations, they are really grouped into three different ones that are done under the Levene’s test. The Levene test and Median Levene Test both use the median as the base. There is a Mean Levene Test that uses the mean and a Trimmed Mean Levene Test which actually computes the trimmed mean based Levene Test. It trims the Lowest 10% and Highest 10 % of the data. This helps with outliers that may occur randomly (Heckert).

                These tests of significance are really good to use when deciding if something has the same variance or not. It can define which statistical test will be the best one to use. These are used in ANOVA’s, and T-test’s. If I was studying the populations in a few of the African tribes I could take certain samples and decide if they has the same variance or not. If the means turn out to be the same with alpha .05 then I can scientifically make assertions about these tribes.   

Works Cited

Bartlett‘s test (or the F test) versus Levene’s test for equal variances. Dec. 14 2006. 27 April 2008. <http://www.minitab.com/support/answers/answer.aspx?log=0&id=1183>.

Bluman, Allan G. Elementary Statistics: A Brief Version. 3^rd ed. New York: McGraw-Hill, 2006.

Glass, Gene V. “Testing Homogeneity of Variances.” American Educational Research Journal, Vol. 3, No. 3 (May, 1966): 187-190 <http://www.jstor.org/stable/view/1161802?seq=4>.

Heckert, Alan. Dataplot. 4 April 2003. National Institute of Standards and Technology. 27 April 2008. <http://www.itl.nist.gov/div898/software/dataplot/refman1/auxillar/levetest.htm>.

Keyes, Tim K. Martin S. Levy. “Analysis of Levene’s Test Under Design Imbalance” Journal of Educational and Behavioral Statistics, Vol.22, No.2 (summer, 1997): 227-236. JSTOR. 27 April 2008. <http://www.jstor.org/stable/view/1165379?seq=9>.

Dear XXXXX,

            I remember meeting you at the NR club meeting the other day and we talked about a part time job opportunity for the summer. I am sending you a copy of my resume for you to look over and see if there is a place for me at Mud Creek Conservancy. 

            I am a freshman looking for a good start on anything environmental. Its a vast field and any experience would be good for me. I know how much getting a head start helped you in your career and I would love to have that experience as well. 

            My resume is posted on my website if you happen to misplace it as well and I will be calling soon to catch up on anything. 

Sincerely,

Amy Sperback

317.965.3430cell

317.247.5847

asperback@bsu.edu

Picture thanks to the SVS website: www.bsu.edu/svs 

I am part of Student Voluntary Services and have completed over 300 hours of service my freshman year in college.  

MORE PICTURES TO COME!!!!!!

LINK: http://www.mudcreekconservancy.org/howtojoin.htm

site link: http://www.eaglecreekpark.org/

                This article had a lot to say about the adoption of renewable portfolio standards (RPS). The article written by Ming-Yuan Huang, Janake R.R. Alavalapatie, Douglas R. Carter, and Matthew H. Langholts, was published in the November 2007 issue volume 35 of Energy Policy. They did a study on why some states in the U.S. have adopted or intend to adopt RPS and others have not.  Before they go into what the study states the authors start out by helping the reader understand the thing it will be analyzing. The bias is detected by the way they describe the RPS, and how wonderful it is. It sets up the hypothesis well by inserting their thinking and how they see the issue.

They decided to look at six different factors and come up with an equation to see the states likelihood of adopting RPS.  Their hypothesis was as stated, “We hypothesize that socio-economic, political and environmental factors influence state’s choice to either adopt or not adopt RPS.”(Ming) The hypothesis that they used was general, but they wanted to know why some agreed to RPS and others did not. They wanted to take a look at it in the scientific community. To support to support the hypothesis they used a binary method and a logistic function that approximates the normal distribution. The binary limits them to having a 1 or 0 which they assigned “a value of 0 if a state did not adopt and 1 otherwise” (Ming).  Not only were equations used but they added in the article descriptive statistics for variables used in the analysis, they added in the use of correlation, regression, elasticity at means, P-values and Chi square values. The study did not include confidence intervals it was not that specific. Tables were displayed to show them and they inserted one graph that depicted the percentage of renewable energy and the target year for selected standard in the U.S. It compares the states that already have RPS and at what percent they set it at or intend to reach.

The P-values for variables, Education, Political Party Dominance, and Constant were set at a 95% confidence level with significance set at the 5% level; meaning that they are willing to be wrong within 5%. When the study dealt with variables, Natural Resource Expenditures, Gross Rate of Production, and Gross State Product, they raised that level of significance to .10 or to 10%. They showed the elasticity values in percentages. The continuous variables did well with these comparisons since they are elastic unlike the “dummy variable” that does not apply. Some of the variables were hard to define because of too much variance, like in the case of the Political Party Dominance, because each person is different and humans lie. So the study had to state that they configured it with all “other variables fixed”. It was a theoretical arrangement.   A few of the relationships did even not come out as they expected and they gave proper explanation of each of them. So the hypothesis was not correct. However, there were parts that did support the claim but the authors did state that they would need to do further research to conclude better results. The most positive part in the conclusion was the encouragement to go out and be productive. Overall they kept the reader engaged on a personal level showing human interest in a movement.

The article was not entirely easy for me to read. It was not overtly long but dealt with a lot of statistics in depth. It was nice to see vocabulary dealing with statistics in an article about statistics and being able to understand it. Although, I did have to re-read it 3 times to get the general overview of the article and not get lost in the linguistics. The research done was pretty deep. There was a citation of seventeen different sources. They were a combination of scholarly journals and information from the government and environmental energy companies.

Works Cited

Ming-Yuan Huang, Janaki R.R. Alavalapati, douglas R. Carter and Matthew H. Langholtz. Energy Policy.  Vol. 35 Issue 11, Nov. 2007. Science Direct. School of Forest Resources and Conservation University of Florida. 25 March 2008.

Here is the link to see for yourself: http://www.ases.org/index.htm