Analysis of Variance (ANOVA) - Definition

Analysis of Variance, or ANOVA for short, is a statistical test that looks for significant differences between means on a particular measure. For example, say you are interested in studying the education level of athletes in a community, so you survey people on various teams. You start to wonder, however, if the education level is different among the different teams. You could use an ANOVA to determine if the mean education level is different among the softball team versus the rugby team versus the Ultimate Frisbee team. Key Takeaways: Analysis of Variance (ANOVA) Researchers conduct an ANOVA when they are interested in determining whether two groups differ significantly on a particular measure or test.There are four basic types of ANOVA models: one-way between groups, one-way repeated measures, two-way between groups, and two-way repeated measures.Statistical software programs can be used to make conducting an ANOVA easier and more efficient. ANOVA Models There are four types of basic ANOVA models (although it is also possible to conduct more complex ANOVA tests as well). Following are descriptions and examples of each. One-way between groups ANOVA A one-way between groups ANOVA is used when you want to test the difference between two or more groups. The example above, of education level among different sports teams, would be an example of this type of model. It is called a one-way ANOVA because there is only one variable (type of sport played) that is being used to divide participants into different groups. One-way repeated measures ANOVA If you are interested in assessing a single group at more than one time point, you should use a one-way repeated measures ANOVA. For example, if you wanted to test students’ understanding of a subject, you could administer the same test at the beginning of the course, in the middle of the course, and at the end of the course. Conducting a one-way repeated measures ANOVA would allow you to find out whether the students’ test scores changed significantly from the beginning to the end of the course. Two-way between groups ANOVA Imagine now that you have two different ways in which you want to group your participants (or, in statistical terms, you have two different independent variables). For example, imagine you were interested in testing whether test scores differed between student athletes and non-athletes, as well as for freshmen versus seniors. In this case, you would conduct a two-way between groups ANOVA. You would have three effects from this ANOVA—two main effects and an interaction effect. The main effects are the effect of being an athlete and the effect of class year. The interaction effect looks at the impact of both being an athlete and class year. Each of the main effects is a one-way test. The interaction effect is simply asking if the two main effects impact each other: for example, if student athletes scored differently than non-athletes did, but this was only the case when studying freshmen, there would be an interaction between class year and being an athlete. Two-way repeated measures ANOVA If you want to look at how different groups change across time, you can use a two-way repeated measures ANOVA. Imagine you’re interested in looking at how test scores change across time (as in the example above for a one-way repeated measures ANOVA). However, this time you’re also interested in assessing gender as well. For example, do males and females improve their test scores at the same rate, or is there a gender difference? A two-way repeated measures ANOVA can be used to answer these types of questions. Assumptions of ANOVA The following assumptions exist when you perform an analysis of variance: The expected values of the errors are zero.The variances of all errors are equal to each other.The errors are independent from one another.The errors are normally distributed. How an ANOVA is Done The mean is calculated for each of your groups. Using the example of education and sports teams from the introduction in the first paragraph above, the mean education level is calculated for each sports team.The overall mean is then calculated for all of the groups combined.Within each group, the total deviation of each individual’s score from the group mean is calculated. This tells us whether the individuals in the group tend to have similar scores or whether there is a lot of variability between different people in the same group. Statisticians call this within group variation.Next, how much each group mean deviates from the overall mean is calculated. This is called between group variation.Finally, an F statistic is calculated, which is the ratio of between group variation to the within group variation. If there is significantly greater between group variation than within group variation (in other words, when the F statistic is larger), then it is likely that the difference between the groups is statistically significant. Statistical software can be used to calculate the F statistic and determine whether it is significant or not. All types of ANOVA follow the basic principles outlined above. However, as the number of groups and the interaction effects increase, the sources of variation will become more complex. Performing an ANOVA Because conducting an ANOVA by hand is a time-consuming process, most researchers use statistical software programs when they are interested in conducting an ANOVA. SPSS can be used to conduct ANOVAs, as can R, a free software program. In Excel, you can do an ANOVA by using the Data Analysis Add-on. SAS, STATA, Minitab, and other  statistical software programs  that are equipped for handling bigger and more complex data sets can also be used to perform an ANOVA. References Monash University. Analysis of Variance (ANOVA). http://www.csse.monash.edu.au/~smarkham/resources/anova.htm

The role of Jocasta in Oedipus the King is crucial....

The role of Jocasta in Oedipus the King is crucial. Jocasta sees the reality of the situation before Oedipus and the chorus do. The prophecies made themselves known long ago, and Jocasta believed that they would come true. Jocasta did have faith in the oracles, but only enough faith to suit her own purpose. She worked to suppress much of the faith Oedipus had in them, in the interest of keeping the city, herself, and Oedipus in a powerful yet strong position. Jocastas role in the story influenced Oedipus to think back to Laius death and begin to try to solve the Sphinxs riddle. Jocasta explains that an oracle called for her husbands death to be at the hand of his own son. Seeing that thieves evidently killed the king, Oedipus as the†¦show more content†¦Running away gave Oedipus the ability to avoid the oracle. Oedipus avoiding his prophecy, and Jocasta and Laius avoiding theirs, enabled Jocasta to convinced herself that chance ruled their lives, not prophecies. In Oedipus t he King, it seems as though chance is a motif. King Laius was said to be killed at three crossroads. When Oedipus ran from Corinth, he admitted to killing a man who caused conflict along the way. The chance this could be the same man is very slim; the two stories did not match up. Jocasta demands Oedipus tell her what he is thinking when he is trying to solve the kings murder. It crosses Oedipus mind that he could be the killer, however; guilt left him in strong defense when he tells Jocasta, I cannot be the killer. One cant equal many (Sophocles, 934). This foreshadowing shows a possible suspect, and Oedipus guilty conscience. The witnesses to the death recall multiple thieves being resent, and also that the murder took place at the three crossroads. The Greek goddess of the crossroads, Hecate, was said to have three heads. Each head looked down a different path – one saw the past, one the present, and one the future. Though Hecate isnt mentioned in the play, perhaps the thr ee-way crossroads in Oedipus the King has a similar symbolism. (www.shmmoop.com). The three crossroads relate to Jocasta in that she has determines Oedipus fate from when he wasShow MoreRelatedOedipus Data Sheet2569 Words   |  11 Pages Major Works Data Sheet Oedipus the King Title: ________________________________ Sophicles Author: ______________________________ Date of Publication: ____________________ Around 450 BC Tragic Drama/Theater Genre: _______________________________ Historical information about the setting The work was written around 450 BC, a time of high Greek culture where literature and drama were placed at the forefront of society. Sophocles was a key player in this movement, and his playsRead MoreAntigone : A Portrait Of Ancient Greece2905 Words   |  12 Pagesproduction of tragedies, Ancient Greece often employed the use of drama and conflict to illustrate tales relevant to the society at the time. The playwright Sophocles is a prime example of this. In his tragedy Antigone, Sophocles tackles issues such as the role of the gods, the proper behavior of women, and the power of a leader. These motifs not only add value to the narrative, but offer the reader a glimpse of the state of Greek society of the time. Artifacts such as the ones found at the Penn Museum of

The Coming Anarchy - Robert Kaplan free essay sample

Robert Kaplan published his essay entitled, The Coming Anarchy. In his essay, Mr. Kaplan theorized that the region of Western Africa is becoming the â€Å"symbol of worldwide demographic, environmental, and societal stress†. He identified numerous political, social, economic, and environmental issues affecting Western Africa, which in his opinion, would lead to the demise of that African region within the next 50 years. Mr. Kaplan further theorized that nations worldwide would eventually contract the same problems occurring in Western Africa and collapse into anarchy. Mr. Kaplan’s prediction of worldwide anarchy is inaccurate, since his argument relies on broad generalizations and insufficient credible examples and sources of information. Western Africa exhibits many of the problems common in the world’s developing nations, including overpopulation, crime, drug cartels, limited marketable commodities, the prevalence of infectious diseases, and scarcity of natural resources. Kaplan predicted that as time continued, the countries of Western Africa would also continue to decline. In doing so, his diagnosis fails to address opportunities in innovation, advances in technology, and an international system capable of self-correction. In previous decades, international assistance to West African countries was in the form of food and monetary aid or a reduction of debt. Today, foreign investment through energy partnerships and trade agreements with North American, European, and Asian countries are increasing, especially with the oil-rich country of Nigeria. Germany is investing heavily in Nigerian crude oil for its industrial uses, and in turn, Nigeria is importing German equipment and other industrial goods. Great Britain, another major player in the European market, has recently agreed to invest $250 million dollars over the next four years to improve border crossings in Western Africa, which will help facilitate trade throughout the continent. China is initiating large-scale infrastructure related construction projects, including a new railway system, road improvements, bridges, energy stations, schools, and cellular-phone networks in several African nations. In his 1994 essay, Kaplan describes the country of Liberia as one that is war-torn, led by inexperienced rebel leaders, and has over 1 million displaced civilians. Today, Liberia has had a decade of peace, held presidential and general elections, improved its social services and infrastructure, and protected human rights. As recently as 2013, the United States and Liberia entered into an agreement to cooperate and improve Liberia’s agriculture and energy sectors. Liberia now ranks among the fastest-growing economies in sub-Saharan Africa, even though the nation is still navigating through long standing issues typical of a developing Western African nation. The ability of Liberia to rebound from its political, economic, and social issues of the past exposes a serious flaw in Kaplan’s theory, and further demonstrates the ability of the international community to self-correct. As a region, Western Africa has recently experienced positive economic growth. The Western African economy grew at a rate of 6. 9 percent during 2012, an increase over the 5. 9 percent in 2011. The achieved economic growth in the sub-region was more than double the global rate, according to a report delivered at the just-ended 42nd Economic Community of West African States (ECOWAS) Summit in the Ivory Coast. In 2012, Sierra Leone, once considered a microcosm of the upcoming anarchy by Mr. Kaplan, experienced the highest growth rate (18. 3%) of any Western African nation. In his analysis, Kaplan supports his worldwide anarchy theory using Sierra Leone and Ivory Coast, as examples to characterize the entire sixteen country Western African region. Sierra Leone and Ivory Coast are both located on the southern coast of Western Africa, and endured military coups, economic troubles, and trade conflicts during the 1980’s. Sierra Leone and Ivory Coast have similar economies dominated by trade and exportation of goods, and are not oil-producing nations. Kaplan made a mistake by selecting countries that were too geographically and economically similar, and thus, discredits his statement of Sierra Leone being a â€Å"microcosm of what is occurring† in Western Africa. Kaplan considered Nigeria, with its extensive supply of oil reserves, to be the country with the greatest future growth potential in Western Africa. However, Kaplan’s fixation with his worldwide anarchy theory caused him to still overlook Nigeria’s energy potential, and assume that a Nigeria of the future would be borderless, overpopulated, impoverished, and ripe with famines. Additional, unbiased research on Nigeria’s energy potential by Kaplan would have demonstrated that Nigeria’s future was bright, despite the social, political, and environmental problems existing in 1994. Given the political, economic, social, and environmental differences that exist in Western Africa, Kaplan further erred by only selecting three countries in ormulating his theory of worldwide anarchy. By using only three countries in a sixteen country region that is so diverse, Kaplan’s conclusions seem incomplete. Incorporating pertinent data and information from the entire region of Western Africa would have given more credibility to his theory. Kaplan’s analysis also seems flawed since some of his information is obtained from personal observations and testimonies from historians and potentially biased commentators, including a devoted environmentalist (Thomas Fraser Homer-Dixon). Kaplan’s prediction that the downfall of Western Africa would trigger worldwide anarchy was not fundamentally sound. Kaplan underestimated the ability of the international community to self-regulate and reverse a negative course of action. If Kaplan had not used broad generalizations to support his theory of worldwide demise and instead used sound, unbiased, scientific and demographic data, I believe he would not have predicted such a grim worldwide outlook for the next 50 years.