# One-Way ANOVA Exploring World Fertility Rates

Statistical Topic:
One-way ANOVA can be thought of in two different ways. First ANOVA extends testing sample means beyond the two sample mean situation used for t-tests.  Second one-way ANOVA is the simplest statistical procedure for more complicated experimental designs.  The logic behind ANOVA is that we are partitioning variation into variation explained by differences in samples means  and variation not explained by differences in sample means or what we call error.  Once the variance for each type of variation is computed, we can test to see if these variances are equal to each other using the F-distribution.
Student Issue:
How do fertility rates compare with other regions of the country?
Data Set:
Go to the United Nations Cyber School Bus web site.  Choose INFONATION to go to the UN database with over 30 different fields of information on 185 different countries.
Goal of Data Analysis Lab:
Using ANOVA, determine if there is a difference in fertility rates for four different regions of the world.
Statistical Techniques:
1. Choose four regions of the world from the six regions specificed by the UN database.  One of these regions must be North America.  Within each of these four regions randomly select ten countries (okay if one or two have missing information) to investigate. Included is a copy of the all the six regions of the world and all countries in each regions.  In the North American region, one of the countries selected must be the United States since you are studying how your country relates to other countries in the world for fertility.  For each of these countries choose three data fields:  total fertility rate, GDP Per Capita and Threatened Species as shown in the printscreen for the INFONATION database.  For the ANOVA data analysis lab you are going to only use the numerical variable total fertility rate but for the next data analysis lab using linear regression we are going to use GDP Per Capita and Threatened Species for the same countries.  On a piece of data create five columns to input to SPSS, one for each variable.  The first column is the country name, the second is a code of 1-4 for each region of the world each country belongs, the third is the fertility rate, the fourth is GDP Per Capita and the fifth is the number of threatened species.
2. Using the One-way ANOVA, test the research question that the mean fertility rate is different for the four different regions of the world.  Use Tukey's multiple comparison test to determine which regions of the world are different from each with an alpha of .05.
3. What are the test assumptions for ANOVA? Have these assumptions been met for this example?
4. State what SSB, SSW and SSTotal actually represent in the context of this data seet.  Why do we use a F distribution to test means in ANOVA rather than a t distribution?
5. Write an APA results paragraph explaining the inferential test you just completed.
Social Commentary:
1. How does fertility rate affect the economy of a country?
2. Is the fertility rate of a man different than a woman?