Regression/ANOVA (probability and statistics) - Essay Example

Statistics Report The aim of this paper is to present a report on the comparison of home and away scores of each country using regression/ANOVA. The report will also include tests that were carried out to test if the scores of different countries exhibit any form of correlation. Correlation between the score of the countries when playing home and away and the interaction between the sum of score of different countries will also be reported on. The eight countries that were included in this survey are Australia, New Zealand, Pakistan, Pakistan, India, South Africa, England, Sri Lanka, and West Indies. Six pairs of scores (home and away) were recorded for each country
The overall average score for both home and away matches was 373.95.
A test for difference between means (ANOVA) of home and away scores for all countries gives a p-value 0.543. Comparing this value with that of alpha (α =0.05), it is observed that the calculated p-value is greater than α. This indicates that the test is not significant. The test also gave an F- calculated value of 0.922. Comparing this value with the F-crit value of 1.793, we observe that the former is lesser than the latter, i.e. F-calculated is greater than F-crit. Based on the calculated values of α and F, we concluded that the difference between the scores is statistically significant (Spiegel, 1992, 45). The F value is 0.922 and the p-value is 0.543, therefore there is not enough evidence to reject H0 at 95% level of significance.
Tests on the correlation between different measures are not significant too. Testing for the correlation between the score of different countries, a p-value of 0.35 and F-tabulated value 1.132 are obtained. Based on these values, there is enough evidence to reject, H0 at 95% level of significance and conclude that there is no correlation between the scores of different countries. As expected, different countries train differently and this accounts for the lack of correlation.
A second test on the correlation between the scores of the countries when playing home and away yields similar results. From this test, a p-value of 0.437 and F-tabulated value 0.611 are obtained. Based on these values, there is enough evidence to reject H0 at 95% level of significance and conclude that there is no correlation between the scores of the countries when playing home and away. Although there is supposed to be a correlation between home and away scores, it must be realized that home advantage every team every differently.
A third test on the correlation between the interaction of the sum of score of different countries yields similar results. From this test, a p-value of 0.623 and F-tabulated value 0.757 are obtained. Based on these values, there is enough evidence to reject H0 at 95% level of significance and conclude that there is no correlation between the interaction of the sum of score of different countries yields similar results. There could have been some interaction as each country played the same amount of matches home and away, however, the difference is not statistically significant.
Reference
Spiegel, M. R. (1992). Theory and Problems of Probability and Statistics, 2nd ed. New York: McGraw-Hill. Read More