Variance Analysis

Analysis of variance is a term used in statistics which involves a collection of statistical models and procedures that are associated with them where the observed variance in a particular variable is partitioned into components that can be attributed to different sources of variations. it is therefore a statistical technique that is useful for evaluation whether there are differences between average values or mean across several population groups, It can simply be defined as a statistical test that of whether or not the means associated with several groups are all equal and hence it generalizes t-tests to more than two groups. If multiple t-tests are two are used there would be increased chances of type one error being committed for that reason variance analysis is a useful for a comparison of two, three or more means. This model operates by comparing the amounts of dispersion that is experienced by each of the groups to the total amount of dispersion in the data (Lowry, 2012)

This model also entails that the response variable is continuous in nature while the predictor variables can be categorized. For there to be a test for statistical significance between means then there has to be a comparison i.e. analyzing variances hence the name of the model. There are various concepts in variance analysis these are; the partitioning of sums of squares .at the core of variance analysis is the fact that variances can be divided or partitioned. This means that variance that has been computed as the sum of deviations that are squared from the overall mean then divided by the sample size minus one. Hence from a given sample, the variance is a function of the sums of deviation squares or partitioning of variance. Another concept is SS Error and SS Effect, the variability within a group which is SS is referred to as error variance. This term denotes the fact that it cannot be accounted for in the design.SS Effect can be explained as to arise from the differences in means between the groups. In other words group membership explains variability since there are differences in means. Another concept is significance testing, where the basis of comparison of variance due to the between group variability known as the mean square effect with the within group variability. Under a null hypothesis variance is estimated based on within-group should be same as the variance due to between group variability (Lowry, 2012)

A comparison between the two variances is made through an f-test to see if the two variances estimates are significantly greater than one. Hence a conclusion can be made that the variances for the two groups differ significantly from each other. The basic concept in variance analysis is the test for the difference in means for variables or groups for statistical significance. This is accomplished by analyzing the variance by partitioning the total variance into the component that is due to random error i.e. within group SS and the component that are due to the difference between the means. These latter variance components are then tested for statistical significance and then a decision to either accept or reject a null hypothesis that had been presented depending on the difference between the means.

Variance analysis is useful in the clinical field for instance when the tests for effectiveness of a particular drugs. For instance between hypersensitive patients, variance analysis can be used to compare the effectiveness of three different drugs in lowering the blood pressure.

Accuracy in statistics is the degree of closeness of a measurement of a quantity to the quantities true or actual value. Precision also termed as the reproducibility or repeatability is the degree to which repeated measurements under conditions that are not changed. A measurement in a system can be accurate but not precise and also accurate but not precise; it can also be neither or both. Type 1 error is also known as error of the first kind and it occurs when the null hypothesis is true but is rejected. Type 2 error is also known as the error of the second kind and occurs when the null hypothesis is false but is not rejected erroneously. An example of the relationship between accuracy and precision if for instance when one reads out time right to the second even if one knows very well that the watch they are reading from is one minute slow, this means that the reading is precise but it is not accurate. An example of the relationship between type 1 and type 2 errors in the world of medicine a null hypothesis being that a particular drug cures an illness, Type 1 error is made when a conclusion is made that the drug does not work when it actually does. While a type two error is made when a conclusion is made that the drug does not work when it actually does (Shera, 2006)

References

Lowry, R (2012).Conceptual introduction to the Analysis of Variance. Retrieved October 26,2012 from http://www.vassarstats.net/textbook/ch13pt1.htmlStatSoft, Inc (2012). Introduction to ANOVA / MANOVA.Retrieved October 26, 2012 from http://www.statsoft.com/textbook/anova-manova Shera, J (2006). STATISTICAL ERRORS (TYPE I, TYPE II, POWER).Retrieved October 26, 2012 from

http://www.herkimershideaway.org/writings/type12.htmTervo, R (1997) Accuracy and Precision. Retrieved October 26, 2012 from http://www.ee.unb.ca/tervo/ee2791/intro.htm