Fisher’s F-distribution

In statistics, ANalysis Of VAriance (ANOVA) is a collection of statistical models and their associated procedures in which the observed variance is partitioned into components because of different explanatory variables. The initial techniques of the analysis of variance were developed by the statistician and geneticist R.A. Fisher in the 1920s and 1930s, and are sometimes known as Fisher s ANOVA or Fisher s analysis of variance due to the use of Fisher s F-distribution as part of the test of statistical significance. 

The arguments leading to the determination of the lower and upper endpoints of the confidence interval are analogous to those of the preceding section. Instead of summing over a Poisson distribution this has to be done over a binomial distribution according to Eq. (9.35) for a number failures which are smaller, respectively larger than the observed number x. If the relationship between sums over binomial distributions and Fisher s F-distribution is used [24], we obtain for the lower endpoint with a level of confidence of y... 

Z. (1) The symbol for a standardized value of a Normal variable. (2) The symbol for the test statistic in Whitehead s boundary approach to sequential clinical trials (see Chapter 19). (3) The symbol which R.A. Fisher used to designate half the difference of the natural logarithms of two independent estimates of variances when comparing them. (Nowadays we tend to use the ratio instead, which we compare to the F-distribution.) (4) The last entry in this glossary. 

The universally accepted approach to statistical evaluation of small data sets is that originated by WUham Gosset (Gosset 1908) and developed and publicized by Richard Fisher (Fisher 1925, 1990). The so-caUed Student s t-distribution (see the accompanying text box) addresses the problem of estimating the uncertainty in the mean of an assumed normal distribution based on a small number of data points assumed to be random samples from that distribution. It forms the basis of f-tests commonly used for the statistical significance of the difference between the means of two small data sets believed to be drawn from the same normal distribution, and for determination of the confidence interval for the difference between two such data set means. 

Shimadzu Xex = 486nm, A,em = 516 nm) with a chart recorder (Fisher Recordall, Series 5000, Springfield, NJ). F-PHEA concentrations in perfusate were determined by area comparison of the eluted curves to that of the standard. Curves of logMW vs. elution volume, Ve, were constructed for each column using the integral-MWD method as described previously (9). Molecular weight distributions of absorbed material were determined from the calibration curves and the sample s chromatograph by curve summation (9). 

In a first step the chosen mathematical model, containing the functional model (27) or (34) and the stochastic model (33), has to be proved. By Baarda s test of the model the agreement of the a priori variance factor and the a posteriori variance factor will be tested. Supposing the modell is correct (hypothesis Ho), the test value Ti has a central Fisher-distribution with f degrees of freedoms (30) and will be provided to... 

Singer, K., and Fisher, B. 1952. Studies on ahnormal hemoglobins. V. The distribution of type S (si< e cell) hemoglobin and type F (alkali-resistant) hemoglobin within the red cell population in sickle cell anemia. Blood 7, 1216. 

---