F-test

The program performs F-test for significantly different variances. The test trying to reject the null hypothesis that variances of two distributions are actually consistent. The statistic F is the ratio of one variance to the other. The values of the statistic either >> 1 or <<1 will indicate very significant differences. The null hypothesis (of equal variances) is trying to be rejected by either very large or very small values of F, so the significance is two-tailed.

This program use statistical functions from "R" free software environment for statistical computing and graphics (http://www.r-project.org).

This program requires the R-package to be installed on your computer.

Input file should contain table of numerical data: lines for observations (cases) columns should be separated by tabulation or user-defines symbol (; , etc); for example, if comma (,) separator is used, the file format is the same as the CSV (comma separated values) format. No missing data allowed.

Example of output data:


F-test for varince difference (two-tailed):
VarName	M	Var
Feat1	-2.6040	101.8692
Feat5	2.0072	102.6015
F-statistics	1.0072
df1	49
df2	49
prob	0.9801

First line is the header. Second line prints data descriptions, separated by tabulation (VarName - names for selected variables; M - mean values for variables; Var - variances for variables). Next lines are the list data for variables (names, means and variances), separated by tabulation. After the variable list the following parameters are printed out: Pooled Variance (PooledVariance), F-statistics, number of degrees of freedom for variables (df1 and df2) and the probability the value of F-statistics under the null hypothesis of equal variances (prob).

Example of input data file format:


ItemName   Feat1	Feat2		Feat3		Feat4		Feat5	   ClassVar
Item1	-11.761101	-5.295846	-2.491684	4.151158	9.777093	1
Item2	-11.425886	-6.753716	0.136692	5.161748	13.618702	1
Item3	-7.069796	0.545457	0.097140	0.678579	10.302988	1
Item4	-13.480880	-3.867702	0.119297	2.333842	10.992096	1
Item5	-9.707938	-2.597949	-2.329997	2.928526	8.441053	1
Item6	-10.013794	-2.165258	-3.169195	2.625904	10.611103	1
Item7	-9.057161	-4.766594	1.691733	1.655782	7.046236	1
Item8	-8.562761	-1.272652	-3.990204	2.286294	12.768212	1
Item9	-12.724631	-4.710623	-2.114719	2.812189	6.434645	1
Item10	-9.593738	-5.478652	-1.799524	4.306497	9.514756	1
Item11	-7.699759	-1.546648	-0.423322	4.889767	9.228675	1
Item12	-13.158116	-2.891354	0.595935	2.264199	12.004761	1
Item13	-10.509598	-3.414075	-1.962310	1.263863	10.199896	1
Item14	-6.547624	-3.594928	-2.117222	5.168950	10.838221	1
Item15	-12.375988	-3.130436	-2.169164	1.537614	11.112888	1
Item16	-12.953032	-2.805048	0.085116	3.303354	7.405194	1
Item17	-11.370708	-2.848384	-0.848201	3.885525	10.569231	1
Item18	-13.117222	-7.025575	1.406507	7.069338	12.230415	1
Item19	-11.573168	0.288003	-2.826167	4.397137	10.851711	1
Item20	-7.993835	-1.204352	-1.924345	0.829829	10.314768	1
Item21	-9.225135	-2.512925	-1.608051	1.420301	9.766411	1
Item22	-8.402783	-0.890500	3.189703	3.754479	7.481063	1
Item23	-9.888180	-3.345775	1.965667	2.906369	11.488815	1
Item24	-11.686270	-5.389477	2.556932	1.661153	9.717826	1
Item25	-12.599567	-0.266091	-3.936308	0.751762	10.405225	1
Item26	-11.365093	-1.919706	-0.458052	1.861843	9.521104	1
Item27	-11.027619	-2.944884	-2.792962	4.144322	7.958556	1
Item28	-11.795160	-6.769646	0.908383	1.005066	11.240333	1
Item29	-13.629933	0.674184	-3.386853	-0.095859	10.490432	1
Item30	-7.823298	-5.452589	-2.336894	1.919889	9.421125	1
Item31	6.360118	6.794549	4.168188	-4.492538	-12.297555	0
Item32	8.774682	0.492721	1.587909	-5.486587	-12.361278	0
Item33	7.768181	3.989776	3.289377	-0.895444	-13.067171	0
Item34	8.581133	2.922361	3.952544	-4.450362	-6.787133	0
Item35	6.176519	4.526292	-2.771599	-3.477187	-7.316202	0
Item36	11.539781	-0.892880	2.868221	-1.456557	-11.008881	0
Item37	11.743034	3.527726	-0.635792	-2.067965	-7.151524	0
Item38	10.527299	1.460768	0.862300	-1.967742	-8.819727	0
Item39	8.148808	5.157964	-0.916135	-1.551958	-9.467513	0
Item40	9.241432	1.483108	-0.981933	1.046571	-8.504166	0
Item41	9.444197	4.963927	1.127201	-0.523484	-9.102817	0
Item42	11.545396	4.604968	4.818171	-5.046815	-13.494675	0
Item43	11.890988	1.220710	-2.069796	-2.942747	-8.996673	0
Item44	11.810480	2.031465	2.987976	-5.699606	-10.026246	0
Item45	10.806543	5.275155	4.969420	-2.792596	-11.345561	0
Item46	10.261177	3.586077	3.340220	-3.339244	-7.795038	0
Item47	8.407544	2.887997	3.104312	-3.734519	-9.758477	0
Item48	7.317484	5.553850	1.618000	-2.525315	-13.613147	0
Item49	10.654500	2.579577	1.922452	-3.765160	-10.414136	0
Item50	6.940641	3.525834	-0.660756	-4.105869	-10.064455	0