.- help for ^circ2sam^ .- Two-sample tests for circular data ---------------------------------- ^circ2sam^ varname [^if^ exp] [^in^ range] ^, by(^groupvar^)^ Description ----------- ^circ2sam^ carries out two-sample tests for circular variables with scales between 0 and 360 degrees due to Watson (1962) and Kuiper (1960). The values of varname are grouped according to the precisely two distinct values defined by groupvar together with any restrictions imposed by ^if^ or ^in^. The hypothesis under test is that the distributions so defined are identical. The test statistics are based on the empirical distribution functions of the two samples. Option ------ ^by(^groupvar^)^ is in fact not optional. Example ------- . ^circ2sam dir , by(group)^ Note on P-values and statistical tables --------------------------------------- For the Watson U-square statistic, critical values are given here for a few examples of sample sizes n_1 and n_2 and significance level P. For many problems with large or moderate samples, the values for infinite sizes will serve as adequate approximations. n_1 n_2 P = 0.5 0.2 0.1 0.05 0.01 0.005 0.001 5 5 0.089 0.161 0.225 0.225 7 7 0.079 0.135 0.158 0.199 0.304 0.304 9 9 0.077 0.125 0.155 0.187 0.266 0.286 0.384 12 12 0.075 0.122 0.153 0.186 0.256 0.284 0.344 20 20 0.069 0.117 0.151 0.185 0.261 0.293 0.367 40 40 0.069 0.117 0.152 0.186 0.264 0.298 0.374 100 100 0.069 0.117 0.152 0.187 0.267 0.300 0.378 infinite 0.071 0.117 0.152 0.187 0.268 0.304 0.385 Fuller tables can be found in Mardia (1972, p.314), Batschelet (1981, p.348) and Zar (1999, Table B.38), the last being the most extensive of these. For the Kuiper statistics, tables can be found in Batschelet (1981, pp.341, 346-7) and in Upton and Fingleton (1989, pp.393, 395). So long as at least one sample is more than 12, k* may be compared with the following critical values (see discussion in Upton and Fingleton, p.279): P = 0.1 0.05 0.01 0.005 0.001 1.62 1.75 2.00 2.10 2.30 Saved values ------------ S_1 smaller sample size S_2 larger sample size S_3 Watson U-square statistic S_4 Kuiper V statistic S_5 Kuiper k statistic S_6 Kuiper k* statistic References ---------- Batschelet, E. 1981. Circular statistics in biology. London: Academic Press. Mardia, K.V. 1972. Statistics of directional data. London: Academic Press. Upton, G.J.G. and Fingleton, B. 1989. Spatial data analysis by example. Volume 2: Categorical and directional data. Chichester: John Wiley. Zar, J.H. 1999. Biostatistical analysis. Upper Saddle River, NJ: Prentice-Hall. Author ------ Nicholas J. Cox, University of Durham, U.K. n.j.cox@@durham.ac.uk Also see -------- On-line: help for @circwwm@