Bjorn Lantz
3.2 Brown-Forsythe test
The results regarding the Brown-Forsythe test are presented in tables 5a–5d. When the effect size is 0.00, the MAPE values are generally low when all sample sizes are large (albeit higher than when ANOVA is used to analyze data), and generally high when all sample sizes are small. When sample sizes are unequal, the MAPE values are considerably higher under the Brown-Forsythe test than under the ANOVA test. In these cases, many results differ significantly from the equidistant case. This indicates that the actual significance level is rather sensitive to non-equidistance. The MAPE values are also generally higher when data are skewed, for all combinations of sample sizes. Table 5a: Brown-Forsythe test, symmetric case with equally spaced means f 0.00
n1,n2,n3 25,25,25 5,5,5 5,5,25 5,25,25
Eq 0.051 0.046 0.050 0.055
V1 0.050 0.042* 0.047 0.052
V2 0.050 0.034* 0.044* 0.049*
V3 0.051 0.047 0.054 0.063*
V4 0.051 0.047 0.052 0.059*
V5 0.050 0.036* 0.051 0.056
V6 0.051 0.044 0.049 0.054
MAPE 2.1% 21.0% 5.7% 11.1%
0.10
25,25,25 5,5,5 5,5,25 5,25,25
0.106 0.053 0.064 0.077
0.103 0.048* 0.060* 0.073
0.101 0.040* 0.044* 0.061*
0.104 0.054 0.066 0.082*
0.105 0.053 0.065 0.081
0.101 0.040* 0.083* 0.091*
0.104 0.050 0.060* 0.074
2.5% 20.2% 16.7% 10.5%
0.25
25,25,25 5,5,5 5,5,25 5,25,25
0.452 0.098 0.152 0.215
0.447 0.090* 0.143* 0.206*
0.435* 0.079* 0.104* 0.167*
0.437* 0.100 0.145* 0.209
0.447 0.099 0.145* 0.211
0.429* 0.077* 0.195* 0.251*
0.450 0.094 0.141* 0.206*
2.7% 17.8% 24.4% 11.6%
0.844 0.188 0.299* 0.435*
0.827* 0.150* 0.378* 0.508*
0.848 0.180* 0.302* 0.437*
1.4% 16.1% 27.2% 12.6%
0.40
25,25,25 0.849 0.845 0.832* 0.832* 5,5,5 0.188 0.175* 0.154* 0.186 5,5,25 0.318 0.302* 0.241* 0.296* 5,25,25 0.453 0.437* 0.372* 0.434* Note: ’*’ indicates a significant difference from the equidistant case
Table 5b: Brown-Forsythe test, symmetric case with one extreme and two equal means f 0.00
n1,n2,n3 25,25,25 5,5,5 5,5,25 5,25,25
Eq 0.050 0.045 0.048 0.054
V1 0.049 0.041* 0.045 0.052
V2 0.049 0.034* 0.043* 0.048*
V3 0.051 0.046 0.053* 0.061*
V4 0.050 0.046 0.051 0.059*
V5 0.049 0.036* 0.050 0.054
V6 0.049 0.043 0.047 0.053
MAPE 1.3% 20.0% 6.6% 12.9%
0.10
25,25,25 5,5,5 5,5,25 5,25,25
0.108 0.052 0.061 0.098
0.107 0.048* 0.059 0.096
0.104 0.040* 0.062 0.087*
0.108 0.053 0.067* 0.098
0.109 0.053 0.065 0.100
0.106 0.042* 0.050* 0.106*
0.107 0.050 0.062 0.096
1.6% 18.1% 7.0% 4.6%
0.25
25,25,25 5,5,5 5,5,25 5,25,25
0.451 0.095 0.123 0.335
0.446 0.090* 0.120 0.329
0.426* 0.075* 0.123 0.308*
0.432* 0.090* 0.127 0.306*
0.439* 0.091 0.127 0.313*
0.445 0.084* 0.095* 0.358*
0.447 0.091 0.124 0.328
2.8% 17.9% 11.3% 14.5%
0.842* 0.167* 0.243 0.649*
0.849* 0.178 0.206* 0.707*
0.854 0.174* 0.248 0.674*
1.5% 16.9% 14.2% 14.1%
0.40
25,25,25 0.856 0.852 0.836* 0.835* 5,5,5 0.182 0.173* 0.147* 0.165* 5,5,25 0.247 0.244 0.240* 0.241 5,25,25 0.686 0.676* 0.647* 0.639* Note: ’*’ indicates a significant difference from the equidistant case www.ejbrm.com
21
©ACPIL