An automated image analysis method to measure regularity in biological patterns: a case study in a Drosophila neurodegenerative model

Table 2 Test of the discrimination power of 9 selected variables

		Sum of squares	Degrees of freedom	Mean squares	F	Significance
TOTMAX	Between-groups	313102.269	2	156551.135	37.026	0.000
	Within-groups	629991.204	149	4228.129
	Total	943093.474	151
MPCM	Between-groups	13.228	2	6.614	52.478	0.000
	Within-groups	18.779	149	0.126
	Total	32.007	151
MPCVAR	Between-groups	0.99	2	0.495	7.345	0.001
	Within-groups	10.041	149	0.067
	Total	11.031	151
MPCSKEW	Between-groups	6.51	2	3.255	33.911	0.000
	Within-groups	14.302	149	0.096
	Total	20.812	151
SKEWVAR	Between-groups	66.349	2	33.175	9.356	0.000
	Within-groups	528.341	149	3.546
	Total	594.69	151
DISTM	Between-groups	37.854	2	18.927
	Within-groups	62.047	149	0.416	45.451	0.000
	Total	99.901	151
DISTVAR	Between-groups	79.766	2	39.883
	Within-groups	386.099	149	2.591	15.391	0.000
	Total	465.865	151
DISTSKEW	Between-groups	5.542	2	2.771	37.751	0.000
	Within-groups	10.937	149	0.073
	Total	16.479	151
LOGNNVAR	Between-groups	17.848	2	8.924	49.302	0.000
	Within-groups	26.97	149	0.181
	Total	44.817	151

ANOVA test was performed on 9 out of 18 variables that passed the correlation test and resulted in reasonable discrimination between degeneration groups by PCA analysis. TOTMAX is the total number of maxima detected per image. MPCM, MPCVAR and MPCSKEW refer to the mean, variance and skewness of the maxima per cell, respectively. SKEWVAR is the skewness of the intensity values variance per cell. DISTM, DISTVAR and DISTSKEW refer to the mean, variance and skewness of the centroid-to-mass-center distance, respectively. LOGNNVAR is the logarithm of the nearest neighbor variance. The between-groups and within-groups components of the variance are estimated computing the squared errors (sum of squares) and averaging by the degrees of freedom (df, obtained as k-1 between groups, N-k within groups and N-1 overall; where k is the number of groups involved, and N the sample size), thus resulting in the quadratic mean (\( {\widehat{s}}_b^2 \) between groups and \( {\widehat{s}}_w^2 \) within groups). The F-value is \( {\widehat{s}}_b^2/{\widehat{s}}_w^2 \), whose significance is evaluated following a F _2,149 distribution.