One-factorial ANOVA assessing spatial bias

Description

This function performs an one-factorial analysis of variance to test for spatial bias for a single array. The predictor variable is the average logged intensity of both channels and the response variable is the logged fold-change.

Usage

anovaspatial(obj,index,xN=5,yN=5,visu=FALSE)

Arguments

Details

The function anovaspatial performs a one-factorial ANOVA for objects of class “marrayRaw” or “marrayNorm”. The predictor variable is the average logged intensity of both channels (A=0.5*(log2(Ch1)+log2(Ch2))). Ch1,Ch2 are the fluorescence intensities of channel 1 and channel 2, respectively. The response variable is the logged fold-change (M=(log2(Ch2)-log2(Ch1))). The spot locations on the array is divided into xN intervals in x-direction and yN intervals in y-direction. This division defines (xN x yN) rectangular spatial blocks on the array, and thus, (xN x yN) levels (or treatments) for A. Note that values chosen for xN and yN should divide the array columns and rows approx. equally. The null hypothesis is the equality of mean(M) of the different levels. The model formula used by anovaspatial is M ~ (A - 1) (without an intercept term).

Value

The return value is a list of summary statistics of the fitted model as produced by summary.lm. For example, the squared multiple correlation coefficient R-square equals the proportion of the variation of M that can be related to the spot location (based on the chosen ANOVA.) Optionally, the distribution of p-values (as derived by t-test and stated in the summary statistics) can be visualised.

Author(s)

Matthias E. Futschik (http://itb.biologie.hu-berlin.de/~futschik)

See Also

anova, summary.lm, anovaint, marrayRaw, marrayNorm

Examples

# CHECK RAW DATA FOR SPATIAL BIAS
data(sw)
print(anovaspatial(sw,index=1,xN=8,yN=8,visu=TRUE))


# CHECK  DATA NORMALISED BY OLIN FOR SPATIAL BIAS
data(sw.olin)
print(anovaspatial(sw.olin,index=1,xN=8,yN=8,visu=TRUE)) 
# note the different scale of the colour bar

Results

R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(OLIN)
Loading required package: locfit
locfit 1.5-9.1 	 2013-03-22
Loading required package: marray
Loading required package: limma
> png(filename="/home/ddbj/snapshot/RGM3/R_BC/result/OLIN/anovaspatial.Rd_%03d_medium.png", width=480, height=480)
> ### Name: anovaspatial
> ### Title: One-factorial ANOVA assessing spatial bias
> ### Aliases: anovaspatial
> ### Keywords: models regression
> 
> ### ** Examples
> 
> # CHECK RAW DATA FOR SPATIAL BIAS
> data(sw)
> print(anovaspatial(sw,index=1,xN=8,yN=8,visu=TRUE))

Call:
lm(formula = as.vector(M) ~ factor(block) - 1)

Residuals:
     Min       1Q   Median       3Q      Max 
-3.04880 -0.29599  0.00474  0.28153  2.52965 

Coefficients:
                  Estimate Std. Error t value Pr(>|t|)    
factor(block)1  -0.9654777  0.0618191 -15.618  < 2e-16 ***
factor(block)2  -0.8163338  0.0618191 -13.205  < 2e-16 ***
factor(block)3  -0.4594468  0.0618191  -7.432 1.29e-13 ***
factor(block)4  -0.3616640  0.0618191  -5.850 5.28e-09 ***
factor(block)5  -0.0551087  0.0618191  -0.891 0.372739    
factor(block)6   0.2269960  0.0618191   3.672 0.000244 ***
factor(block)7   0.6213434  0.0618191  10.051  < 2e-16 ***
factor(block)8   0.8845512  0.0618191  14.309  < 2e-16 ***
factor(block)9  -0.8452423  0.0618191 -13.673  < 2e-16 ***
factor(block)10 -0.6882680  0.0618191 -11.134  < 2e-16 ***
factor(block)11 -0.4471502  0.0618191  -7.233 5.59e-13 ***
factor(block)12 -0.3416448  0.0618191  -5.527 3.47e-08 ***
factor(block)13  0.0086121  0.0618191   0.139 0.889212    
factor(block)14  0.1917838  0.0618191   3.102 0.001933 ** 
factor(block)15  0.7149640  0.0618191  11.565  < 2e-16 ***
factor(block)16  0.9256309  0.0618191  14.973  < 2e-16 ***
factor(block)17 -0.7742514  0.0618191 -12.524  < 2e-16 ***
factor(block)18 -0.6490230  0.0618191 -10.499  < 2e-16 ***
factor(block)19 -0.4425972  0.0618191  -7.160 9.52e-13 ***
factor(block)20 -0.3854886  0.0618191  -6.236 4.94e-10 ***
factor(block)21 -0.1530968  0.0618191  -2.477 0.013306 *  
factor(block)22  0.0470847  0.0618191   0.762 0.446310    
factor(block)23  0.4482664  0.0618191   7.251 4.90e-13 ***
factor(block)24  0.9157485  0.0618191  14.813  < 2e-16 ***
factor(block)25 -0.7126618  0.0618191 -11.528  < 2e-16 ***
factor(block)26 -0.5836128  0.0618191  -9.441  < 2e-16 ***
factor(block)27 -0.4903762  0.0618191  -7.932 2.74e-15 ***
factor(block)28 -0.4161683  0.0618191  -6.732 1.90e-11 ***
factor(block)29 -0.1285373  0.0618191  -2.079 0.037656 *  
factor(block)30  0.1469066  0.0618191   2.376 0.017528 *  
factor(block)31  0.4838255  0.0618191   7.826 6.32e-15 ***
factor(block)32  0.7691278  0.0618191  12.442  < 2e-16 ***
factor(block)33 -0.4054033  0.0618191  -6.558 6.13e-11 ***
factor(block)34 -0.2695021  0.0618191  -4.360 1.33e-05 ***
factor(block)35 -0.3482214  0.0618191  -5.633 1.89e-08 ***
factor(block)36 -0.4048784  0.0618191  -6.549 6.48e-11 ***
factor(block)37 -0.1490995  0.0618191  -2.412 0.015914 *  
factor(block)38  0.0147999  0.0618191   0.239 0.810802    
factor(block)39  0.4028761  0.0618191   6.517 8.03e-11 ***
factor(block)40  0.6024267  0.0618191   9.745  < 2e-16 ***
factor(block)41 -0.1635685  0.0618191  -2.646 0.008178 ** 
factor(block)42 -0.1188741  0.0618191  -1.923 0.054557 .  
factor(block)43 -0.1313807  0.0618191  -2.125 0.033625 *  
factor(block)44 -0.1901258  0.0618191  -3.076 0.002115 ** 
factor(block)45 -0.1154434  0.0618191  -1.867 0.061911 .  
factor(block)46 -0.0167989  0.0618191  -0.272 0.785833    
factor(block)47  0.5785432  0.0618191   9.359  < 2e-16 ***
factor(block)48  0.7047983  0.0618191  11.401  < 2e-16 ***
factor(block)49  0.1376708  0.0618191   2.227 0.026001 *  
factor(block)50  0.1014679  0.0618191   1.641 0.100797    
factor(block)51 -0.0692517  0.0618191  -1.120 0.262680    
factor(block)52  0.0362919  0.0618191   0.587 0.557192    
factor(block)53  0.0353528  0.0618191   0.572 0.567437    
factor(block)54  0.0971955  0.0618191   1.572 0.115967    
factor(block)55  0.5620149  0.0618191   9.091  < 2e-16 ***
factor(block)56  0.5884679  0.0618191   9.519  < 2e-16 ***
factor(block)57 -0.0008855  0.0460773  -0.019 0.984668    
factor(block)58 -0.0136021  0.0460773  -0.295 0.767854    
factor(block)59 -0.0955905  0.0460773  -2.075 0.038088 *  
factor(block)60 -0.1961225  0.0460773  -4.256 2.12e-05 ***
factor(block)61 -0.1929842  0.0460773  -4.188 2.87e-05 ***
factor(block)62 -0.1146842  0.0460773  -2.489 0.012851 *  
factor(block)63  0.1908167  0.0460773   4.141 3.52e-05 ***
factor(block)64  0.3764879  0.0460773   8.171 4.02e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.4788 on 4160 degrees of freedom
Multiple R-squared:  0.4655,	Adjusted R-squared:  0.4573 
F-statistic:  56.6 on 64 and 4160 DF,  p-value: < 2.2e-16

> 
> 
> # CHECK  DATA NORMALISED BY OLIN FOR SPATIAL BIAS
> data(sw.olin)
> print(anovaspatial(sw.olin,index=1,xN=8,yN=8,visu=TRUE)) 

Call:
lm(formula = as.vector(M) ~ factor(block) - 1)

Residuals:
    Min      1Q  Median      3Q     Max 
-3.2153 -0.1665  0.0138  0.1789  2.4621 

Coefficients:
                  Estimate Std. Error t value Pr(>|t|)
factor(block)1  -0.0033065  0.0498601  -0.066    0.947
factor(block)2  -0.0215496  0.0498601  -0.432    0.666
factor(block)3   0.0033983  0.0498601   0.068    0.946
factor(block)4  -0.0007232  0.0498601  -0.015    0.988
factor(block)5   0.0013500  0.0498601   0.027    0.978
factor(block)6   0.0300595  0.0498601   0.603    0.547
factor(block)7  -0.0419285  0.0498601  -0.841    0.400
factor(block)8   0.0106547  0.0498601   0.214    0.831
factor(block)9   0.0086288  0.0498601   0.173    0.863
factor(block)10  0.0263100  0.0498601   0.528    0.598
factor(block)11  0.0069643  0.0498601   0.140    0.889
factor(block)12  0.0265694  0.0498601   0.533    0.594
factor(block)13  0.0348534  0.0498601   0.699    0.485
factor(block)14 -0.0005567  0.0498601  -0.011    0.991
factor(block)15  0.0447804  0.0498601   0.898    0.369
factor(block)16  0.0134916  0.0498601   0.271    0.787
factor(block)17 -0.0446339  0.0498601  -0.895    0.371
factor(block)18 -0.0082794  0.0498601  -0.166    0.868
factor(block)19  0.0569828  0.0498601   1.143    0.253
factor(block)20 -0.0227180  0.0498601  -0.456    0.649
factor(block)21 -0.0106875  0.0498601  -0.214    0.830
factor(block)22 -0.0336463  0.0498601  -0.675    0.500
factor(block)23 -0.0692836  0.0498601  -1.390    0.165
factor(block)24  0.0462709  0.0498601   0.928    0.353
factor(block)25 -0.0375197  0.0498601  -0.752    0.452
factor(block)26  0.0059531  0.0498601   0.119    0.905
factor(block)27 -0.0272394  0.0498601  -0.546    0.585
factor(block)28 -0.0377998  0.0498601  -0.758    0.448
factor(block)29  0.0314399  0.0498601   0.631    0.528
factor(block)30  0.0774899  0.0498601   1.554    0.120
factor(block)31 -0.0224376  0.0498601  -0.450    0.653
factor(block)32 -0.0062391  0.0498601  -0.125    0.900
factor(block)33  0.0293269  0.0498601   0.588    0.556
factor(block)34  0.0473647  0.0498601   0.950    0.342
factor(block)35 -0.0016106  0.0498601  -0.032    0.974
factor(block)36 -0.0480839  0.0498601  -0.964    0.335
factor(block)37 -0.0118535  0.0498601  -0.238    0.812
factor(block)38 -0.0078246  0.0498601  -0.157    0.875
factor(block)39 -0.0686859  0.0498601  -1.378    0.168
factor(block)40 -0.0223675  0.0498601  -0.449    0.654
factor(block)41 -0.0206801  0.0498601  -0.415    0.678
factor(block)42 -0.0319311  0.0498601  -0.640    0.522
factor(block)43  0.0286646  0.0498601   0.575    0.565
factor(block)44 -0.0060567  0.0498601  -0.121    0.903
factor(block)45  0.0032303  0.0498601   0.065    0.948
factor(block)46  0.0006503  0.0498601   0.013    0.990
factor(block)47  0.0563123  0.0498601   1.129    0.259
factor(block)48  0.0095686  0.0498601   0.192    0.848
factor(block)49  0.0410204  0.0498601   0.823    0.411
factor(block)50  0.0238266  0.0498601   0.478    0.633
factor(block)51 -0.0702298  0.0498601  -1.409    0.159
factor(block)52  0.0754324  0.0498601   1.513    0.130
factor(block)53  0.0070427  0.0498601   0.141    0.888
factor(block)54  0.0155062  0.0498601   0.311    0.756
factor(block)55  0.0218938  0.0498601   0.439    0.661
factor(block)56 -0.0651155  0.0498601  -1.306    0.192
factor(block)57 -0.0237302  0.0371635  -0.639    0.523
factor(block)58  0.0208438  0.0371635   0.561    0.575
factor(block)59  0.0036944  0.0371635   0.099    0.921
factor(block)60 -0.0056216  0.0371635  -0.151    0.880
factor(block)61 -0.0084312  0.0371635  -0.227    0.821
factor(block)62  0.0011146  0.0371635   0.030    0.976
factor(block)63  0.0005883  0.0371635   0.016    0.987
factor(block)64 -0.0099045  0.0371635  -0.267    0.790

Residual standard error: 0.3862 on 4160 degrees of freedom
Multiple R-squared:  0.006707,	Adjusted R-squared:  -0.008574 
F-statistic: 0.4389 on 64 and 4160 DF,  p-value: 1

> # note the different scale of the colour bar
> 
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>