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Influence of n°total of Pixel on Reprojection Error

Hi i'm using openCv and cameraCalibration to work about my thesis. I use a Canon EOS400, the size of image is 3888x2592 ( full resolution)but i have an asymmetric circles grid printed on paper so it isn't very accurate ( i use tha maximum zoom for my aim) and OpenCv doesn't ricognize the circles so it doesn't work. For this reason i have to reduce the size of image with Photoshop to obtained photo which size is 972x648(4 times smaller). Does this reduction influence Reprojection Error? It will be 4 times smaller? Is there a paper, a document, something which prove this? Finally can i express Repr.Error dividing the value with N°total of pixel to compare the results of different size of images?