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Quarterly Financial Data (Unaudited) (Details) - USD ($)
$ / shares in Units, $ in Thousands
 1 Months Ended 3 Months Ended 12 Months Ended
Nov. 30, 2017
Dec. 29, 2018
Sep. 29, 2018
Jun. 30, 2018
Mar. 31, 2018
Dec. 30, 2017
Sep. 30, 2017
Jul. 01, 2017
Apr. 01, 2017
Dec. 29, 2018
Dec. 30, 2017
Dec. 31, 2016
Quarterly Financial Data (Unaudited)                        
Revenues   $ 108,763 $ 103,871 $ 105,538 $ 99,476 $ 97,016 $ 91,325 $ 93,563 $ 88,171 $ 417,648 $ 370,075 $ 324,779
Income (loss) from operations   7,845 5,225 9,661 6,204 (642) 5,647 5,848 4,911 28,935 15,764 18,919
Income (loss) before provision for income taxes   8,331 4,939 9,737 5,926 (898) 5,535 5,919 4,608 28,933 15,164 21,889
Net income (loss)   6,839 3,908 6,839 4,886 (2,261) 3,225 3,907 2,830 22,472 7,701 14,233
Net (income) loss attributable to noncontrolling interest, net of tax   20       5 (11) (94) 23 20 (77) (1,345)
Net income attributable to CRA as reported   $ 6,859 $ 3,908 $ 6,839 $ 4,886 $ (2,256) $ 3,214 $ 3,813 $ 2,853 $ 22,492 $ 7,624 $ 12,888
Basic net income (loss) per share (in dollars per share)   $ 0.85 $ 0.48 $ 0.84 $ 0.59 $ (0.27) $ 0.39 $ 0.45 $ 0.34 $ 2.76 $ 0.91 $ 1.50
Diluted net income (loss) per share (in dollars per share)   $ 0.81 $ 0.46 $ 0.79 $ 0.57 $ (0.28) $ 0.38 $ 0.44 $ 0.33 $ 2.61 $ 0.89 $ 1.49
Claims under the Transaction agreement with IQVIA Inc settled $ 5,700