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圆形分布资料采用圆形分布方法分析,其变量均值采用角均值(度)表示。由于在求角均值 a 时需求反三角函数,而直接求得的反三角函数的值域并不在整个360度范围内,还需根据 X 和 Y,或 sinα和 cosα值的符号确定角口所在象限后才能在360度范围内求得角均值α。这一具体过程在许多统计学著作中没有具体给出,因而容易出错。洪楠曾对这一问题作了探讨,指出一些文献中在确定角α时的错误,并提出相应确定角α的计算公式,如式(1):
The circular distribution data is analyzed using a circular distribution method, and the average value of the variables is represented by the angular mean (degrees). Since the inverse trigonometric function is required when calculating the mean a, and the range of the directly obtained inverse trigonometric function is not within the entire 360 degree range, it is necessary to determine the quadrant of the corner based on the signs of X and Y, or the sin α and cos α values. After that, the angular mean value α can be obtained within 360 degrees. This specific process is not specifically given in many statistical works and is therefore prone to errors. Hong Nan once discussed this issue and pointed out some errors in determining the angle α in some documents, and proposed a formula for determining the corresponding angle α, as in equation (1):