tailieunhanh - Sensing Intelligence Motion - How Robots & Humans Move - Vladimir J. Lumelsky Part 14

Tham khảo tài liệu 'sensing intelligence motion - how robots & humans move - vladimir j. lumelsky part 14', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 366 HUMAN PERFORMANCE IN MOTION PLANNING Xi -Jffj Xj. average for the row i of A over related subjects scores Xj IJN Xj. average for the column j of B over related subjects scores X J fi Xi. I 2j . overall mean of all the scores. With this notation if we only test for the main effect of factor B similarly for the main effect of factor A the null and alternative hypotheses can be written as H0 B ụj ụ for all j H1 B ụj ụ for at least one j The Main Sum Between MSB for J cells of factor B is the average of estimated variance of estimated column means this ignoring factor A . That is MSB J-1 - X 2 The Main Sum Within is the same error variance MSw considered above it is equal to the average of separately estimated variances within the individual cells. Under the null hypothesis MSB msW F J 1 N-IJ That is the ratio of two main averages has an F distribution with J 1 degrees of freedom in the numerator and N IJ degrees of freedom in the denominator which is the total number of observations N minus the total number of cells IJ. Interaction Between Factors. Unfortunately the main effects are not sufficient to answer questions such as Does the effect of factor A remain the same at different levels of factor B For example in some observations of Experiment One the main effect of the visibility factor is that it significantly affects the subjects path length The invisible task results in longer path lengths compared to the visible task. However we notice that the subjects scores on the visibility factor are also affected by the interface factor Namely in the physical test in the booth the visibility factor has no significant effect on the path length whereas in the virtual test the visibility factor has a significant effect on the path length. This suggests that the tests on main effects may be missing such interaction effects. The latter can be tested by the following formulas of interaction for details refer to Refs. 126 and 127 SSAB n Xij. Xi. . X. 2 .