The different shapes of the LO that we cosidered here were:

Case 1: the unrotated figure

Case 2: the figure rotated through Theta1 degree

Case 3: the figure rotated through Theta2 degree

In the tests run, the RO was a square of fixed size, and its position was also kept invariant.
The size of each LO was taken to be the same.

We also performed the test for two different LO shapes: rectangle and right triangle.

Thus in a particular suite of tests corresponding to a single LO shape( rectangle or right triangle), the only independent variable was the orientation of the LO.
The dependent variable was the position of the sweet spot.

To see the conclusion for this section press here.

On performing ANOVA for the Y-Coordinate of the centre of the LO, we obtained the following results :

The above data shows that the Y-Coordinate of the center of the LO is placed at about 350, which is the coordinate of the center of the RO.

Also, the F-ratio value is less than the maximum specified limit, thus validating our NULL HYPOTHESIS that the location of the Y-Coordinate of the center of the LO does not depend on the orientation of the LO.

On performing ANOVA for the X-Coordinate of the center of the LO, we obtained the following results :

The X-Coordinate values are clustered about 343.
Also, the F-ratio value is very low, indicating a very high degree of acceptance of the NULL HYPOTHESIS that the position of the X-Coordinate of the center of the LO does not depend on the orientation of the LO.

From the above analysis, it can be concluded that in case of rectangular shape of the LO, the position of the LO w.r.t. the RO is independent of the orientation of the LO.

On performing ANOVA for the Y-Coordinate of the centre of the LO, we obtained the following results :

The value we were expecting for the location of the Y-Coordinate of the LO was 350, the X-Coordinate of the center of the RO. The values obtained above, though not exactly matching the expected value, are in the required range.
Also, the F-ratio value is within acceptable limits. So, we can assume validation of our NULL HYPOTHESIS that the Y-Coordinate of the center of the LO is independent of the orientation of the LO.

Here, a point to be noted is that when the center of the LO is calculated as its centroid, then the aforementioned data is obtained. Though this data does match the expected value, it is not as good a match as one would desire. However, if we conjecture that the subject places the triangle LO in such a way as to make its Y-center, as defined as the mean of the maximum and the minimum Y-values, in line with the center of the RO then results much closer to the expected value are obtained.
This, in fact, is a problem which should be studied further: Whether a human subject defines the center of a figure as the location of its centroid or as the tuple( (Xmin + Xmax)/2, (Ymin + Ymax)/2 ).

On performing ANOVA for the X-Coordinate of the center of the LO, we obtained the following results :

The above data shows no discernible pattern.
Though the value of the F-ratio obtained on analysis is less than the maximum allowed limit, the individual means do not seem to be clustering about any point. From this data, thus we do not get the confirmation of the NULL HYPOTHESIS.

From the analysis done above, we can conclude that the location of the center of the LO is independent of the orientatin of the LO in case of a rectangular LO. In case of a triangular LO, however, we do not get this clean lack of dependence. This is a point which is not in keeping with our NULL HYPOTHESIS and needs to be studied further.