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

Case 1: a circle

Case 2: a rectangle

Case 3: a square

Case 4: a right-triangle

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

We also performed the test for two different prepositions: front and right.

Thus in a particular suite of tests corresponding to a single preposition ( front or right), the only independent variable was the shape 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 :

Clustering of the Y-Coordinate positions of the centre of the LO is about 410.

From this table, the value of the F-ratio can be seen to be 0.1590, which is much less than the maximum acceptable value of F as calculated from statistical tables.
Also, the means of the Y-Coordinate positions of the center of the LO are remarkably similar for the four different shapes of the LO.

Thus our NULL HYPOTHESIS that the Y-coordinate of the centre of the LO is independent of the shape of the LO is validated.

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

The data from the above examples seems to show no discernible pattern.
Our hypothesis that the X-Coordinate of the centre of the LO should be independent of the shape of the LO is not confirmed by these results.

However if we consider the data obtained by considering only the first 3 LO shapes i.e. if we leave out the triangle, then we get the following table:

From this table, we can observe that the X-Coordinate position of the centre of the LO is almost exactly the same for all the 3 shapes cosidered, and the F value is also very low, pointing to a validation of our NULL HYPOTHESIS.

Based on this observation, we have concluded that the final positioning of the LO is indeed independent of the shape of the LO.
However, this final position does depend on the initial position of the LO .

This is because in the case of the first three cases, the LO was initially in the lower right corner of the screen and then the subject was asked to place it according to the
specified instruction.
In case of the triangle, the initial position was in the bottom left corner of the screen, and this, we believe, resulted in the triangle being placed more to the left than the other 3 LOs.

On the whole, the results obtained point to independece of the positioning of the LO w.r.t. the shape of the LO.

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

Clustering of the Y-Coordinate positions of the centre of the LO is about 350, which is the Y-Coordinate of the center of the RO.

From this table, the value of the F-ratio can be seen to be 0.8004, which is much less than the maximum acceptable value of F as calculated from statistical tables.
Also, the means of the Y-Coordinate positions of the center of the LO are remarkably similar for the four different shapes of the LO.

Thus our NULL HYPOTHESIS that the Y-coordinate of the centre of the LO is independent of the shape of the LO is validated.

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

The data from the above examples seems to show no discernible pattern.
Our hypothesis that the X-Coordinate of the centre of the LO should be independent of the shape of the LO is not confirmed by these results.

However if we consider the data obtained by considering only the first 3 LO shapes i.e. if we leave out the triangle, then we get the following table:

From this table, we can observe that the X-Coordinate position of the centre of the LO is almost exactly the same for all the 3 shapes cosidered, and the F value is also very low, pointing to a validation of our NULL HYPOTHESIS.

Based on this observation, we have concluded that the final positioning of the LO is indeed independent of the shape of the LO.
However, this final position does depend on the initial position of the LO .

This is because in the case of the first three cases, the LO was initially in the lower right corner of the screen and then the subject was asked to place it according to the
specified instruction.
In case of the triangle, the initial position was in the bottom left corner of the screen, and this, we believe, resulted in the triangle being placed more to the left than the other 3 LOs.

On the whole, the results obtained point to independence of the positioning of the LO w.r.t. the shape of the LO.

Thus in case of each of the prepositions considered above, from the data we have obtained and the analysis done on that data, we conclude that human subjects position the LO independent of its shape.