How does the omnidirectional external antenna orientation affect the range test?

If i am using an omnidirectional external antenna in my zigbee module, How much will its orientation effect the range test.

Zigbee test example

I mean suppose i have placed one device in the basement, and theantenna orientation in it is not vertical, then i am getting max range upto 3rd floor.

If i make it vertical how much effect it will give on range

For best coupling between antennas they should have the same polarization in the same field.

vertical orientation will have not as much range as the horizontal orientation will gave u but if u place ur antenna in vertical position the it will gave u best result

The earlier comment about matched polarization is correct. Going a little further best performance also requires each device to be in the area where the gain is maximum.

You describe the situation wherre one device is on one floor and the other is on another floor. You probably have monopole antennas which have nulls in the patterns along the line of the monopole (think of the pattern as like a torus). No power is radiated along the antenna regardless of the polarization. One box directly over another probably wont work unless you get lucky with a multipath bounce. You can sometimes increase the signal received by compromising on polarization and increasing the gain. Isn't this fun.

Propagation inside a building with walls, reflections, etc. can really get convoluted. The best answer is to just experiment and if one location does not work try moving a few feet and the signal may get stronger.