Now from a technical and strict academic point of view.

Beware of your tests, tests must be done in a correct way if not you get flaved results and the most weak point is your source image used for the tests.

The source image that you use as starting point must be an image that never had been compressed in jpeg format. If the image was once compressed with jpeg, the first compression has removed almost all the information to be analysed. Further compression will remove very little and can led you to the wrong conclussion that nothing was lost.

You can be doing wrong the tests, you download some image in png format, then use this image for the tests, compress in jpeg, compare the two images and reach the conclussion that is all the same, but you can be wrong because the image that you used in the tests once was compressed in jpeg, who knows how much it was compressed and then some other person took this image and uploaded it in png format.

You must use vigin images for the tests, images that never has been saved in jpeg.

From where can you get these images? The better source is a good digital camera with images saved in a loseless format. Scanned images of photographs are not very good, unless you have a very expensive professional scanner the scanner performs some compression and interpolation.

Another good source can be quality CD collections or even downloaded where you believe that the original quality of the image was preserved in all its past history. The images are big in size and in file size.

Another good source are images generated by software as gradients and patters. It are good for testing artifacts, but not for quality tests.

Rendered images are not good for tests, it doesn't matter if you saved as psd or png. Rendered images have little high frequency components, so much less is lost in a further jpeg compression. A photo has much more high frecuency componets and so much more is lost if you later compress in jpeg.

For an theorical and academic test:

1- Take some image in png format and save it in png format.

2- Take again the png image and save it in bmp format (must be bmp!)

3- Take the saved jpeg image and saved it also in bmp format.

4- Use some software to compare both bmp files.

5- Count the number of bytes that are different in these two files

6- Divide the different bytes by the file size and multiply by 100

7- Now you have in percent how much different are the png and jpeg.

8- If you get small or very big numbers, what does it mean?

9- Well, it is subjective and don't be rude with the answer....

Stupidity also evolves!