I assume that you've already learned a bit about how soaps work in your chemistry class, so you know that the interesting properties of a soap are due to the combination of a hydrophobic tail which binds to grease and a hydrophilic head which interacts with water. Unfortunately, I'm not sure how chemists actually rate the "power" or effectiveness of a given soap, but I think that this would be the best type of data to gather. You should probably try and do a bit of research into the chemistry and soap industry, but here's what I would do:

Soaps work by forming an emulsion of grease and/or dirt in water. However, for a giving amount of soap, only so much grease can be carried in the emulsion before it separates back out as grease and water. Try taking a very clean glass and add a fixed amount of water, soap, and a small amount of oil. Mix. Repeat this with different amounts of oil to determine the maximum carrying capacity of the emulsion. Remember, the glassware should be spotlessly clean and the volume and temperature of the water should be the same for all experiments. Also, the method of mixing probably will affect the emulsion, so you may want to use a standard method, i.e. a (clean) hand blender on medium speed for 5 sec, or something like that. Finally, soap is a product that everyone uses (hopefully) everyday in the shower, doing laundry, washing the dishes, etc. In addition to exploring the science of soaps and comparing the effectiveness of 2 gms of soap X versus 2 gms of soap Y, it would be very interesting to compare soaps on a cost versus effectiveness basis. I.e. if you need to twice as much of one soap for a given amount of grease, but it costs three times less, than it may be the better soap for practical use.

I hope this helps, and have fun.

Here are some suggestions:

1. See what quantity of soap, for a given volume of water, and for a given number of test-tube shakes is required to make a measured head of foam. For example, if you add 0.5 g of soap to 30 ml of water and shake 10 times, how many cm of foam do you get on the top.

2. A slightly more involved experiment is to see how much soap is required to mix oil and water. Take 1 ml of cooking oil and 20 ml of water, and shake. It will not mix. Now start adding small amounts of soap, and see how much is required so that the oil and water mix. Do this for the different soaps. Good luck !

The most important quantitative measure in a chemical reaction where you are making something out of something else is in general terms the yield. The yield of a reaction (in your case the reaction is named saponification. )

Saponification is the relation between the mass or the amount of substance in the products divided by the mass or amount of substance in the reactants.

So, to start gathering quantitative data, think of how you can measure the amount of soap that is formed from whatever amount of fat and base you start with. There are other test specific for the analysis of soap but I am on a trip right now (this answer is being typed from Berlin, Germany, and do not have access to any source where I could check them out), Good luck!