What statistical analysis should/could I use in this scenario?

[DntInferno]

Hello!

I am currently doing my Extended Essay for Biology and I am not sure what stat test to use for my results. I am comparing audio frequency with the rate of antennal activity of the pill bug. I have found that from 0 Hz, the antennal movement also increases up to 400 Hz where it peaks and thereafter, as the frequency goes higher, the antennal movement would decrease. I have 6 samples (controlled aka 0Hz, 400Hz, 1500Hz, 3000Hz, 4000Hz, 5000Hz) and I have tried the Spearman's rank correlation so far but it gave me a -0.14 correlation since it was not linear. I also tried the student t test, but from what i know, it does not seem to be valid in this experiment. Does the two sample means have to be within the same units of measurement to actually be compared in a T-test? Or can I compare frequency (hz) and # of antennal twitches with the t-test?

I am looking into quadratic regression stats at the moment, but I am quite confused as to what regression is and whether or not it is the same as "correlation"? The format appears similar to the spearman's test, but is it the same?

Thank you!

 

[Stephen Tashi]

Statistics is nominally a branch of mathematics and it has the limitations of mathematics. One limitation of mathematics is that you can't get an answer to a mathematical problem unless you define what your are solving for. Another limitation is that you can't solve problems unless there are enough "givens".

In attempting to apply statistics to real world problems, many people dont' bother to define what they are trying to accomplish. Many also refuse to make enough assumptions about the situation to turn it into a solvable mathematical problem. They hope somehow that "statistics" will do these jobs for them. (Granted, if you pick a certain statistical procedure, this will imply you have made certain assumptions, but it keeps that fact hidden from the public. For example, the Spearman test assumes the two variables both increase or decrease with each other, which your own belief about a peak in the data contradicts.)

You should first define what you are trying to do. It's OK to define this mundanely - for example "I'm trying to impress Dr. Glurdly" or "I"m trying to convince the foundation to give me additional funds for research". You can work from that goal toward more mathematical ones.

The two major divisions of traditional statistics are hypothesis testing and estimation. A hypothesis testing approach to your problem is to test an idea such as "The frequencies have no effect on antenna activity". Based on that assumption, you compute the probability of observing data similar (in some sense) to what you observed. If the probability is small you "reject" the hypothesis. In estimation, you have a family of equations or distributions that model the data. The task is to estimate the parameters that define the particular members of this family that fit the data. One way to begin thinking about your situation is to decide if either of these goals applies to what you want to do.