Thank you for your reply.
Indeed, there is a exponential function that fit the X~Y data. That function has two parameters A and B. I can used student-t test to calculate the P-values for A and B. However, I hope to avoid analysis on parameters A and B.
From the error plot, it is obvious that the control group has higher Cauchy stress level than the pregnant group. I am just wondering whether there is a method to quantify this overall difference. Thanks.