After stinging its victim, the honeybee leaves behind the barbed stinger, poison sac, and muscles that continue to pump venom into the wound.

Visscher et al. (1996) compared the effects of two methods of removing the stinger left behind: scraping off with a credit card or pinching off with thumb and index finger. A total of 40 stings were induced on volunteers.

Twenty were removed with the credit card method, and 20 were removed with the pinching method. The size of the subsequent welt by each sting was measured after 10 minutes. All 40 measurements came from two volunteers (both authors of the study), each of whom received one treatment 10 times on one arm and the other treatment 10 times on the other arm. Pinching led to a slightly smaller average welt, but the difference between methods was not significant.

a. All 40 measurements were combined to estimate means, standard errors, and the P-value for a two-sample t-test of the difference between treatment means. What is wrong with this approach?

b. How should the data be analyzed? Describe how the quantities would be calculated and what type of statistical test would be used.

c. Suggest two improvements to the experimental design.