Question

12. There was an outbreak of gastroenteritis among attendees of corporate picnics in Pennsylvania. The incidence rate of gastroenteritis at Pienie I was 15% and the incidence rate of gastroenteritis at Pienic 2 was 27%. At first glance, it seems that Picnie 2 had higher incidence of gastroenteritis, however researchers wanted to dig a little bit deeper for the cause. Specifically, they wanted to determine if there was evidence of Simpson's Paradox. They examined incidence of gastroenteritis based on who ate potato salad at the picnie and collected the data below. Ate Potato Salad Did Not Eat Potato Salad Picnic Picnic 2 Picnic 1 Picnic 2 Gastroenteritis 52 12 Gastroenteritis 15 63 18 21 No Gastroenteritis No Gastroenteritis 65 104 8173 Total Total 77 119 a. What is the definition of Simpson's Paradox? (2 points) b. Does the data provide evidence of Simpson's Paradox? Why or why not? points)

Answer 1

a) Simpson's paradox occurs when groups of data show one particular trend, but this trend is reversed when the groups are combined together.

b) The incidence rate of gastroenteritis for picnic 1 and picnic 2 overall are 15% and 27% but when calculated separately we get the following results ,which shows that gastroenteritis was more for picnic1. This is evidence of Simpson's Paradox.

12] b] yes, the data pronides enidence Simpron's Paradox. Ate Potato salad Picnic 1: Proportion Gastroenteritis 0.77 %3D %3D G astroenteritis Picnic 2: Proportio n 52 0.71 73 71/. Did not zat Potuto saulad Gastroenteri tis Picnic 1: Proportion 0.15 77 Picnic a: Gashontrst's Proportion = IS 119 - 0:12 : 12/ 12:/ Jotal : 77/ + 15/- 92/- Picric 1 = 71/ +12%. Pichic 2 = 83%%