Page 319 - Statistics for Dummies

Chapter 19: Two-Way Tables and Independence
✓ All campers who camp with pets and support a pet section.
✓ All campers who camp with pets and oppose a pet section.
✓ All campers who don’t camp with pets and support a pet section.
✓ All campers who don’t camp with pets and oppose a pet section.

The key phrase in all of the proportions mentioned in the preceding list is
all campers. You are taking the entire group of all campers in the survey and
breaking them into four separate groups. When you see the word all, think
joint distribution. Table 19-6 shows the joint distribution for all campers in the
pet camping survey.
Table 19-6
Support Separate
Oppose Separate
Pet Section
Pet Section
Camp with Pets Joint Distribution for the Pet Camping Survey Data 303
20 ÷ 100 = 0.20
10 ÷ 100 = 0.10
Don’t Camp with Pets 55 ÷ 100 = 0.55 15 ÷ 100 = 0.15
To find a joint distribution for a two-way table, you take the cell count (the
number of individuals in a cell) divided by the grand total, for each cell in
the table. The total of all these proportions should be 1 (subject to rounding
error).
To get the numbers in the cells of Table 19-6, take the cells of Table 19-3 and
divide by their corresponding grand total (100, in this case). Using the results
listed in Table 19-6, you report the following:
✓ 20% of all campers surveyed camp with pets and support a pet section.
(See the upper left-hand cell of the table.)
✓ 10% of all campers surveyed camp with pets and oppose a pet section.
(See the upper right-hand cell of the table.)
✓ 55% of all campers surveyed don’t camp with pets and do support the
pet section policy. (See the lower left-hand cell of the table.)
✓ 15% of all campers surveyed don’t camp with pets and oppose the pet
section policy. (See the lower right-hand cell of the table.)
Adding all the proportions shown in Table 19-6, you get 0.20 + 0.10 + 0.55 + 0.15 =
1.00. Every camper shows up in one and only one of the cells of the table.

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