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Let's say I want to quantify the preference that people have towards shoe color as a function of their age. For simplicity, assume there are only black, gray, and brown shoes.

First I ask 1,000 random people their age and the color of the shoes they are wearing.

Next I recruit 100 (different) random people and every year (for 10 years) I ask them to tell me the color of the shoes they are wearing.

In both cases I get 1,000 data points; e.g., (34 yrs old, black shoes), (66 yrs old, gray shoes), etc. It seems naive to combine all the data points from both cases, and compute the percentages of shoe colors for each age (e.g., 36% of 34 yrs old wear black shoes).

The preferences of the 100 people in the second case seem to carry more weight because each of them contribute 10 data points to my calculations.

What is the correct way to compute the shoe color preferences for each age using both data sets?

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  • $\begingroup$ Using both at the same time? Or what would you do in each of the 2 situations? $\endgroup$ Feb 2, 2016 at 22:36
  • $\begingroup$ Yes, using both at the same time. Sorry for being unclear. $\endgroup$ Feb 4, 2016 at 0:17

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