4. The limitations of the chi square tests

Does advertising influence children as young as three years old?

Researchers at Stanford University conducted a taste test with preschoolers. Each preschooler tasted two identical samples of five food items (hamburger, french fries, chicken nuggets, baby carrots, and milk). For each item, the children tasted one sample wrapped in a McDonald's wrapper and the other sample in an identical, but unbranded, wrapper. Some children tasted the sample in the branded wrapper first, while others tasted the sample in the unbranded wrapper first. Consistently for all food items, the majority of preschoolers preferred the food in the McDonald's wrapper over the one in the unbranded wrapper, even though both samples were identical. [Source:T. N. Robinson, et al. 2007. "Effects of Fast Food Branding on Young Children's Taste Preferences." Archives of Pediatrics and Adolescent Medicine 161: 792-97.]

The researchers found that the preschoolers who watched more television or ate more often at McDonald's were more likely to prefer the food wrapped in a McDonald's wrapper. However, is it possible that the children were attracted to the branded wrapper because it had more writing and colors on it, rather than because they recognized the McDonald's logo? They were also curious about whether children would behave differently with the McDonald's signature foods, such as hamburgers, french fries, and chicken nuggets, than they would with foods with less name brand significance, such as baby carrots.

You decide to conduct a similar experiment with 60 toddlers. The results are as follows:

Observed Frequencies for Package Preference by Food Type

	Food
Packaging	Hamburger	French Fries	Chicken Nuggets	Baby Carrots	Totals
McDonald's wrapper	15	15	11	3	44
Unbranded wrapper	5	4	2	5	16
Totals	20	19	13	8	60

Chi square analysis does have limitations. What is the potential violation of these limitations with this particular chi square distribution?

There is at least one cell with expected frequency (fe) of 5 or fewer.

There is at least one cell with an observed frequency (fo) of 5 or fewer.

Chi square test are not reliable unless there is a total sample size of at least 100.

There is no problem with this chi square distribution.

Would combining just the categories with small frequencies help? If so, why? If not, why not?

No, there is no need to combine the cells, as there is no problem with cell size.

Yes, combining the small categories with small frequencies would resolve the issues with the chi square distribution.

No, combining the categories with small frequencies would erase meaningful distinctions.

You want to figure out what it is about the wrapper that the children are recognizing, so you are thinking of adding the chocolate shakewhich is highly recognizableand using several forms of packaging: completely plain packaging, completely branded packaging, packaging with the McDonald's colors, packaging with the McDonald's logo but not the McDonald's colors, and packaging from another fast food chain that does not advertise on television.

What could be a problem with the chi square analysis for this design?

There is no difficulty because the children will be getting an opportunity to drink chocolate shakes.

The categories are not distinct enough.

Chi square tests become difficult to interpret when the variables have many categories.

There is no difficulty with a chi square analysis for this design.