Does the cross tabulation show a valid explanation? If it is logical to believe that changes in the independent variable(s) can cause changes in the dependent variable, then the explanation revealed by the cross tabulation is thought to be valid one. For example, the relationship revealed indicates that as students move from a state of unawareness and become aware of and obtain accurate knowledge of the Pizza truck, they are likely to give up being undecided and to develop a favorable attitude towards the service. Since it seems to be logical that awareness and knowledge could have an effect on attitudes, the explanation would be considered valid.
Does the cross tabulation show a spurious relationship? An explanation is thought to be a spurious one if the implied relationship between the dependent and independent variables does not seem to be logical. For example, family size and income appear to be “logically” related to household consumption of certain basic food products. However, it may not be logical to relate the number of automobiles owned with the brand of toothpaste preferred, or to relate the type of family pet with the occupation of the head of the family. If the independent variable does not logically have an effect or influence on the dependent variable, the relationship that a cross tabulation seems to show may not be valid cause and effect relationship, and therefore may be a spurious relationship.
Example: One of the cross tabulations that researchers constructed in the pizza study showed pizza truck patronage broken down by whether or not the student had an automobile on campus. Researchers created this cross tabulation because they thought it might indicate that students with automobiles would be more likely to drive to pizza restaurants than patronize the pizza truck.
The results of this cross tabulation showed that pizza truck patronage was greater among those having an automobile than among those not having an automobile. Assuming these differences to be significant, this appears to be a spurious relationship since it does not seem logical to explain that greater patronization is due to having an automobile on campus.
Pizza Truck Patronization by Automobile on campus
Patronize the truck Doesn’t have an automobile (%) Has an Automobile(%)
Yes 29 51
No 71 49
With a finding such as that shown above, researchers might investigate if a third variable (e.g. income) is in some way operating to affect both pizza truck patronage and having an automobile on campus. If the researchers cannot find variable that logically explains why having an automobile on campus influences greater patronization of the pizza truck, the researchers are likely to conclude that table above shows a spurious relationship.
How many independent variables should be used?
When cross tabulating an independent variable that seems logically related to the dependent variable, what should researchers do if the results do not reveal a clear cut relationship? Two possible courses of action are available.
1. Try another cross tabulation, but this time using one of the other independent variables hypothesized to be important when the study was designed.
2. A preferred course of action is to introduce each additional independent variable simultaneously with, rather than as an alternative to, the first independent variable tried in the cross tabulation. By doing so, it is possible to study the interrelationships between the dependent variable and two or more independent variables.
Is there a practical limit to the number of independent variables that can be used? As researchers include additional independent variables in a cross tabulation, they are creating more and more unique cells of data. For example, with only one independent variable (has / doesn’t have an automobile on campus) to explain truck patronization, there are four cells of data (see above). With two independent variables, there are eight cells. If 400 students were interviewed in the pizza truck study, some of the cells might contain as few as 20-25 respondents. These numbers are fairly small, and not be practical to reduce them further by the addition of a third or a fourth independent variable to the cross tabulation. For this reason, most cross tabulations involve no more than two or three independent variables.