Experimentation - Appendix Latin Square Design
Experimentation - Appendix Latin Square Design
The Latin square design is a method to reduce the number of groups involved when interactions between the treatment levels and the control variables can be considered relatively unimportant. We will use a laboratory nutritional labeling experiment to describe and illustrate the Latin square design.
The goal of the experiment was to contribute to the judgment of those proposing and evaluating several public policy nutritional labeling alternatives. In particular, the research goal was to determine the impact upon shopper perceptions and preferences of variations in nutritional information on labels of canned peas. Four levels of information were tested. The first provided only a simple quality statement. The second listed some major nutrient components and whether the product was high or low on them. The third provided the amounts of each nutrient. The fourth listed all nutritional components and was the most complete.
There were two control or block variables, the store and the brand. Four brands of canned peas, each with associated prices, were used. Four locations, each adjacent to a supermarket, were used and 50 shoppers were interviewed in each. It was felt that interactions among the nutritional information treatments and the brands or stores would be insignificant, so the Latin square could be used. The design is shown in Figure 10-3. Note that treatment level I appears with each store once and only once, and with each brand once and only once. Thus, the results for treatment level I should not benefit from the fact that one of the brands is rated higher than the others or that shoppers from one of the stores are more sensitive to nutrition.
Each respondent was exposed to four cans of peas. For example, at store 1 respondents were exposed to Private Brand A at 21 cents with the
treatment III label information, to Private Brand B at 22 cents with treatment II, and so on. After being exposed to the four cans, the respondents were asked to evaluate each on six different nine-point scales. Thus, this experiment illustrates the use of multiple measures of the results. The mean score for each treatment level is shown in Table 10-4. Again, the issue as tc whether the results are "statistically significant" will be deferred until Chapter 14.
In a randomized block design, each cell would require four experimental groups, one for each treatment level. In the Latin square design each cell requires only one treatment level so that a minimum of 16 groups is required instead of 64. The Latin square normally would have a separate sample for each cell. In this study, the same 50 respondents from store 1 were used for all the cells in the first column. Each respondent reacted tc four brands. Thus, the store block served effectively to control for not only the store but many other characteristics of the sample. As a result the experiment was more sensitive. However, the experience of rating one brand may have had a carryover effect on the task of rating another, which could generate a bias of some kind.
The Latin square design allows one to control two variables without requiring an expanded sample. It does require the same number of rows, columns, and treatment levels, so it does impose constraints in that respect. Also, it cannot be used to determine interaction effects. Thus, if nutritional information should have a different effect on private-label brands than major brands, this design could not discern such differences.
The Latin square design is a method to reduce the number of groups involved when interactions between the treatment levels and the control variables can be considered relatively unimportant. We will use a laboratory nutritional labeling experiment to describe and illustrate the Latin square design.
The goal of the experiment was to contribute to the judgment of those proposing and evaluating several public policy nutritional labeling alternatives. In particular, the research goal was to determine the impact upon shopper perceptions and preferences of variations in nutritional information on labels of canned peas. Four levels of information were tested. The first provided only a simple quality statement. The second listed some major nutrient components and whether the product was high or low on them. The third provided the amounts of each nutrient. The fourth listed all nutritional components and was the most complete.
There were two control or block variables, the store and the brand. Four brands of canned peas, each with associated prices, were used. Four locations, each adjacent to a supermarket, were used and 50 shoppers were interviewed in each. It was felt that interactions among the nutritional information treatments and the brands or stores would be insignificant, so the Latin square could be used. The design is shown in Figure 10-3. Note that treatment level I appears with each store once and only once, and with each brand once and only once. Thus, the results for treatment level I should not benefit from the fact that one of the brands is rated higher than the others or that shoppers from one of the stores are more sensitive to nutrition.
Each respondent was exposed to four cans of peas. For example, at store 1 respondents were exposed to Private Brand A at 21 cents with the
treatment III label information, to Private Brand B at 22 cents with treatment II, and so on. After being exposed to the four cans, the respondents were asked to evaluate each on six different nine-point scales. Thus, this experiment illustrates the use of multiple measures of the results. The mean score for each treatment level is shown in Table 10-4. Again, the issue as tc whether the results are "statistically significant" will be deferred until Chapter 14.
In a randomized block design, each cell would require four experimental groups, one for each treatment level. In the Latin square design each cell requires only one treatment level so that a minimum of 16 groups is required instead of 64. The Latin square normally would have a separate sample for each cell. In this study, the same 50 respondents from store 1 were used for all the cells in the first column. Each respondent reacted tc four brands. Thus, the store block served effectively to control for not only the store but many other characteristics of the sample. As a result the experiment was more sensitive. However, the experience of rating one brand may have had a carryover effect on the task of rating another, which could generate a bias of some kind.
The Latin square design allows one to control two variables without requiring an expanded sample. It does require the same number of rows, columns, and treatment levels, so it does impose constraints in that respect. Also, it cannot be used to determine interaction effects. Thus, if nutritional information should have a different effect on private-label brands than major brands, this design could not discern such differences.
Comments
Post a Comment