This blog deals with an example of evaluating the characteristics of multiple products, using "Cochrann's Q test" as a method to examine the agreement of evaluations between products, and "correspondence analysis" as a method to examine the relationship between products and evaluations. I'll show you how.
"Cochran's Q test" may be a little-known test method, but it is useful as a test method for evaluating multiple products like this example. Please use it by all means.
Comparison of characteristics of multiple canned coffee
Example: Evaluation of sweetness, roasted feeling, bitterness, etc. for 7 types of canned coffee
For 7 canned coffee (A, B, C, D, E, F, G), 12 panelists (evaluators) evaluated the following 5 characteristics of coffee
Aroma : scent
Acidity : sour
Sweetness : sweetness
Bitterness : Bitter feeling
Roastness : Roasted taste
Evaluate
Each panelist checks each canned coffee that strongly felt the above characteristics.
As in this example, the evaluator checks the corresponding features (evaluation items) of the product, counts the number of checks, and examines the features of the product. CATA (Check All That Apply) Act It is mainly used for marketing research.
The share chart below summarizes the results of the evaluation. A value of "1" indicates checked, a value of "0" indicates not checked. In short, for each coffee and each feature (Item), the higher the ratio of 1, the more panelists felt that feature.
At this time, Cochran's Q test is used to examine whether there is a difference in the percentage checked for a certain feature between products.
Cochran's Q test is a method of examining whether there is a difference in proportions between variables for three or more paired binary variables (categorical data with two values).
In this example, 7 canned coffees are evaluated, so there are 3 or more variables, and the panelists are evaluating multiple canned coffees, so the data has correspondence. Furthermore, the evaluation can only take two values, "1" or "0", so it is binary data and satisfies the requirements for using Cochran's Q test.
Multiple correspondence analysis and Cochran's Q test
JMP provides Cochran's Q test as an option in Multiple Correspondence Analysis. Let's perform Cochran's Q test for this example of canned coffee evaluation.
The share chart in the previous section was created from the following data table.
Items : Characteristics (5 evaluation items)
Panelists : Evaluators (12 people from P1 to P12)
Coffee A to Coffee G : 7 types of canned coffee. "1" is entered when each feature is checked, and "0" is entered when it is not checked.
Analyze > Multivariate > Multiple Correspondence Analysis , assign the columns as shown in the lower left figure, and from the red triangle button on the upper left of the displayed analysis report Correspondence Analysis > Cochran's Q Test Choose.
Of the five evaluation items, two reports, Binnerness and Aroma, are shown here. The Correspondence Analysis report is shown along with the Cochran's Q Test report.
If the significance level of the test is 0.05, the p-value for Bitterness in the upper left of the figure is 0.0134, indicating a significant difference, and the p-value for Aroma in the upper right of the figure is 0.3946, indicating no significant difference.
From this, it can be said that there is a difference in the percentage of bitterness felt for the 7 types of canned coffee, but it cannot be said that there is a difference in the aroma.
This interpretation can also be intuitively known from the correspondence analysis diagram.
Correspondence analysis plots "0" and "1" points for each coffee, but Bitterness 0 and 1 are not located close to each other and are mixed on two dimensions. This is a state where there is no similarity in ratings between products. On the other hand, for Aroma, "0" is located on the left side and "1" is located on the right side to some extent, so it can be said that there is a similarity in the evaluation. A similarity in ratings indicates that no difference can be found between the products.
Actually, Cochran's Q test is performed for five features (evaluation items), so from the right-click menu [Concatenate to create data table] to show them all in one table.
There are significant differences in items other than aroma, that is, evaluations of sweetness, roast, bitterness, and sourness differ between products.
Product positioning with contingency table-based correspondence analysis
Let's aggregate the frequency of Item and Coffee in the above data, and perform a correspondence analysis on the aggregated data. The purpose is to conduct correspondence analysis based on the two-way analysis table of Coffee and Item, and to investigate the relationship between products and evaluation items.
Shows the correspondence analysis report. Dimension 1 (horizontal axis) explains 66% of the variation and dimension 2 (vertical axis) explains 22.5% of the variation, so the two dimensions also explain 88.5% of the variation in the data. It can be said that the two-dimensional plot is sufficient to show the relationship between products and endpoints.
Looking at the correspondence analysis report, we can see that B, C, and D are Bitterness and Roastness, F is Acidity, and A is a canned coffee with Sweetness.
In this way, correspondence analysis reports can map the relationships between categories in two dimensions. For example, it is a convenient method for explaining the differences between the features of your company's products and those of other companies and the positioning of products in an easy-to-understand manner.
By Naohiro Masukawa (JMP Japan)
