24. Choice-Based Conjoint Analysis

OBJECTIVE

Identify customers and potential customers’ preferences for specific attributes of a product. It can also be used to define the willingness to pay and market share of different products.

DESCRIPTION

This method is preferred to conjoint analysis because it represents a more realistic purchase situation and, in the case of having a large number of possible combinations, because it is sufficient to show only a certain number of combinations to each respondent. Then the responses are analyzed together and the utility is defined at the aggregated level (not at the individual level as in conjoint analysis).

For this method it is also very important to choose carefully the attributes (as a rule of thumb, no more than seven including the price) and the product profiles to present, that is, the combinations of attributes. Once the attributes and product profiles have been defined, choice scenarios are designed. A scenario is a combination of several products that is presented to the respondents. When defining scenarios, these recommendations should be followed:

• A “none” choice should be included among the products presented in each purchase scenario;
• Each scenario should not have more than 5 products;
• Between 12 and 18 scenarios are usually presented to each respondent.

Usually, all the combinations cannot be presented in the same scenario, and a good practice is to show from two to five products in each scenario. When choosing the combination of products for each scenario, it is important that all the products are shown an equal number of times and that each product is compared equally with other alternatives.

Once the data have been collected, utilities are estimated at the aggregate level. The market share of each product can be calculated using the “share of preferences”:

• Products’ utilities are calculated by summing all the attributes’ utilities;
• Products’ utilities are exponentiated;
• The market share is calculated as the product’s exponentiated utility divided by the sum of all the exponentiated utilities.

To obtain utilities at the individual level, a method called “hierarchical Bayes” is used. This method enables us to calculate a more reliable market share based on the choice of each respondent using three main techniques:

• First choice: each respondent chooses the product that maximizes her utility (this technique is suggested for expensive products that imply a careful evaluation, such as houses and cars);
• Share of preference: each respondent purchases a share of each product based on the share of utilities (suggested when a product is purchased several times during a certain period);
• Randomized first choice: each respondent chooses one product with a probability proportional to its utility.

This method is also useful for predicting variations in the market share compared with competitors by creating simulations in which prices or other products’ attributes are changed. For example, we can analyze whether a discount can attract a big enough market share to compensate for the reduction in price. In this kind of simulation, we assume that competitors are not modifying both attributes and price, but in reality this could not be the case. This is why we should at least simulate several scenarios including possible competitors’ reactions. A more complex approach would be to include a game theory model (see 76. GAME THEORYMODELS).

TEMPLATE

Here you can find a template in Excel which can help you both in the design of the survey (definition of combinations and surveys including optimal reduction of options) and in the analysis using conditional multinomial logit.

---

52. Wilcoxon Signed-Rank Test

OBJECTIVE

Verify whether the difference in two groups is significantly different (in the case that the assumptions for parametric tests are not met).

DESCRIPTION

It is a non-parametric substitute of the t-test in the case that normality cannot be verified or the sample is too small (smaller than 30), but, differing from the Mann–Whitney test, it is used for paired samples (the groups are not independent). The example presented here is a “signed-rank Wilcoxon test” (for paired samples and as a counterpart of the parametric paired t-test).

The assumptions for this test are: the samples are from the same population, the pairs are chosen independently, the data are measured at least on an ordinal scale (continuous, discrete, or ordinal), and the distribution is not especially skewed (that is to say it is approximately symmetrical).

Wilcoxon Signed-Ranks Test

To perform the test, the difference between observations is calculated and ranked. When we have samples with fewer than 25 observations, we use a table with a t-critical value to verify the significance; specifically, we reject the null hypothesis (there is no difference in the samples) if T is lower than T-critical. If we have a larger sample, we can use the p-value for the assessment of the significance.

TEMPLATE

Download the Wilcoxon Signed-Rank excel template

46. ANOVA

OBJECTIVE

Verify whether two or more groups are significantly different.

DESCRIPTION

While with a t-test we can only test two groups, with ANOVA we can test several groups and decide whether the means of these samples are significantly different. The simplest analysis is one-way ANOVA, in which the variance depends on one factor. Suppose that we want to know whether the age of people buying three different products is significantly different to focus the promotional campaigns better. In this case we have just one factor (type of product); therefore, we run a one-way ANOVA after checking the normality assumption (see 36. INTRODUCTION TO REGRESSIONS).

Output of a One-way ANOVA Analysis

Once the test is concluded, we check the p-value (< 0.05) and F-value (larger than the F-critical value) to reject the null hypothesis and infer that the populations are not equal. In the proposed example, there is a significant age difference among products. However, we should perform a t-test of each pair of groups to determine where the difference lies.

In a two-way ANOVA we have two factors to be tested. For example, we are selling products A, B, and C in three countries (1, 2, and 3). In the proposed example, we use a two-way ANOVA “without replication,” since only one observation is recorded for each factor’s combination (we will use an ANOVA “with replication” if there are more observations recorded for each combination). In a two-way ANOVA, there are two null hypotheses to be tested, one for each factor, and it is possible that the hypothesis will be rejected for one factor but not for the other one.

In our example we reject the null hypothesis for the factor “type of product” (rows), since its p-value is smaller than 0.05, but we cannot reject the null hypothesis for the factor “country” (columns).

Output of a Two-Way ANOVA Analysis

We can also perform an ANOVA with repeated measures when we have repeated measures within the same group. In our example a company decided to start a four-week training program for five employees to diminish the number of errors made at work. In this case the repeated measures are the errors of each employee in the same week of training.

Results of a Single-Factor ANOVA with Repeated Measures

The template contains the calculations for a single-factor repeated-measures ANOVA. In our example, since the p-value is lower than 0.05 (our chosen alpha), we reject the null hypothesis of no difference among the week’s means and infer that the training has had an impact on the number of errors.

We can use the Excel Data Analysis complement to perform a two-factor repeated-measures ANOVA, choosing the test “Anova: Two-Factor With Replication.” In the proposed example, we are selling different product versions in different markets, and we want to test whether either the product or the market (or both) have an impact on the number of products sold. The results show that, while the kind of product (rows) affects the sales (p-value < 0.05), the market (columns) does not.

Results of a Two-Factor ANOVA with Repeated Measures

An extension of ANOVA is MANOVA, which allows the test to be run with more than one dependent variable. For example, it is possible to run a MANOVA using “level of education” as the categorical independent variable and “test score” and “yearly income” as the continuous dependent variables.

TEMPLATE

Download the ANOVA Excel Template

48. CHI-SQUARE

OBJECTIVE

Verify whether the difference between the observed frequencies and the expected frequencies is significant or not.

DESCRIPTION

A chi-square test is used to test the frequencies of independent observations (not suitable for paired testing) with two main purposes:

• Test of independence: to determine the association between two categorical variables, for example if the kind of civil status does not affect the kind of service that customers buy;

• Test of goodness of fit: to determine the difference between the observed values and the expected values (for example whether a sample taken from a population follows the expected population distribution or a theoretical distribution).

In either case the method used is the same; specifically, we apply a chi-square test using the observed values and the expected values. When using a chi-square test, it is important to bear in mind that this test is sensitive to the sample size (with fewer than 50 this test is not appropriate) and needs to have a minimum frequency in each bin or class (at least 5). If these conditions are not met, we should consider using Fisher’s exact test.

TEST OF INDEPENDENCE

In the example we are testing the independence of the variables “civil status” and “service level” chosen by customers.

Observed Values vs Expected Values in a Chi-Square Test

For this test we assume that the probability of having a specific service level and the probability of being married, single, or divorced are independent events. With these assumptions, we compare the actual distribution of the products sold in each country and the expected distribution based on the independent probabilities of the two events (see the template). In other words, the test compares the expected frequencies with the actual frequencies. The Excel formula “=CHITEST” is then applied, and if the resulting p-value is smaller than 0.05 (or a different alpha), we reject the null hypothesis (the two variables are independent) and we can infer that the two variables are associated. In other words, we can say that civil status affects the level of service purchased.

GOODNESS OF FIT

Goodness of fit can be calculated in Excel using the same formula (=CHITEST), which is applied to a column (or row) with observed values and a column with expected values. For example, if we throw a die, we expect that each number has the same probability of appearing (1/6) but suspect the die to have been loaded. In our example we throw the die 60 times and expect to produce each number 10 times. If the p-value is lower than 0.05, we reject the null hypothesis, which is that the variables are independent (as in the chi-square independence test). Since the p-value is larger than 0.05, we conclude that the die is not loaded.

Data and Results of a Goodness of-Fit Chi-Square Test

We can also compare our observed values with a theoretical distribution.

TEST OF PROPORTIONS

The chi-square test can also be used instead of the z-test in the test of proportions (see 44. TEST OF PROPORTIONS) when the assumptions for using the parametric test are not met. In this case we will compare the observed proportion with the expected proportion with a double-entry contingency table (the same table used in the independence test but with only two categories per row and two categories per column).

TEMPLATE

Download the Chi-square Excel Template

20. GABOR–GRANGER PRICING METHOD

OBJECTIVE

Define the optimal price range for a product or service.

DESCRIPTION

This method is useful in taking general pricing decisions. Data are collected through surveys in which each respondent is asked about his intention to purchase and shown several prices that move up or down depending on the previous answers. Alternatively, prices can be shown randomly or in a fixed series. The highest price at which a respondent reports that he would buy is considered to be his WTP. Once we have a specific price limit (WTP) for each interviewee, we can draw an accumulated demand curve.

Gabor–Granger Pricing Method

Since we have the information about demand and WTP available, we can calculate the revenue curve in the graph and establish the optimal price at which revenues are maximized.


Donwload the Gabor-Granger Excel Template