Mitra Lohrasbpour
Stella Young
14.11 – Assignment 7
May 2, 2006
Choice of Cheese: Preliminary Results
You may also add graphs or figures if you feel that they would be useful for illustrating your
findings. (where should I talk about these?)
Satisfaction with choice, confidence in making the best choice, and difficulty of choice were ranked by subjects on a seven-point scale, with 7 being the “most” and 1 being the “least” for each of those questions. Our summary statistics show that on average, people are satisfied with their choice (5.3), are somewhat confident in their choice (4.3) and do not find the task to be very difficult (3.6). For the most part, answers span the full range of possibilities, though nobody expressed being not all at satisfied with his choice. Standard deviations are smallest for satisfaction (1.09) and largest for confidence (1.62).
Subjects also expressed the most they are willing to pay for a brick-sized amount of their choice of cheese and for any of the cheeses offered. The average price people are willing to pay is $10.72 for their choice of cheese and $13.14 for any of the cheeses. It makes sense that on average people are willing to pay more for any of the cheeses than for their particular choice, because though they may not like the cheese they tasted, they probably value at least one of the cheeses offered on the tray. Standard deviations for willingness to pay are quite large at $12.32 for choice and $15.27 for any. A few people are not willing to pay anything for a brick of cheese, which is surprising, because if they dislike cheese, we would not expect them to participate in the study. On the other end of the spectrum, some people are willing to pay much more than market prices for a brick-sized amount of cheese. One person is willing to pay $150 for any of the cheeses, and two others are willing to pay $100. We consider these observations to be outliers, which was apparent when we graphed the data. We do not want our results to be skewed, so we remove them from our dataset when analyzing willingness to pay.
The means for the dummy variables tells us the proportion of subjects with a certain characteristic. For example, the mean for sex reveals the proportion of subjects that are female, which turns out to be exactly one-third. About 47.6% of our sample is Asian (including Indians) and 9.3% is non-Asian and non-white, which leaves 43.1% to be white (including Hispanics).
The proportion of observations from each display is also shown. We have one-ninth (24/216) of our observations from the row A display, one-ninth from the row B display, and one-ninth from the row C display, for a total of one-third of our data coming from the six-choice displays. We have almost one-ninth (23/216) of our observations from the rows AB display, approximately one-ninth (25/216) from the row BC display, and one-ninth from the row AC display, for a total of one-third of our data coming from the twelve-choice displays. Finally, we have one-third of our observations from the eighteen-choice display. You can also see the even distribution of observations among number of choices by looking at the means for the choice variables.
Our experiment was carried out from April 18, 2006 through April 27, 2006. In general, we collected data on one display per night; although, on the last night, we collected data for both the AC and the BC displays.
When we look at the mean satisfaction, confidence, and difficulty by the number of choices given, we get a sense for which variables are affected by number of choice. The average satisfaction is 5.2, 5.5, and 5.2 for six choices, twelve choices, and eighteen choices, respectively. Average confidence is 4.6, 4.2, and 4.1 for six choices, twelve choices, and eighteen choices, respectively. Average difficulty is 3.2, 3.7, and 3.9 for six choices, twelve choices, and eighteen choices, respectively.
We run regressions with the following structural forms:
(Satisfactioni) = + 1(12 choicesi) + 2(18 choicesi) + r + d(demographicss) +
(Confidencei) = + 1(12 choicesi) + 2(18 choicesi) + r + d(demographicss) +
(Difficultyi) = + 1(12 choicesi) + 2(18 choicesi) + r + d(demographicss) +
(Pricei) = + 1(12 choicesi) + 2(18 choicesi) + r + d(demographicss) +
[6 choices is used as the reference; demographics represents a vector of variables, represents a vector of fixed effects for the combinations of cheeses used in the limited choice rounds]
When controlling for display fixed effects, we find that coefficients on display are not significant. We also try controlling for date, which is almost collinear with display, in case our attitudes as investigators varied by day. The coefficients on the date fixed effects were also insignificant. Thus, although we report the regression results including display and date fixed effects in columns 1 and 2, we focus our discussion on the regressions without these fixed effects. Including the fixed effects causes the standard errors to be larger, so we are unable to obtain significant coefficients on choice. When we drop the fixed effects from the regressions, we obtain significant results for both confidence and difficulty.
For confidence, coefficients on both the twelve-choice and eighteen-choice categorical variables are negative and significant in column 3 of Table B. Subjects are less confident that they made the best choice when the number of choices increases from six to twelve. They are even less confident when the number of choices increases from twelve to eighteen. Likewise, column 3 of Table C shows that coefficients for twelve-choice and eighteen-choice are positive and significant when regressed on difficulty. Subjects feel that their choice is more difficult when number of choices increases both from six to twelve and from twelve to eighteen. Interestingly, there is a much bigger change in confidence and difficulty going from six to twelve than going from twelve to eighteen. Perhaps presenting twelve choices is already reaching the extensive choice threshold, so that there is not much difference in going from twelve to eighteen choices.
We try running regressions for males and females separately, and then also for whites, Asians, and other races separately for all five dependent variables – satisfaction, confidence, difficulty, price for choice, and price for any cheese – though we only report the results that are meaningful. We find that women become significantly less confident when the number of options increases from six to twelve, but do not experience a significant change when options increase from twelve to eighteen. Men, on the other hand, demonstrate the opposite effect. They do not experience a significant change in confidence when options increase from six to twelve, but they do see a significant drop in confidence we options increase from twelve to eighteen. Please see columns 4-5 of Table B. These results might suggest that women have a lower threshold than men for what constitutes extensive choice. Similarly, white subjects see a significant drop in confidence when options increase from twelve to eighteen but not otherwise, and Asian subjects see a significant drop in confidence when options increase from six to twelve, but not otherwise. Subjects in the other race category did not have any significant coefficients, but it could be because there were only 20 observations. Please see columns 6-8 in Table B. We also find that women do not report a significant increase in difficulty choosing when choices increase from six to twelve or from twelve to eighteen. Instead, the significance found seems to come entirely from the men; we see a significant increase in difficulty corresponding with both the jump from six to twelve and the jump from twelve to eighteen. Please see columns 4-5 in Table C.
Even after dropping the fixed effects, no significant relationship between number of choices and satisfaction was found. Please see column 3 in Table A. This could be explained by the fact that the number of choices does not actually affect the taste of the cheese itself. At least in the context of cheese, people do not seem to care how many choices were originally offered to them in their subsequent evaluation of satisfaction.
By looking at mean valuation of cheese sampled and mean valuation of any of the cheeses offered, we can tell that regression results for the two price variables probably will not be significant. The average maximum people are willing to pay for the cheese they chose is $10.20, $9.53, and $9.94 for six, twelve, and eighteen choices, respectively. The average maximum people are willing to pay for any cheese offered to them is $11.91, $11.19, and $11.94. Since standard deviations are large (i.e. close to the means), the differences between the means should not be significant. Indeed, when we run the regressions for both dependent variables, we find that coefficients on twelve choices and eighteen choices are insignificantly different from zero. Please see columns 1-3 for Tables D and E.
As expected, increasing the number of choices decreases confidenceof making the best choice and increases the difficulty of choosing. Our results confirm the alternative hypothesis for these two measures. However, increasing the number of choices does not affect average satisfaction with the one cheese actually sampled, nor does it affect willingness to pay for that cheese or any cheese. The null hypothesis that increasing choice has no effect is confirmed for these three measures.
We made a few interesting observations while conducting our experiment which could have biased survey responses. Some people wanted to please us by indicating that they were satisfied with their choice or by being willing to pay a higher price. Other people bragged about how confident they are with all of their decisions.
Many people also misinterpreted our question about willingness to pay. People didn’t always know what a brick-sized amount of cheese was. Some of them asked about it, so we explained it to them. Others that did not ask may also have been confused, but we only started regularly explaining that brick-sized refers to a red construction brick in the latter half of our experiment, after we realized that many people were confused. Some even asked us if brick-sized referred to the two-inch cube sample on the tray. There were also many students that insisted that they rarely buy cheese, so they have no idea how much it should cost, and asked us to give them a benchmark price. Of course we did not give them one, so some of them seemed to be taking a shot in the dark rather than thinking about their valuation of the product. Their dependence on knowing the market price before determining their willingness to pay and also their lack of information about the market price makes us suspicious about our price data. Some people understood what we meant by brick-sized, but they didn’t understand what we meant by “any cheese.” They thought that we would randomly choose a cheese for them, and they would have to pay for it. We wanted to know the most they would pay for any cheese of their choice (as if they were browsing at a supermarket), not a randomly selected cheese. We know that people were confused on this point because a few people asked us about it, and some people wrote a lower price for any cheese than the price they wrote for their chosen cheese. Presumably, if they could choose any cheese, they could choose the one that they already tasted, so they should be willing to pay at least as much for any cheese as they paid for the one they sampled. If we could conduct this experiment again, we would make sure to specify a size that everybody understands and carry around an example of that size, and we would specify that “any cheese” refers to “any cheese of your choice.”