For this project, you will write a paper that involves designing, conducting, an

Question

For this project, you will write a paper that involves designing, conducting, and analyzing results from your own experiment to test the sensory discrimination of one of your friends. Choose a friend who claims to be able to tell the difference between two very similar objects.
1. First, you should brainstorm to find a friend who is either a self-proclaimed expert or has some food/beverage related idiosyncracy(1).
2. Determine a protocol for administering the test
a) What should be done about random variations in the items to be tested? For example, how do you prevent temperature change in the product, or to make sure each cup of coffee is equally sweet or has the same amount of cream? Before conducting your experiment, carefully lay out the procedure for administering the test, such as how the coffee will be made, how the wine will be decanted, and so forth. This is related to the important issue of ensuring that each trial is independent (i.e. the previous trials aren’t tainting your taster’s sense of taste). If you have ever been to a wine tasting, you’ll notice that you can tell the difference between the first few sips of wine, but once you get to the 11th and 12th glass, it’s all sort of a blur (and not due to inebriation!). Carefully consider how you will attempt to overcome this problem.
b) How many trials should be used in the test (for this, see Levine Chapter 7, Levine 271-273, or read up on the Fisher exact test)? Should they be paired or independent(2)? In what order should the items be presented? Should the experiment be run in one sitting or spaced out over a number of days? Done properly, the experiment should be designed such that if the expert has no expert skills, the result will be wholly governed by chance. The number and ordering of the trials should allow an expert to prove his or her abilities while simultaneously preventing a fraud from succeeding. You will want to keep the binomial distribution in mind when making these decisions.
c) What conclusion could be drawn from a perfect score or from a test with one or more errors? For the design you are considering, list all possible results of the experiment. For each possible result, decide in advance what conclusion you will make if it occurs. In determining this mapping of outcomes to conclusions, consider the probability that someone with no powers of discrimination could wind up with each outcome. You may want to make adjustments in your design to increase the sensitivity of your experiment. For example, if someone can’t distinguish decaf coffee from regular, then just by guessing, he/she should still be right half of the time and there will be a small chance, which you should calculate, of being right 100% of the time. On the other hand, if the taster possesses some, but not perfect, skill in differentiation, he or she will make some mistakes.
3. Write out an instruction sheet for your experimental process. Conduct a “dress rehearsal” on somebody other than your subject to work out kinks in the process. After the practice run, determine whether or not you want to make changes in your instruction sheet to address any problems that arose. This practice run is an extremely important step; many people make big mistakes in their first attempt and historically, students who have taken this step seriously have scored much more highly on this project than those who do not.
4. You should now be ready to run your experiment. Record your results CAREFULLY, and note any unusual occurrences in the experimental process. It may be a good idea to keep track of the order in which the samples are served to your subject.
5. Numerically, summarize the results and analyze the data. Do they support or contradict the claim that the subject possesses no sensory discrimination? Use your list of all possible events and subsequent actions to come to a conclusion.



Answer:

Statistical hypothesis testing is a way of formalizing the decision-making process so that a decision can be rendered about the value of the parameter. Hypothesis testing is a procedure where claims about the value of a population parameter may be investigated using the sample evidence (Larose, 2009).

Subject:
Haagen Dasz plain vanilla ice cream (HGV) and Ben and Jerry’s plain vanilla ice cream (BJV).

Goal:
My husband (Tony) claims that he can tell the difference between the flavors of Haagen Dasz and Ben and Jerry’s ice cream To determine if Tony’s sensory discrimination is accurate, I tested him on Haagen Dazs vanilla ice cream and Ben and Jerry’s vanilla ice cream.

Null Hypotheses:
For purposes of the test, the null hypothesis, a representation of what I have tentatively assumed about the value of the parameter is that I believe that tony knows the difference between Haagen Dazs vanilla ice cream flavors and is sweeter than Ben and Jerry vanilla flavors.



Parameter:
The test will have a preference. This preference will be recorded as probability of my husband differentiating between Haagen Dazs vanilla over Ben and Jerry’s vanilla. This is P(HDV). If the null hypothesis were to be true, then P(HDV) = P(null) = 0.5. If the alternate hypothesis is true, then P(HDV) > P(null) = 0.5.

Significance Level:
Significance level is the value that “represents the boundary between results that are statistically significant and results that are not statistically significant” (Larose, 2009. 469). The significance level used to determine the probability of a type 1 error. To contradict the null hypothesis there should be statistically significant results. For purposes of the experiment a significance level of .05 will be chosen, which leaves a 5% chance of the null hypothesis being true, or a type 1 error. In this setting, a type 1 error corresponds to Tony finding any difference between Haagen Dazs vanilla and Ben and Jerry vanilla.

Equipment:
The test was performed five days a week over a period. I used 15 x 2 = 30 paper cups and plastic spoons. Every day, I put ¼ of a cup of Haagen Dazs vanilla in one and same quantity of Ben and Jerry vanilla in the other cup. I therefore used ¼ * 30 = 7.5 cups of each ice cream. I also provided palette cleansing crackers that he was obliged to take after each test.

Protocol:
To prevent biases, I scooped a ¼ of each of the ice creams into unmarked cups. I always put the Haagen Dazs variety on the left and the Ben and Jerry’s on the right. Tony cleansed his palette after each taste. After each test, he was asked to determine which one was HDV or BJV. All his responses were recorded using a Fisher's Exact Test.

Pre-test Population:
For the pretest, I tested Tony with the two samples, using the same protocol as I would do in the proper test. The pretest was successful as I was able to follow the guidelines of putting HDV in left unmarked cup and BJV in the right unmarked cup. Just for the record, he was able to differentiate between the flavors in the pretest.
Outcome
HDV BJV
0 1
0 1
1 0
0 1
1 0
0 1
0 1
0 1
0 1
0 1
1 0
1 0
1 0
0 1
0 1

0=unable to identify ice cream type
1 = able to identify ice cream type

HDV BJV
0.33 0.67 mean
0.49 0.49 std. dev.
15 15 n





P1= proportion of the number of times Tony is able to identify the taste of Haagen Dazs Vanilla.
P2= proportion of the number of times Tony is able to identify the taste of Ben and Jerry’s Vanilla.
The hypothesis to be tested are:
H0: P1= P2=.05
Sample size= 15
Number of times Tony Identified HDV = 5
Number of times Tony Identified BJV =10
Sample proportion of HDV =
P1=X1/N1 = 5/15 = .3333
Sample proportion of BJV=
P2 = X2/N2=10/15 = .6667
Pooled estimate of the common value of P
P= 5/15 +10/15 = .05
SEpooled=v(?.5(1-.05)(1/15+1/15)?^ )
=.0182574186
The test statistics is calculated as :
Z=(.03333 - .06667) / .182574186
= 1.8.8257
The P value is P(Z>-1.8257) ˜ 0.066
Conclusion:
Since p- value is large, the test fail to reject H0 (at a = 0.05 level of significance)
The sample data does not provide conclusive evidence that Tony is able to differentiate between the taste of Haagen Dazs Vanilla and Ben and Jerry’s vanilla.

Explanation / Answer

Statistical hypothesis testing is a way of formalizing the decision-making process so that a decision can be rendered about the value of the parameter. Hypothesis testing is a procedure where claims about the value of a population parameter may be investigated using the sample evidence (Larose, 2009). Subject: Haagen Dasz plain vanilla ice cream (HGV) and Ben and Jerry’s plain vanilla ice cream (BJV). Goal: My husband (Tony) claims that he can tell the difference between the flavors of Haagen Dasz and Ben and Jerry’s ice cream To determine if Tony’s sensory discrimination is accurate, I tested him on Haagen Dazs vanilla ice cream and Ben and Jerry’s vanilla ice cream. Null Hypotheses: For purposes of the test, the null hypothesis, a representation of what I have tentatively assumed about the value of the parameter is that I believe that tony knows the difference between Haagen Dazs vanilla ice cream flavors and is sweeter than Ben and Jerry vanilla flavors. Parameter: The test will have a preference. This preference will be recorded as probability of my husband differentiating between Haagen Dazs vanilla over Ben and Jerry’s vanilla. This is P(HDV). If the null hypothesis were to be true, then P(HDV) = P(null) = 0.5. If the alternate hypothesis is true, then P(HDV) > P(null) = 0.5. Significance Level: Significance level is the value that “represents the boundary between results that are statistically significant and results that are not statistically significant” (Larose, 2009. 469). The significance level used to determine the probability of a type 1 error. To contradict the null hypothesis there should be statistically significant results. For purposes of the experiment a significance level of .05 will be chosen, which leaves a 5% chance of the null hypothesis being true, or a type 1 error. In this setting, a type 1 error corresponds to Tony finding any difference between Haagen Dazs vanilla and Ben and Jerry vanilla. Equipment: The test was performed five days a week over a period. I used 15 x 2 = 30 paper cups and plastic spoons. Every day, I put ¼ of a cup of Haagen Dazs vanilla in one and same quantity of Ben and Jerry vanilla in the other cup. I therefore used ¼ * 30 = 7.5 cups of each ice cream. I also provided palette cleansing crackers that he was obliged to take after each test. Protocol: To prevent biases, I scooped a ¼ of each of the ice creams into unmarked cups. I always put the Haagen Dazs variety on the left and the Ben and Jerry’s on the right. Tony cleansed his palette after each taste. After each test, he was asked to determine which one was HDV or BJV. All his responses were recorded using a Fisher's Exact Test. Pre-test Population: For the pretest, I tested Tony with the two samples, using the same protocol as I would do in the proper test. The pretest was successful as I was able to follow the guidelines of putting HDV in left unmarked cup and BJV in the right unmarked cup. Just for the record, he was able to differentiate between the flavors in the pretest. Outcome HDV BJV 0 1 0 1 1 0 0 1 1 0 0 1 0 1 0 1 0 1 0 1 1 0 1 0 1 0 0 1 0 1 0=unable to identify ice cream type 1 = able to identify ice cream type HDV BJV 0.33 0.67 mean 0.49 0.49 std. dev. 15 15 n P1= proportion of the number of times Tony is able to identify the taste of Haagen Dazs Vanilla. P2= proportion of the number of times Tony is able to identify the taste of Ben and Jerry’s Vanilla. The hypothesis to be tested are: H0: P1= P2=.05 Sample size= 15 Number of times Tony Identified HDV = 5 Number of times Tony Identified BJV =10 Sample proportion of HDV = P1=X1/N1 = 5/15 = .3333 Sample proportion of BJV= P2 = X2/N2=10/15 = .6667 Pooled estimate of the common value of P P= 5/15 +10/15 = .05 SEpooled=v(?.5(1-.05)(1/15+1/15)?^ ) =.0182574186 The test statistics is calculated as : Z=(.03333 - .06667) / .182574186 = 1.8.8257 The P value is P(Z>-1.8257) ˜ 0.066 Conclusion: Since p- value is large, the test fail to reject H0 (at a = 0.05 level of significance) The sample data does not provide conclusive evidence that Tony is able to differentiate between the taste of Haagen Dazs Vanilla and Ben and Jerry’s vanilla.

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