To smell or not to smell…

Our Math 5 Smelling Pre-test

Robin Deliso, Clare Gupta and Amory Loring

Our Goals:

• People spend an inordinate amount of money on beauty products, particularly perfume. Our goal is to assess whether those pricey scents are really “better smelling?” Can people smell money??

• More precisely, can a group of Dartmouth students tell a difference between a designer perfume—CK One—versus the WalMart knock-off version? And if so, which do they prefer?

Our pre-test beliefs

• We felt that a majority of the people sampled would prefer the real CK One over the knock-off. Specifically, we estimated that 75% of the opinionated smellers (i.e. ppower = .75) would prefer the more expensive scent.

Wait…Dartmouth students have cheap taste?!

RESULTS…• Out of our 50 sampled individuals, 37

expressed that they could smell a difference. We labeled them “opinionated smellers.” They made up 74 % of our test population.

• Of these opinionated smellers, only 37.8% preferred the original scent, whereas 62.1% preferred the cheaper version.

Confounding Factors

• Our pre-test was administered in Collis, an area that may attract a certain type of person with a certain preference. Would results have been different if we had conducted our test in Food Court?

More confounding factors…

• We administered our test Winter Carnival weekend, a popular weekend for friends to come up. Thus, our population was not exclusively Dartmouth students as we had intended

• We sprayed our perfume sample card every 5 trials, but the amount we sprayed on the card each time may have varied slightly.

• By nature of the season during which we tested (i.e. winter), a higher percentage of non-smellers may have resulted, due to nasal congestion, colds, etc.

Given that we did find 37 opinionated smellers in our 50 person sample group, we think that our confounding factors are negligible

• Thus, it seems most likely that our conclusion was just WRONG!

• However, it may just be that people preferred the cheap perfume on the perfume tester card..

Perfume card versus skin?

• During our experiment, a number of people expressed that their preference of the cheaper scent was due to its lower intensity in smell.

• Perhaps if we had sprayed the perfume on our participants’ skin, it would have smelled different and changed our results.

What exactly did we do?

THE TEST• We presented each participant with two

paper strips, one sprayed with the real CK One perfume and the other sprayed with the WalMart knockoff, without telling them which was which.

• We first asked if they could tell a difference in the two scents.

More protocol…

• If they could tell a difference, we asked which scent they preferred.

• We recorded all results and transferred to an Excel spreadsheet.

Null Hypothesis

• That the participants are equally likely to prefer the knock-off CK One perfume as they are the real one.

• Specifically, the null hypothesis is that

p = 0.5, when p is the percent of participants who prefer the real CK One, among the participants who have a preference.

The Alternate Hypothesis

• That our Collis lunchtime population will prefer the expensive real CK One perfume

• P > . 5

• But what we REALLY thought was that a lot more than just a majority (i.e. 50%) would prefer the real CK One!

We believed…

• That at least 75% of our opinionated smellers would prefer the real CK One.

• Thus we used p = . 75 to estimate the power of our test. This means that we are using p = .75 to estimate how likely it is that we are correct about our belief and that our test confirms this belief. (Remember, power equals 1 – ß)

Null and Power Hypotheses

Null and Power Hypotheses

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values

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Null Hypothesis

Pow er Hypothesis

Using a 5% significance level…

We find a Critical Value of 63.5%. From our results, we chose to use the value

of 24 as our baseline.

Significance Level

00.020.040.060.08

0.10.120.14

Values

P

Null Hypothesis

Critical Value

POWER!

The Power of our test is 94.6%.

Power Hypothesis

00.020.040.060.080.1

0.120.140.16

Values

P Power Hypothesis

Critical Value

Must we accept our Null Hypothesis?

NOOOOOOOOO

• Given that P = K/N where K is the number of smellers who preferred the real scent (in our case, 14 individuals) and N is the total number of Opinionated Smellers (which was 37 people), we found that P = .378 or 37.8% of a population. This falls outside our parameter values of 15-22 so we must reject the Null Hypothesis TOO (we’re on a roll).

We weren’t exactly in the ballpark…

Our p versus the actual p

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Results and Hypotheses

Results and Hypotheses

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Null Hypothesis

Pow er Hypothesis

Critical Value

Our P Value

Interpretation

• Dartmouth students prefer cheap perfume!

• If we had kept our Null Hypothesis the same but made our Alternate Hypothesis, “We believe people prefer cheap perfume,” we would have been much closer to proving our Alternate Hypothesis.

FOR THE FUTURE…

• Test a non-Collis—or non-Dartmouth population.

• Apply the scent directly to skin and omit cardboard.

• Run experiment in a different season—i.e. when nasal congestion is at a lower percentage.

• Do our experiment over again and check differences in results.

*THE END*

(robin-amo-clare)