To smell or not to smell

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To smell or not to smell

• Our Math 5 Smelling Pre-test
• Robin Deliso, Clare Gupta and Amory Loring

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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 perfumeCK
  Oneversus the WalMart knock-off version? And if
  so, which do they prefer?

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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.

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WaitDartmouth students have cheap taste?!
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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.

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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?

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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.

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• 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.

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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..

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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.

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What exactly did we do?

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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.

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More protocol

• If they could tell a difference, we asked which
  scent they preferred.
• We recorded all results and transferred to an
  Excel spreadsheet.

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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.

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The Alternate Hypothesis

• That our Collis lunchtime population will prefer
  the expensive real CK One perfume
• P gt . 5
• But what we REALLY thought was that a lot more
  than just a majority (i.e. 50) would prefer the
  real CK One!

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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)

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Null and Power Hypotheses
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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.

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POWER!

• The Power of our test is 94.6.

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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 (were
  on a roll).

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We werent exactly in the ballpark
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Results and Hypotheses
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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.

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FOR THE FUTURE

• Test a non-Collisor non-Dartmouth population.
• Apply the scent directly to skin and omit
  cardboard.
• Run experiment in a different seasoni.e. when
  nasal congestion is at a lower percentage.
• Do our experiment over again and check
  differences in results.

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THE END

• (robin-amo-clare)