How to Decide Sanely When Bombarded with Advertising
There's this toothpaste ad which claims that you can't distinguish it from the leading brand. Translated into a quantitative statement, the greater the percent of those who cannot distinguish the new brand from the leading brand, the better for the new brand. At presumably cheaper price, its similar taste and effect make it preferable to buy instead (of the leading brand).
Statistically, the null hypothesis is that there is no difference between the taste and effect of the new brand from the leading brand. Using a “taste” test, the probability of distinguishing the new brand from the leading brand should be nil; that is, the new brand should be perceived as tasting the same with the leading brand despite its cheaper price. A “great” probability of perceiving the difference means that there is indeed a difference between the brands, or in other words, that the new brand is truly different and not at all comparable with the leading brand.
The test proceeds by using the time honored decision of either accepting or rejecting the null hypothesis. We reject it if the probability of distinction is extremely small, meaning that there is no difference between the brands. Therefore you can buy the new brand and get as much satisfaction and utility from the leading brand.
Because the decision is either the same or not, yes or no, the test will yield a binomial probability, which is very easy to calculate. Using the binomial distibution formula, r is the obtained number of success, or either a yes or a no, and n is the sample size
Binomial Distribution Formula : Binomial Distribution P(X = r) = nCr pr (1-p)n-r where, Combination nCr = ( n! / (n- r)! ) / r!
The ad says that “6 out of 10 failed to distinguish (the brands from each other)”.
So the question is, using the proportion (or percent) obtained [6 out of 10] is the new brand really as good as the leading brand (using perceived tastes only. We aren't talking of chemical composition here, OK?)
Using the formula, the probability obtained is 0.2050781. This is a miserable figure for establishing the similarity of the two brands. This means that twenty persons out of a hundred; or the same person undergoing 100 trials will distinguish between the brands 60 times. That is too often to be statistically significant. It is not at all rare that any person picked at random will perceive the difference, and consequently prefer the leading brand instead of patronizing the new brand.
Statistically, the null hypothesis is that there is no difference between the taste and effect of the new brand from the leading brand. Using a “taste” test, the probability of distinguishing the new brand from the leading brand should be nil; that is, the new brand should be perceived as tasting the same with the leading brand despite its cheaper price. A “great” probability of perceiving the difference means that there is indeed a difference between the brands, or in other words, that the new brand is truly different and not at all comparable with the leading brand.
The test proceeds by using the time honored decision of either accepting or rejecting the null hypothesis. We reject it if the probability of distinction is extremely small, meaning that there is no difference between the brands. Therefore you can buy the new brand and get as much satisfaction and utility from the leading brand.
Because the decision is either the same or not, yes or no, the test will yield a binomial probability, which is very easy to calculate. Using the binomial distibution formula, r is the obtained number of success, or either a yes or a no, and n is the sample size
Binomial Distribution Formula : Binomial Distribution P(X = r) = nCr pr (1-p)n-r where, Combination nCr = ( n! / (n- r)! ) / r!
The ad says that “6 out of 10 failed to distinguish (the brands from each other)”.
So the question is, using the proportion (or percent) obtained [6 out of 10] is the new brand really as good as the leading brand (using perceived tastes only. We aren't talking of chemical composition here, OK?)
Using the formula, the probability obtained is 0.2050781. This is a miserable figure for establishing the similarity of the two brands. This means that twenty persons out of a hundred; or the same person undergoing 100 trials will distinguish between the brands 60 times. That is too often to be statistically significant. It is not at all rare that any person picked at random will perceive the difference, and consequently prefer the leading brand instead of patronizing the new brand.
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