SMARTIES Have a Colourful History
SMARTIES, after my arriving in Canada many years, became one of the iconic candies to me. I continue to anticipate the taste and colours when I open a box.
“A long-time favourite in many countries including the UK, Germany, Australia, South Africa and Canada; they are not disturbed in the United States…. Rowntree’s of York, England, have been making “Chocolate Beans” since at least 1882. The product was renamed “Smarties Chocolate Beans” in 1937. Rowntree’s was forced to drop the words “chocolate beans” in 1937 due to trading standards requirements (the use of the word “beans” was felt to be misleading) so adopted the “Milk Chocolate in a Crisp Sugar Shell… The brand changed to “Smarties” in 1938 and Smarties tubes were introduced…”Smarties come in eight colours: red, orange, yellow, green, blue, mauve, pink and brown…”. See Below.
This article is modeled after a class exercise the author has used to introduce the distribution of categorical (count) variables drawn by randomly sampling from a large population. Expected values will be calculated and fit to the sample data. Goodness of fit will be tested using the Chi-square (χ2) distribution.
Leroux has counted the colour distribution of 5428 Smarties; here is the frequency distribution:
This Table summarizes the n=76 SMARTIES candies that were in a box recently bought by the author. The “N Expected” are calculated by multiplying the frequency in the large population with n=76. Chi-square was calculated using this formula, where O(i) are the observed categories and E(i) are the expected number:
Data from the larger parent population shows that the 8 colours are relatively uniform in distribution. The single box of Smarties that I bought had no “Blue” candies. Deficiencies in Blue, Yellow and Brown candies relative to the larger population accounted for a majority of the deviation from the expected distribution (~98%). A Chi-square of at least 18.245 would be expected in less that 2.50% of the samples of similar size. Therefore, my box of SMARTIES were found to be atypical of the larger population.
Adding additional boxes of candies would help close the gap.
Here is a graphical summary of the results.
This completes a simple demonstration of analyzing count data and testing their fit to the chi-square distribution.
Should you buy a box of Smarties, do the colour count and see how they compare.
Here’s an old SMARIES advert; do you eat the red ones last?
Thanks for taking your time to read my article. If you are in the mood given me a “clap”.
Zack Florence
