Without getting into too much math, the three things a business owner needs to know would be the 1) actual number of respondents in each group for each treatment; 2) probability of respondents to each treatment; and 3) the significance factor.

Say, for instance, you flipped a coin 50 times, and 30 times it came up heads. Your actual occurrence of heads is 60%; but your expected occurrence would be 25 times – or 50%, since there are just one of two possible outcomes. In like manner, when the business owner gets his actual results, he/she should assess the expected probability of each group responding, and then compare the two. He/she would do this by subtracting the expected occurrences from the actual for each response group to each treatment, and then squaring each result and adding them up.

The key thing to avoid having to refer back to a statistics book, is that most business cases require only a 95% confidence level, and a lot of small businesses are not going to be analyzing more than just a few treatments against a few subgroups. If, for instance, Jenny Kaplan in our example were testing three types of coupons and five age groups, thats only 8 degrees of freedom (5-1)*(3-1). Rarely are small businesses going to even need that many.

Your critical chi-squared for 95% confidence, as a rule of thumb, will be: 1 degree of freedom, around 4; 2 d.f=6; 3 d.f.=7.5, 4 d.f.=9.5; and then add on about 1.50 to your critical chi-squared statistic for each degree of freedom, until you reach 10 which is actually 18.3, but you’d have 18.5.

All the business owner needs to do then is compare his/her sum of squared differences with his critical chi-squared, and if they’re higher, then the differences are significant. If they’re close, the business owner should re-test.

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