Size Matters in Statistics

Banana-flavored Banana Split Creme Oreos

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If you’re in social or market research, you’ve heard about this topic before. Statistical significance is the one thing you wait to hear in order to know how likely your findings were the result of pure chance. If you are so lucky to have a p value smaller than 0.05, you raise your hands with excitement and exclaim Eureka! But, when your p value is huge, something like 0.06 or 0.7, you drag your heels in defeat. Why do we do this? Let me offer a couple scenarios.
Option 1: 40% of people purchase regular oreos and 50% of people purchase double stuff oreos. Statistically not significant. Say what?
Option 2: 40% of people purchase regular oreos and 41% of people purchase double stuff oreos. Statistically significant. Yer kidding me…
How can this be? Well, the way you figure out if two numbers are significantly different involves sample size. Let’s say in option 1 you had 10 people. Statistics say that’s not enough people to be absolutely sure it’s not just chance. But, option 2 was calculated from 10 000 people! That’s more than enough people to know that this different isn’t just pure luck.
But wait again….. I think 40% is quite different from 50%. So, maybe even though i got those numbers with just 10 people, I would be inclined to try again and see if that number happened in a larger sample. Just because it wasn’t statistically significant doesn’t mean I would let it go.
On the hand, do I REALLY care about the difference between 40% and 41%? Is 41% more actionable than 40%? I just don’t think so. I couldn’t care less if the difference was statistically significant. It’s just not meaningful. The ‘effect size’ is just too tiny for me to care that it was statistically significant.
Here’s another way of looking at it. Let’s say you ran your study and achieved statistical significance of p<0.06. Darn it, you say, i’m just going to give up on all my research now. But what if you did that study 5 more times and every single time, you got another p value of <0.06. Doesn’t this suggest to you that there really just might be a real difference happening, but just not as large as what you thought? I’d hate to be the person who quit that research and didn’t end up being the person to discover penicillin. (Let’s forget meta-analysis for now.)
So, my advice to you… significance is interesting, but size definitely matters

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