Speaker 1: Hi there, Alberto Savoia here again with another video on the math of success. And today's video is a question and answer. Specifically, I'm going to answer a question from one of the students at the online course offered by Exponentially. So if you want to know more about this course, go to exponentially.com. It's a very, very good, self-paced, online, critical typing course. And the students there have access to me. I participate in the Slack channel, and they ask me questions. Sometimes I reply on Slack with text, and sometimes I decide to make a video because it's a good question that I want to share with the world. Now, today's question is a pretty darn good one, and it's this. How do you determine the sample size for a pretotyping experiment? By the way, if you haven't read the book, if you haven't taken the course, if you haven't watched my previous videos, this makes no sense to you. So there's some prerequisite work. But assuming you know what a pretotyping experiment is and what an XYZ hypothesis is, here is the explanation on how you determine, in a very systematic way, safe with numbers, an optimal sample size for your experiment. So the question is, you have a new product that you want to sell, and I use an example here of my forever markers, and you want to see if people will buy them. Put them on display on a shelf. How many people do I need to see that actually want to buy markers before I have a good enough sample size to know if my product will be successful? So, first of all, remember, always start with the XYZ hypothesis. It's the most important thing that I teach. It's fundamental. It's the one that crystallizes your thinking and your idea and allows you to say it with numbers and collect data. So remember, the format for the XYZ hypothesis is at least X percent of Y will do Z. So in my example, for the forever markers that cost $50, 10 times more than the regular markers, my hypothesis is this. At least 10 percent of whiteboard marker buyers will buy forever markers for $50. So once you have the XYZ hypothesis out, well written, then you can determine what is the optimal sample size for each pretotyping experiment. And remember, you don't do just one experiment. You need to run two, three, four, five. I explained in previous videos how many experiments you need to run. But for each experiment, there is an optimal sample size, right? You cannot wait for a thousand people to try to buy markers at a store. Ten is too little. Maybe it's too little, depending on what you will see. So how do you determine the optimal sample size for each experiment? Well, there is a very, very simple formula. It's a rule of thumb, a heuristic that will do you right. So here's the formula. The optimal sample size for each experiment is equal to 1,000 divided by X. What is X? It's the number from the XYZ hypothesis. Isn't this cool? So let me explain how this works by giving you some example. So you take 1,000, you divide it by X. Another little reveal. So let's go through several X percentages to make it clear. So let's say that your X percent is 100. Yeah, anybody who comes up with 100 is kind of crazy, but it's good for an example. So let's say that you expect 100% of the people who see your product to buy. Then, look, your sample size is going to be 1,000 divided by 100, which is equal to 10. It means that you can just ask 10 people, and if 10 out of 10 or 8 or 9 out of 10 buy, you know that you're pretty close to your sample size. Now, let's assume that you're more realistic, and you say your sample, you expect 50% of people to buy your Forever markers. Now, so because you expect more people to buy it, you need a smaller sample size. So you take 1,000, you divide it by 50, and you get a sample size of 20. Still a very small sample size, but if you expect half the people to buy it, you don't need a lot of people to test that. Let's go down a little. Let's not do all of them. So let's say your sample size is 10, as in here, right? 10% of whiteboard buyers. If you take 1,000 divided by 10, you come up with 100. So if you want to get something that is statistically acceptable, you need to test about 100 people. Now, if your product is a product that is very expensive or very few people in the target market will buy it, say it's a Rolls-Royce silver shadow that costs $500,000, or even people who buy expensive cars are unlikely to buy it. So in that case, let's say your target market is 1%. 1% of really rich people who will buy a luxury car or will buy a Rolls-Royce silver phantom, then your sample size is going to be 1,000 divided by 1, which equals 1,000, right? Because, quite frankly, that's what you need in order to validate the market. The smaller percentage of people that you expect to buy your product, the larger your sample size must be. Does it make sense? Now, there is a pretty interesting thing here, and I call it the rule of 10, right? So let me explain. So let's ignore this 100%. Nobody buys 100% of anything, no group of people. So let's say that your sample size is 50%. Sorry, that your X percent is 50. Your sample size is 20. So what is 50% of 20? 10, right? So if you do this experiment and if your hypothesis rings true, you'll probably sell 10 plus or minus 1 or 2, right, if your hypothesis is correct. Now, if your sample size, let's say, instead of 50 is 10, sorry, if your X percent instead of 50 is 10, your sample size is going to be 100. Again, 1,000 divided by 10 equals 100. Now, if 10% of 100 is what you expect people to buy, then you should expect about 10 people to buy your product. And even if you go down here, right, at the very bottom, if your sample size is 1% of the market will buy your product, you take 1% of 1,000 is equal to 10, right? So this number is pretty constant. What I'm trying to get here, remember, these are rule of thumbs. There are much more complicated mathematical formula for determining accurate sample size and, you know, the dependency of those results, et cetera, et cetera. But this is a very good rule of thumb because what I'm trying to tell you is to say, look, pick a sample size based on your hypothesis that will yield at least 10 people plus or minus 1 or 2, right? These are just still an approximation to buy your product. So if your hypothesis is this crazy one, I mean, this extreme one, 1% of the target market, and if you ask 1,000 people and you get 10 people to buy, then you kind of confirm it. If you get 30, maybe you were too conservative. And if you get 5, you know that even this low market is not likely. So I hope this helps you. Once again, do you see in my system, in my methodology, everything that you do ties into the next step. We say it with numbers from beginning to end. Data beats opinion, right? So I hope this is useful. Remember, the simplest formula, I'm all about simplifying the formulas with heuristics that actually work, heuristics or rules of thumbs. Optimal sample size, take 1,000, divide by x in your x% xyz hypothesis, and you get your optimal sample size. And we'll talk in other videos. Actually, I have talked in other videos how many experiments you need to run. But for each experiment, stick to this rule, and you will get my thumbs up. It will be approved by myself and by most statisticians. Hope you like this. Again, check out the course at exponentially.com. You can have my book, consider my book, and I'll see you for the next lesson very soon. Thank you so much.