Error exponents in hypothesis testing
Imagine you were playing a memory game with your friends. Your friend gives you 10 numbers to remember and after a few seconds, they ask you to recall them in order. Your friend would evaluate how well you did by counting how many numbers you got right and how many you got wrong.
Now let's say your friend quickly flashes the numbers to you for only one second instead of a few seconds. You might find it more difficult to remember all the numbers, right? Your friend might say you remember fewer numbers correctly than before. This measurement allows us to know how much more challenging it is to remember numbers when they are flashed quickly.
Error exponents in hypothesis testing work similarly. In hypothesis testing, we have two competing claims: one claim we wish to prove and another claim we wish to disprove. For example, we might argue that drinking orange juice will make us smarter, and the opposing hypothesis is that drinking orange juice has no effect on intelligence.
We prove which claim is better by collecting data and determining how likely it is that one claim is right compared to the other. We use an error exponent to evaluate how confident we are that we picked the more accurate result.
To determine our error exponent, we look at how much data we have compared to how much knowledge it takes to know for sure. For example, much like it is easier to remember numbers when they are flashed slowly, we might be more confident in our hypothesis testing results if we have more data.
In summary, error exponents in hypothesis testing are a measure of how confident we are in the accuracy of our statistical conclusion based on the amount of available data.
Now let's say your friend quickly flashes the numbers to you for only one second instead of a few seconds. You might find it more difficult to remember all the numbers, right? Your friend might say you remember fewer numbers correctly than before. This measurement allows us to know how much more challenging it is to remember numbers when they are flashed quickly.
Error exponents in hypothesis testing work similarly. In hypothesis testing, we have two competing claims: one claim we wish to prove and another claim we wish to disprove. For example, we might argue that drinking orange juice will make us smarter, and the opposing hypothesis is that drinking orange juice has no effect on intelligence.
We prove which claim is better by collecting data and determining how likely it is that one claim is right compared to the other. We use an error exponent to evaluate how confident we are that we picked the more accurate result.
To determine our error exponent, we look at how much data we have compared to how much knowledge it takes to know for sure. For example, much like it is easier to remember numbers when they are flashed slowly, we might be more confident in our hypothesis testing results if we have more data.
In summary, error exponents in hypothesis testing are a measure of how confident we are in the accuracy of our statistical conclusion based on the amount of available data.