Likelihood ratio test
Okay kiddo, let me explain what a likelihood ratio test is using some simple examples.
Imagine that you and your friend want to guess the weight of a big watermelon. You guess that it weighs 10 pounds, and your friend thinks it's 12 pounds. We could write these guesses down as two different 'hypotheses' about the weight of the watermelon.
Now imagine that we weigh the watermelon and find out that it actually weighs 11 pounds. This is the 'data' that we have gathered.
The likelihood ratio test asks a very important question: How much better is your guess (10 pounds) than your friend's guess (12 pounds) at explaining the data we have (the weight being 11 pounds)?
To answer this question, we need to calculate something called the 'likelihood' for each hypothesis. The likelihood is a number between 0 and 1 that tells us how well each hypothesis explains the data. In this case, the likelihood for your guess would be higher than the likelihood for your friend's guess, because your guess is closer to the actual weight of the watermelon.
The likelihood ratio test takes the ratio of these two likelihoods (your likelihood divided by your friend's likelihood). If the ratio is very large, it means that your guess is much better than your friend's guess at explaining the data - in this case, it means that your guess is 'significantly' better. If the ratio is close to 1, it means that both guesses are equally good (or bad) at explaining the data.
So, to summarize: The likelihood ratio test helps us figure out which hypothesis (guess) is better at explaining the data we have. We do this by calculating the likelihoods for each hypothesis, and then taking the ratio between them. If the ratio is very large, it means that one hypothesis is significantly better than the other. If the ratio is close to 1, it means that both hypotheses are equally good (or bad).
Imagine that you and your friend want to guess the weight of a big watermelon. You guess that it weighs 10 pounds, and your friend thinks it's 12 pounds. We could write these guesses down as two different 'hypotheses' about the weight of the watermelon.
Now imagine that we weigh the watermelon and find out that it actually weighs 11 pounds. This is the 'data' that we have gathered.
The likelihood ratio test asks a very important question: How much better is your guess (10 pounds) than your friend's guess (12 pounds) at explaining the data we have (the weight being 11 pounds)?
To answer this question, we need to calculate something called the 'likelihood' for each hypothesis. The likelihood is a number between 0 and 1 that tells us how well each hypothesis explains the data. In this case, the likelihood for your guess would be higher than the likelihood for your friend's guess, because your guess is closer to the actual weight of the watermelon.
The likelihood ratio test takes the ratio of these two likelihoods (your likelihood divided by your friend's likelihood). If the ratio is very large, it means that your guess is much better than your friend's guess at explaining the data - in this case, it means that your guess is 'significantly' better. If the ratio is close to 1, it means that both guesses are equally good (or bad) at explaining the data.
So, to summarize: The likelihood ratio test helps us figure out which hypothesis (guess) is better at explaining the data we have. We do this by calculating the likelihoods for each hypothesis, and then taking the ratio between them. If the ratio is very large, it means that one hypothesis is significantly better than the other. If the ratio is close to 1, it means that both hypotheses are equally good (or bad).
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