I did a biology undergraduate degree and often did reports where would statistically analyse our results. P value of less than 0.05 shows that the results are statistically significant. How do these tests actually know the data is significant? For example we might look at correlation and get a significant positive correlation between two variables. Given that variables can be literally anything in question, how does doing a few statistical calculations determine it is significant? I always thought there must be more nuance as the actual variables can be so many different things. It might show me a significant relationship for two sociological variables and also for two mathematical, when those variables are so different?
In: Mathematics
>For example we might look at correlation and get a significant positive correlation between two variables. Given that variables can be literally anything in question, how does doing a few statistical calculations determine it is significant?
I don’t think anyone is answering this, but it’s because you’re assuming that the average of both random variables are following a normal distribution. This is because of the Central Limit Theorem which says that as your sample gets arbitrarily large, the probability distribution of the average of all random variables will follow a normal distribution, even if the variables themselves aren’t normally distributed.
So, for example, flipping a coin is 50% heads or 50% tails. The probability of a single coin flip isn’t normally distributed at all, and follows a binomial distribution. However, if you flip 10000 coins and count how many heads you get, you will find that it follows a bell-curve. 50% of the time you’ll get 5000 heads or less, 68% you’ll get a value within 1 standard deviation of 5000, etc. And this works with ANYTHING from ANY Probability distribution as long as n gets large enough. So for real life problems we don’t actually need to know the probability distribution of single events as long as we take a large enough sample size! (well, in general, I know there are other normality tests you can do but I’m not getting into that)
So what you’re doing with a p-test is taking a sample and assuming it’s normal, then comparing that to the theoretical normal distribution with a given mean/standard deviation. The p-test shows the probability that your data DOESN’T follow that hypothetical normal distribution with the given mean, and instead follows some other (normal) distribution with a different mean.
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