Null Hypothesis:
https://www.reddit.com/r/explainlikeimfive/comments/7q46fd/eli5_what_is_the_null_hypothesis/
Null Hypothesis basically says: Nothing is wrong - everything is fair - an event happened merely by chance
https://inst.eecs.berkeley.edu/~cs174/sp08/lecs/lec10/lec10.pdf
Let's say: You roll a die 5 times, everytime you get 6. You might think something is wrong with the die.
So,
The Null Hypothesis becomes: The die is fair.
Now we do testing and see if it is actually fair.
To prove this right/wrong we run a likelihood experiment.
So let's say we try to test the hypothesis by running experiments.
We take the data and see if it makes sense with the distribution we assumed.
Let's say we assume normal distribution
We have a value and we find out what's the probability that the value occurs,
if it's really low, then we reject null hypothesis
else we assume it's random
p-value is the value that we get the probability that it occurred
so if p value is 0.05 or less we reject null hypothesis
youtube.com/watch?v=-FtlH4svqx4
Probability Vs Likelihood
Probability : Given a distribution what is the chance of something occurring?
Say we have a sample data, we have heights of different people and we fit it to a normal distribution with mu=10, sigma=0.6
So, now given this distribution,
P(h>150 | mu=10 and sigma=0.6) ---> This is probability
Likelihood : Given data, is the distribution correct? Or given data, what is the probability it belongs to a distribution
P(mu=10 and sigma=0.6 | h>150) ---> This is likelihood
Probability is used to finding the chance of occurrence of a particular situation, whereas Likelihood is used to generally maximizing the chances of a particular situation to occur.
Probability refers to the chance that a particular outcome occurs based on the values of parameters in a model.
Likelihood refers to how well a sample provides support for particular values of a parameter in a model.
When calculating the probability of some outcome, we assume the parameters in a model are trustworthy.
However, when we calculate likelihood we’re trying to determine if we can trust the parameters in a model based on the sample data that we’ve observed.
https://medium.com/swlh/probability-vs-likelihood-cdac534bf523
https://www.statology.org/likelihood-vs-probability/