Null hypothesis, Alternative hypothesis, Type I error, Type II error, P-value
Hello reader! I hope you are doing well. These topics are a little bit confusing in statistics so I will try to simplify these topics. Happy learning :)
So, first I am going to discuss why these topics are important?
These topics are Important because A hypothesis is a speculative explanation for a group of facts that can be tested by further inquiry. The null hypothesis and the alternative hypothesis are the two main categories. A problem is usually the starting point for a study. The researcher might then use these hypotheses to restate and clarify the study problem.
The null hypothesis and alternative hypothesis for the study problem should be expressed as a connection between two or more variables. The statements must express the relationship between two or more quantifiable variables, according to the requirements. For testing and describing relationships, the null hypothesis and alternative hypothesis should have obvious implications.
Null Hypothesis (Ho)
The null hypothesis is a common arithmetic theory that states that no statistical link or significance exists between two sets of observable data and measured events in a set of single, observed variables. The hypotheses are crucial in determining the significance of variations between experiments and data. The null hypothesis of no change is represented by Ho. It is assumed to be true unless evidence contradicts it.
Null Hypothesis (Ho) = No difference between groups being studied.
Alternative Hypothesis (H1)
In simple words, It is the opposite of the Null hypothesis means when the Null Hypothesis is rejected then we have to accept the Alternative hypothesis (H1).
The Alternative hypothesis is a common arithmetic theory that states that a statistical link or significance exists between two sets of observable data and measured events in a set of single, observed variables.
Alternative Hypothesis (H1) = There is a difference between groups being studied.
Note: A scientist/Researcher wants to know if there’s a link between exercise frequency and appetite. So, Many scientists often neglect null hypothesis in their testing.
Type I error
A type I error in statistical hypothesis testing is the incorrect rejection of a true null hypothesis (also known as a “false positive” finding or conclusion; example: “an innocent person is convicted”).
let’s clarify the above example, Suppose your friend is in jail and you know that he is innocent but there is no evidence that proves that he is innocent then your friend is convicted. This type of error Known as Type I error.
In one line Type I Error = Incorrectly reject Null hypothesis.
α (alpha) =Probability of Type I error.
Type II error
Type II error refers to the acceptance of a null hypothesis that is actually untrue (also known as a “false negative” finding or conclusion; for example: “a guilty person is not convicted”).
Type II error= Fail to reject the Null hypothesis when you should have to reject the Null hypothesis.
β (beta)=Probability of Type II error
Much of statistical theory is centered on reducing one or both of these errors, however total eradication of either is statistically impossible if the outcome is not caused by a known, observable causal process. The hypothesis test’s quality can be improved by using a low threshold (cut-off) value and adjusting the alpha (p) level. Medical science, biometrics, and computer science all benefit from understanding Type I and Type II errors.
Power
Probability of finding a difference between groups if one truly exists.
expression of Power =1-β
we can also say that Power is the probability of not making of Type II error. if β<20% then it is good for study.
some relationship that affects the Power, β, and Likelihood of Type II error
P-Value
The p-value in null hypothesis significance testing is the likelihood of getting test results at least as extreme as the actual results, assuming the null hypothesis is valid. A small p-value indicates that under the null hypothesis, such an extreme observed result would be extremely implausible. P-values of statistical tests are commonly reported in academic articles in a variety of quantitative domains. Because the specific meaning of p-value is difficult to grasp, it is widely misunderstood and has become a hot topic in metascience.
We can also define it as, Probability of obtaining a result at least as extreme as the current one, assuming the Null hypothesis is True.
P(observation|Null hypothesis if True) = Output
Interpreting P-Value
for LOW P -> Reject the NULL hypothesis.
for HIGH P -> Fail to reject NULL.
Rule of Thumb:
P < 0.05 -> statistically, the significance difference means the Null hypothesis is Incorrect.
P>0.05 -> No, statistically significant difference means the Null hypothesis is correct.
Note: P-value is the only tool that can only help us determine the observed data’s level of agreement or disagreement with the Null hypothesis.
As always, thanks for reading
