Hypothesis Testing in Statistics.
Hypothesis — it is an assumption or an idea that can be considered to check whether it's true or not.
What Is Hypothesis Testing?
Hypothesis testing in Statistics is an assumption about a population parameter, experiment, or survey. This assumption may or may not be true.
Inferential statistics are based on Hypothesis Testing.
A hypothesis test is a formal statistical test we use to reject or fail to reject
a statistical hypothesis.
It is generally used when we were to compare:
1. a single group with an external standard
2. two or more groups with each other
Types of Hypothesis Testing:
There are two types of statistical hypotheses:
- Null hypothesis- A population parameter (such as the mean, standard deviation, and so on) is equal to a hypothesized value, according to the null hypothesis(Ho).
Ho generally states =,<=,>=
2. Alternate hypothesis-The alternative hypothesis says that a population parameter is less, more, or different than the null hypothesis’s hypothesized value.
The alternative hypothesis is what you believe or want to prove to be correct.
H1 or Ha generally states <,>,!=
Note:- The Hypothesis test always deals with rejecting the Null Hypothesis or fails to reject the Null Hypothesis.
Level Of Significance:
The significance level, or alpha (α), is a value that the researcher sets in
advance as the threshold for statistical significance.
The p-value(probability value) determines the statistical significance
Usually, the significance level(α) is set to 0.05 or 5%
The rejection of the null hypothesis is based on this value.
Confidence Interval:
There are two aspects of a confidence interval:
Confidence: It indicates the level of surety we wish to attain
Interval: It indicates a range of values that our estimator can take.
A confidence interval displays the probability that a parameter will fall
between a pair of values around the mean.
Confidence intervals measure the degree of uncertainty or certainty in a
sampling method.
The confidence interval of 95% states that the chances or probability of the statement being accurate is 95% and the remaining 5% is the error probability.
For the Sensitive domain, the confidence interval increases as more accuracy are taken into consideration.
Types of Errors:
The Errors are of 2 types-
1. Type I
2. Type II
Type I Error: A type 1 error, often referred to as a false positive, means we try
to reject the null hypothesis although the hypothesis is “True”.
Type II Error: A type II error commonly said as a false negative happens when a researcher fails to reject a true null hypothesis.
Example: Suppose a teacher evaluates the examination paper to decide whether a student passes or fails.
H0: Student has passed
H1: Student has failed
Type I error will be the teacher failing the student (reject H0) although the student has scored passing marks(H0 was true).
Type II error will be the case where the teacher passes the student(do not reject H0) although the student did not score the passing marks(H1 is true).
Interpretations:
The hypothesis test deals with finding out whether assumptions for the particular tests are true or not.
The P-value plays an important role in finding out the rejection of the null
hypothesis.
The P-value is similar to the significance level taken into consideration.
When the p-value is low p (≤ 0.05), it indicates that the null hypothesis for the assumptions is to be rejected. In this case, the alternative hypotheses are taken into consideration.
When the p-value is high p (> 0.05), it indicates that it fails to reject the null
hypothesis.
The p-value is the evidence against a null hypothesis.