Null Hypothesis

Why we need a null hypothesis test?. Hypothesis testing is an important stage in statistics. The test evaluates two mutually exclusive statements about a population to determine which statement is better supported by the sample data drawn from the population. 

The term significance is coming from the hypothesis test. If you want to establish a significant difference in test objective need to include a hypothesis.

The main purpose of a statistical hypothesis testing is to determine whether there is enough statistical evidence in rejecting a null hypothesis, about a parameter.

What is a statistical hypothesis?

The statistical test of a hypothesis H is a procedure which makes one decide about acceptance or rejection of the hypothesis H.

Steps involved in statistical hypothesis

  1. Test Statistic
  2. Sampling distribution of test statistic
  3. Setting of hypotheses
  4. Inference about probable truth

Research Hypothesis Vs Statistical Hypothesis

Research Hypotheses: -Researcher postulates to meet his/her objectives.

Statistical hypothesis: -Testable formulations of research hypothesis about the population parameter.

A statistical hypothesis is a declaration about a population parameter.

Null Hypothesis

According to Fischer, any hypothesis tested for its possible rejection is called null hypothesis and its denoted as Ho. An alternative to the null hypothesis is called the alternative hypothesis and its denoted as H1.

Difference between simple vs composite hypothesis.

If a statistical hypothesis completely specifies a distribution known as a simple hypothesis otherwise composite hypothesis. In most cases H1 will be a composite hypothesis like µ≠µ0, µ<µ0, µ>µ0.

When testing a null hypothesis, we need to understand two types of errors also. There is a probability of committing an error in making a decision.

Types of errors 

Type1 Error and Type 2 Error

Type 1 Error: -Reject Ho when Ho is true

Type 2 Error: -Accept Ho when H1 is true

Usually, probability of type 1 error noted as α and type 2 error noted as β.

Type 2 error is more serious than type 1 error, that is why we need to minimize β even for considering certain risk with α usually 95%, 90%, or less.

The power of the test is more important in the hypothesis test. 1- β called as power of the test. The power of the test helps us to make a correct decision while rejecting a null hypothesis. 

The probability of type 1 error is called as the significance level. If the power of the test is too low, should choose a higher value of α like 0.1, 0.2, 0.3 etc.

How to do one sample analysis in R.

t-test complete information about assumptions, properties and how to perform.

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