Hypothesis testing in Statistics Geography

1. Introduction:

Hypothesis testing is a statistical tool. We use it in making statistical decisions by using different experimental data. Ronald Fisher, Karl Pearson, Jerzy Neyman, and E. Pearson are the famous personalities who introduce Hypothesis testing in their statistical analysis. It is basically an assumption that we make about the population parameter. A hypothesis is an intellectual or educated guess about something in the world around us. Each and every hypothesis should be testable, either by experiment or observation. For example, we can say- “Arsenic album will work better for preventing COVID-19 if it is used in a recommended dose”. So, today we will be learning more about Hypothesis testing in Statistics Geography.

2. Syntax of hypothesis statement:

When we go to propose a hypothesis, we remember the form or syntax of the hypothesis.

The syntax is:

It will be:  If > Subject (I/we/you/someone) > do any action (independent variable) > then > will happen (result) > statement dependent variable.

Example:

 a. If we (use the Arsenic album in a recommended dose) then (COVID-19 can be prevented).

 b. If I (increase the amount of water to a plant) then (it will increase in size).

 c. If Amal (gives exams at noon instead of 7 am) then (his test scores will improve).

 d. If you (look in the equatorial region) then (you will find more new species).

 e. If Government (extended lockdown twice per week) then (COVID-19 positive rate will decrease).

A good hypothesis statement should:

  • According to the University of California, a hypothesis statement includes an “if” and “then” statement.
  • Include both the independent and dependent variables in a hypothesis statement.
  • The hypothesis statement will be testable by experiment, survey, or other scientifically sound technique.
  • For engineering or programming projects hypothesis statements have design criteria.
  • The hypothesis statement will be based on information in prior research. It may be yours or someone else’s.

3. Terminology and concepts:

i) Null hypothesis: 

A null hypothesis is a statistical hypothesis in which there are no significant differences exist between the set of variables.

The null hypothesis is always an accepted fact. It is the original or default statement that is tested. We can reject a null hypothesis, but it cannot accept just on the basis of a single test.

Simple examples of null hypotheses which are true. They are:

  • Everest is the highest peak in the world.
  • Excluding Pluto, there are 8 planets in our solar system.
  • Taking alcohol can increase our risk of liver problems.
  • Generally, in a null hypothesis it is the observation. It is due to a chance factor. 
  • We express the null hypothesis by; H0 or Ha (H-zero or H-a): μ1 = μ2, which shows that there is no difference between the two population means.

ii)  Alternative hypothesis: 

The alternative hypothesis is a statement in which some statistical significance between two measured or tested phenomena or observations.

It is contradictory to the null hypothesis; the alternative hypothesis shows that observations indeed are the result of a real effect. We represent it by H1 (H-one) or Ha (H-a).

The acceptance of the alternative hypothesis depends upon the rejection of the null hypothesis. Generally until and unless the null hypothesis is rejected, an alternative hypothesis cannot be accepted.

iii) Level of significance: 

It refers to the degree of significance in which we accept or reject the null hypothesis.  100% accuracy is not possible for accepting or rejecting a hypothesis, so we, therefore, select a level of significance, and that is usually 5%.

iv) Error: 

Generally, in most cases, we consider two types of errors in hypothesis testing.

Type I error: 

When we reject the null hypothesis, though that hypothesis was true, then a type I error is found.   It is denoted by alpha (α).  In hypothesis testing, the normal probability curve that shows the critical region is called the alpha region.

Different regions in Normal Probability Curve

Figure1. Different regions in Normal Probability Curve

Type II errors: 

We accept the null hypothesis when it is false. It is a type II error. It is denoted by beta (β).  In Hypothesis testing, the normal probability curve that shows the acceptance region is called the beta region.

Errors in Hypothesis
Errors in Hypothesis

Figure 2. Errors in Hypothesis

v) Power: 

We generally consider the probability of correctly accepting the null hypothesis.  1-beta is the power of the analysis in hypothesis testing.

vi) One-tailed test: 

When we see, the given statistical hypothesis is one value like H0: μ1 = μ2. it is the one-tailed test.

vii) Two-tailed test: 

When we see, the given statistics hypothesis assumes a less than (<) or greater (>) than value, it is called the two-tailed test.

viii) P-value: 

In hypothesis testing, P-value is the calculated probability of the null hypothesis (H0 )is true. In a statistical hypothesis, we perform a set of mathematical/statistical calculations to estimate the probability of what we are observing, given the H0 is really true.

If the P-value is lower than the predefined significant level (alpha significant level), then we reject the null hypothesis (H0) in favor of the alternative hypothesis (H1) because there is sufficient evidence to prove the null hypothesis (H0) is wrong. (P-value will discuss elaborately in the T-Test Video lecture)

4.  Area of acceptance & Rejection of Null Hypothesis:

Area of acceptance & rejection of Null Hypothesis.
Area of acceptance & rejection of Null Hypothesis.

Figure 3. Area of acceptance & rejection of Null Hypothesis.

5. Hypothesis testing in Statistics:

  • In statistics, it is a way for us to test the results of a survey or experiment to see if we have meaningful results. We basically test whether our results are valid by figuring out the odds, or our results have happened by chance. If our results may have happened by chance, the experiment would not be repeatable.
  •  At first, we have to identify our null hypothesis. Then it will be easier. All of us should need to do:
  • Figure out our null hypothesis,
  • State our null hypothesis,
  • Choose what kind of test we need to perform,
  • We support or reject the null hypothesis.

6. Examples of Hypothesis testing in Statistics:

A research scholar thinks that, if COVID-19 positive patients take vapor to inhale twice a day (instead of 4 times), their recovery period will be longer. An average recovery time for COVID-19 positive patients is 3.5 weeks.

                The hypothesis statement in this question is that the researcher believes the average recovery time is more than 3.5 weeks. In mathematical terms – H1: μ > 3.5

                Now, the researcher will need to state the null hypothesis. The null hypothesis was, “if the vapor inhales time decrease, then the recovery period will be longer for COVID-19 positive patients”.

                If the researcher is wrong after the sufficient experiment and test then the null hypothesis is rejected and the alternative hypothesis is accepted.

                From the above example, if the researcher is wrong then the recovery time is less than or equal to 3.5 weeks. In the mathematical expression, that is: H0 : μ ≤ 3.5, Error Type II takes place here.

                So, here we should reject the null hypothesis and accept the alternative hypothesis.

  • Mathematical expression for decisions making:
•	Mathematical expression for decisions making:
Mathematical expression for decisions making:

Figure 4. Mathematical expression for decisions making

7.Comparison of two Hypothesis:

Comparison of two Hypothesis
Comparison of two Hypothesis

Figure 5. Comparison of two Hypothesis

8. Conclusion:

There are two outcomes of a statistical test.

First- A null hypothesis is rejected and an alternative hypothesis is accepted.

Second- The null hypothesis is accepted, on the basis of the evidence.

Conclusion table for acceptance & rejection.

Figure 6. Conclusion table for acceptance & rejection.

Video on Hypothesis testing in Statistics:

Here is my video on hypothesis testing, you can watch it for a better understanding and concept.

Video

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9. Homework Assignments for Hypothesis testing in Statistics

HQ1. What is Hypothesis Testing? Explain the different types of hypotheses.  

HQ2. Discuss the acceptance and rejection area of the null hypothesis with a diagram.

HQ3. Figure out a null hypothesis for an example and explain its acceptance or rejection.

Advanced short answer questions(AQ) (Answer expected on the comment box of this article) •

AQ1. What will be the name, if one value in the given statistical hypothesis is like H0: μ1 = μ2?

AQ2. Write an example of a good hypothesis statement.

AQ3. A null hypothesis is true yet we reject it. What type of error it is?

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