**Errors in Statistics**

*(The Type I and Type II Error in Statistics)*

*“An error does not become truth by reason of multiplied propagation,
nor does truth become error because nobody sees it…”
*

**Mahatma Gandhi**

For the better understanding of statistical errors, it is essential to understand the concept of ‘**Level of significance**’, ‘**Null hypothesis** and ‘**Alternate hypothesis**’.

**What is ‘Level of Significance?**

**What is ‘Level of Significance?**

Ø **Definition**: *The Level of significance is the probability of rejecting the null hypothesis in a statistical test when it is true.*

Ø The ‘Level of Significance’ in statistics is conventionally set to **0.05** to **0.01**.

Ø The level of significance in statistics denotes the **confidence level** of an investigator to accept or reject a null hypothesis in the statistical testing.

Ø A level of significance 0.05 denotes 95% confidence in the decision whereas; the level of significance 0.01 denotes 99% confidence.

Ø Such a low level of significance is selected to reduce the erroneous rejection of a **null hypothesis** (H_{0}) after the statistical testing.

**What is Null hypothesis?**

**What is Null hypothesis?**

Ø **Definition**: *The Null hypothesis is a statement that one seeks to nullify with evidence to the contrary.*

Ø The ‘Null hypothesis’ is denoted as H_{0}.

Ø Most commonly, the null hypothesis is a statement that the phenomenon being studied produces NO effect or makes NO difference.

Ø Example: (a study to investigate the effect of urea on the size of leaf in rice plants)

**Null hypothesis**: H_{0} – *Urea does NOT have any effect on the leaf size of rice plants.*

Ø The null hypothesis is always constructed in a negative sense.

Ø The statistical tests only test the possible acceptance or rejection of the null hypothesis.

**What is an Alternate hypothesis?**

**What is an Alternate hypothesis?**

Ø **Definition**: *The Alternate hypothesis is a statement created in the negation of the null hypothesis.*

Ø Alternate hypothesis is denoted as H_{1}.

Ø Usually, the alternate hypothesis is a statement that the phenomenon being studied produces some effect or makes some differences.

Ø Example: (a study to investigate the effect of urea on the size of leaf in rice plants)

** Alternate hypothesis: H1** – *Urea have some effects on the leaf size of rice plants.*

Ø The alternate hypothesis is always constructed in a positive sense. (negation of the negative null hypothesis)

Ø If a statistical test rejects the null hypothesis, the investigator has to accept the alternate hypothesis.

**What are ‘statistical errors’?**

**What are ‘statistical errors’?**

Ø There are two situations in which the decision made on data in the statistics become wrong.

Ø They are called as the **Errors in Statistics** or **Statistical Errors**.

Ø There are **Two** types of statistical errors, they are:

**(1). Type I Error**

**(2). Type II Error**

**What is Type I error?**

**What is Type I error?**

Ø If an H_{0} is true, it should NOT be rejected by the statistical test.

Ø *Suppose an investigator made a decision to reject a true H0, then he/she has committed an error, called the Type I error*.

Ø **Type I error is the wrong rejection of a true null hypothesis.**

Ø The Type I error is also referred to as the ‘**False Positive**’.

Ø Because the type I error is detecting an effect that is not present.

**How to avoid or reduce the type I error?**

Ø The probability of committing type I error is specified by the **level of significance**.

Ø If a high level of significance is selected (0.1 or 0.2) in the statistical test, the probability of rejecting a null hypothesis increases.

Ø This means that, at high significance level, the chance of committing the type I error is high.

Ø Thus in order to avoid or reduce the type I error, a fairly **low level of significance** is selected (0.05 or 0.01).

**What is Type II error?**

**What is Type II error?**

Ø If the H_{0} is false, it should be rejected by the test of hypothesis.

Ø If an investigator selects a significance level (0.005 or 0.001) much lower than the conventional level, then the probability of rejecting a wrong null hypothesis reduces.

Ø Thus the investigator is said to be committed the **type II error**.

Ø **Type II error is the wrong acceptance of a false (wrong) null hypothesis.**

Ø The type II error is also referred as ‘**false negative**’.

Ø Because the type II error is the failure to detect an effect that is actually present.

**How to avoid or reduce the type II error?**

Ø If the null hypothesis in hypothesis testing is failed to be rejected when it should have been rejected, the type II error is said to have been committed.

Ø Lower levels of significance increase the chance of type II error in statistical test.

Ø Thus in order to avoid the type II error, very low level of significance should not be selected in the statistical test.

*Key questions*

*1. What is level of significance?
2. What is null hypothesis? Give an example
3. What is alternate hypothesis? Give an example
4. What are statistical errors?
5. What is type I error?
6. How to reduce the chance of committing type I error?
7. What is type II error
8. How to reduce the chance of committing type II error?*

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