# 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?

Ø  DefinitionThe 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 (H0) after the statistical testing.

### What is Null hypothesis?

Ø  DefinitionThe Null hypothesis is a statement that one seeks to nullify with evidence to the contrary.

Ø  The ‘Null hypothesis’ is denoted as H0.

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: H0Urea 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?

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

Ø  Alternate hypothesis is denoted as H1.

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: H1Urea 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’?

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?

Ø  If an H0 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?

Ø  If the H0 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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