# Hypothesis Testing

The main purpose of statistics is to test a hypothesis. A hypothesis is an**educated guess**that is made on the basis of some evidence.

**Hypothesis testing**is a form of inferential statistics that allows you to draw conclusions about an entire population based on a representative sample. The

**hypothesis-testing procedure**involves using sample data to determine whether or not

**Null Hypothesis (H0)**can be rejected. If Null Hypothesis is rejected, the statistical conclusion is that the

**Alternative Hypothesis (Ha)**is true.

**Key terms and concepts :**

## Null Hypothesis (H0)

The**Null Hypothesis**states that there is no relationship between two population parameters. It denoted by H0 symbolizes the null hypothesis of no difference. If the

**null hypothesis**returns false, it means that there is a relationship in the measured phenomenon. So, researchers work to reject, nullify or disprove the

**null hypothesis**. If the hypothesis shows a relationship between the two parameters, the outcome could be due to an experimental or sampling error.

## Alternative Hypothesis (H1 or Ha)

The**Alternative Hypothesis**, denoted by H1 or Ha, defines there is a statistically important relationship between two variables. This means that a population parameter is smaller, greater, or different than the hypothesized value in the

**null hypothesis (H0)**. The alternative hypothesis is what you might believe to be true or hope to prove true. It is a claim about the population that is contradictory to H0 and what you conclude when you reject H0. In most cases, the

**alternate hypothesis**will just be the opposite of the null hypothesis.

## One-tailed and Two-tailed tests

In a Statistical Test, the tail refers to the**end of the distribution**of the test statistic for the particular analysis that you are conducting. A

**One-tailed tests**allow for the possibility of an effect in one direction, so that it is either greater than or less than a certain value, but not both. Also, it completely disregarding the possibility of a relationship in another direction. A

**two-tailed test**, also known as non-directional , is a method in which the critical area of a distribution is two-sided and tests whether a sample is greater or less than a range of values. It is associated to an alternative hypotheses for which the sign of the potential difference is unknown. It is used in null-hypothesis testing and testing for

**statistical significance**.

## Level of significance (alpha)

The**significance level**, also denoted as alpha, is the probability of rejecting the Null Hypothesis (H0) when it is true and conclude that the effect is

**statistically significant**. For example, a significance level of 0.05 indicates a 5% risk of concluding that a difference exists when there is no actual difference. If a test of significance gives a p-value lower than or equal to the

**significance level**, the Null Hypothesis (H0) is rejected at that level.

## P-value

A**p-value**helps you to determine the significance of your results in relation to the null hypothesis. Smaller the p-value, the stronger the evidence that you should reject the

**null hypothesis**. If the p-value is ( < = 0.05) , then the null hypothesis is rejected in favour of the alternative hypothesis. And, if the P-value is ( > 0.05) , then the null hypothesis is not rejected.

## Z-Test

Z-test is a**statistical tool**used to determine whether two sample means are approximately the same or different when their variance is known and the

**sample size**is large (should be > = 30). Particularly the mean in a sample from a normally distributed population or between two independent samples.

## T-Test

A t-test (also known as Student's t-test) is a**statistical hypothesis**test that is used to compare the means of two groups. It may be used to evaluate whether a single group differs from a known value (one-sample t-test), whether two groups differ from each other (independent two-sample t-test), or whether there is a significant difference in

**paired measurements**(paired t-test).

## ANOVA (Analysis of Variance)

An**ANOVA**test is a way to find out if survey or experiment results are significant. It assess the importance of one or more factors by comparing the response variable means at the

**different factor levels**. Also, it help you to figure out if you need to reject the null hypothesis or accept the

**alternate hypothesis**. ANOVAs are used in three ways: one-way ANOVA, two-way ANOVA, and N-way ANOVA.

## Errors in Statistical Tests

Two potential types of statistical error are**Type I Error**and

**Type II Error**. Type I error, also known as a

**"false positive"**: the error of rejecting a null hypothesis when it is actually true. Type II error, also known as a

**"false negative"**: the error of not rejecting a null hypothesis when the alternative hypothesis is the true state of nature.

**Related Topics**