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 :

Hypothesis Testing in statistics

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.


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 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.


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.