Hypothesis tests

Hypothesis Testing

Overview and Concepts

Hypothesis testing is a fundamental procedure in statistics, used to determine whether there is enough evidence in a sample of data to infer that a certain condition is true for the entire population.
A hypothesis is a claim or a statement about a property of a population, often about parameters like the population mean, variance, or distribution form.
Hypothesis testing typically involves two competing hypotheses: the null hypothesis, denoted by H₀, and the alternative hypothesis, denoted by H₁ or Ha.
The null hypothesis represents a statement of no effect or no difference, while the alternative hypothesis represents the claim to be tested.
The level of significance (often denoted by α) is the probability of the study rejecting the null hypothesis, given that it were true. Commonly used values for significance are 0.05 (5% risk), 0.01, and 0.001.
If the p-value is less than or equal to the significance level, you reject the null hypothesis and accept the alternative hypothesis. Conversely, if the p-value is greater than the significance level, you fail to reject the null hypothesis.

Steps involved in Hypothesis Testing

Formulate the null and alternative hypotheses: construct specific statements about the population parameter being tested.
Choose a significance level: usually at 0.05 or 0.01, representing your willingness to accept a type I error.
Compute the test statistic: based on the null hypothesis, calculate a test statistic that will determine if the null hypothesis is to be rejected. This could be a z-score (for a z-test), a t-score (for a t-test), etc.
Determine the critical value or p-value: find the critical value for the test statistic in a table (or use a normal calculation for p-value). This represents the probability of observing a value as extreme (or more) under the null hypothesis.
Compare and make a decision: if the test statistic falls into the critical value(s) or if the p-value is less than your alpha (significance level), reject the null hypothesis.

Types of Errors

A hypothesis test can lead to two types of errors. A Type I error occurs when the null hypothesis is true, but is incorrectly rejected. It’s the false alarm.
A Type II error happens when the null hypothesis is false, but it is wrongly failed to be rejected. It’s a missed opportunity.

Real-World Applications of Hypothesis Testing

Hypothesis testing is vital in verifying assumption and theories, and is commonly used in fields that demand decision making with empirical evidence, such as business, economics, medicine, psychology, and sociology.

Remember, hypothesis testing is all about making inferences from data. The data never proves any hypothesis to be true, rather it can just offer evidence against a hypothesis by favouring the alternative.