## Statistical hypothesis testing

### Statistical Hypothesis Testing

Statistical hypothesis testing forms a cornerstone of statistics, operating as a methodology for scrutinizing the legitimacy of a population-based claim with reference to a data sample. The strategy hinges on juxtaposing observed data with anticipated outcomes under a defined assumption known as the null hypothesis. Significant deviations in the observed data from the expected outcomes invite the potential rejection of the null hypothesis, leading to the acceptance of the alternative hypothesis.

### Steps in Hypothesis Testing

The journey of hypothesis testing navigates through several key milestones:
Formulate the null and alternative hypotheses: The null hypothesis (H0) assumes the absence of a significant difference or impact, whilst the alternative hypothesis (H1) contends with the claim under evaluation, contrary to the null hypothesis.
Choose a significance level: The significance level (α) represents the risk of discarding the null hypothesis when it stands true. Predominant significance levels include 0.05, 0.01, and 0.001.
Select a test statistic: The test statistic, a value standardized from the sample data, plays a pivotal role in determining the chance of observing the data under the null hypothesis.
Compute the p-value: The p-value signifies the probability of landing a test statistic as extreme or more so than the observed one, given the truth of the null hypothesis.
Make a decision: The crossroads of decision-making involve comparing the p-value with the predetermined significance level. If the p-value sinks below or matches the significance level, the journey veers towards the rejection of the null hypothesis in favor of the alternative. However, if the p-value overshadows the significance level, the null hypothesis remains intact.

### Types of Errors in Hypothesis Testing

The route of hypothesis testing can encounter two categories of errors:
Type I error: A Type I error is an unfortunate event where the null hypothesis is shunned even though it is true. The likelihood of stumbling upon a Type I error equates to the selected significance level (α).
Type II error: A Type II error is a scenario where the null hypothesis slips past rejection despite its falseness. The likelihood of a Type II error is symbolized by β, and the test's power is outlined as 1 - β.

### Common Statistical Tests

A suite of statistical tests is available for hypothesis testing, subject to the type of data and the specific claim being examined. Among them are:
t-test: Puts the means of two groups under scrutiny.
Chi-square test: Probes into the association interlinking categorical variables.
ANOVA: Investigates the means across more than two groups.
Correlation test: Appraises the strength and trajectory of the correlation between two continuous variables.
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