Inferential Statistics
Hypothesis testing, confidence intervals, p-value, t-test, chi-square, ANOVA, linear regression
1What is the null hypothesis (H₀) in hypothesis testing?
What is the null hypothesis (H₀) in hypothesis testing?
Answer
The null hypothesis (H₀) is the default statement that assumes no effect or significant difference exists. It is the hypothesis we seek to reject or fail to reject based on the collected data. For example, H₀ might state that a new treatment has no effect compared to a placebo. The statistical test evaluates whether the data provides sufficient evidence to reject this hypothesis in favor of the alternative hypothesis (H₁).
2What does the p-value represent in a statistical test?
What does the p-value represent in a statistical test?
Answer
The p-value is the probability of obtaining a result at least as extreme as the one observed, assuming the null hypothesis is true. A low p-value (typically < 0.05) indicates that the observed data is unlikely under H₀, leading to its rejection. Note: the p-value is not the probability that H₀ is true, nor is it the probability that results are due to chance.
3What is a Type I error in inferential statistics?
What is a Type I error in inferential statistics?
Answer
A Type I error (false positive) occurs when we reject the null hypothesis when it is actually true. The significance level α (often 0.05) represents the maximum acceptable probability of making this error. For example, concluding that a drug is effective when it is not constitutes a Type I error. This error is controlled by the choice of significance level.
What is a Type II error in inferential statistics?
What does a 95% confidence interval represent?
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