統計を英語で勉強する　その２

Continuing with the glossary of statistical terms from the lecture slides, here are the next 10 technical terms with their detailed descriptions:

11. Confidence Interval

• Definition: A range of values, derived from the statistics of observed data, that is likely to contain the value of an unknown population parameter. The interval has an associated confidence level that quantifies the level of confidence that the parameter lies within the interval.

• Application: Used to indicate the reliability of an estimate.

12. Hypothesis Testing

• Definition: A method of statistical inference used to decide whether a hypothesis about a parameter of a population is consistent with the data observed.

• Process: Involves the comparison of the observed data to what we would expect to see if the hypothesis were true, using a test statistic.

13. P-value

• Definition: The probability of obtaining an observed sample result (or more extreme) when the null hypothesis of a study question is true.

• Usage: A small p-value (typically ≤ 0.05) indicates strong evidence against the null hypothesis, so it is rejected.

14. Null Hypothesis (H0)

• Definition: A statement of no effect or no difference, used as a default hypothesis in statistical hypothesis testing.

• Characteristic: The null hypothesis is what is tested directly and is assumed to be true until evidence indicates otherwise.

15. Alternative Hypothesis (H1)

• Definition: The hypothesis that sample observations are influenced by some non-random cause. It proposes an effect or difference.

• Relation to Null Hypothesis: It is what a researcher seeks to prove, contrasting with the null hypothesis.

16. Type I Error

• Definition: The incorrect rejection of a true null hypothesis, also known as a "false positive." The probability of making a Type I error is denoted by alpha (α).

• Control: Setting a lower significance level (α) reduces the likelihood of this error.

17. Type II Error

• Definition: The failure to reject a false null hypothesis, also known as a "false negative." The probability of making a Type II error is denoted by beta (β).

• Mitigation: Increasing the sample size can help reduce the likelihood of this error.

18. Power of a Test

• Definition: The probability that the test correctly rejects a false null hypothesis (1 - β). It measures a test's ability to detect an effect or difference when one exists.

• Influence: Factors affecting power include the sample size, significance level, and the true effect size.

19. Sampling Distribution

• Definition: The probability distribution of a given statistic based on a random sample. It shows how the statistic would vary from sample to sample.

• Importance: It is foundational for calculating margins of error and confidence levels in inferential statistics.

20. Maximum Likelihood Estimation (MLE)

• Definition: A method of estimating the parameters of a statistical model. MLE finds the parameter values that maximize the likelihood of making the observations given the parameters.

• Application: Widely used in statistical modeling for parameter estimation.

These additional terms expand upon the fundamental concepts necessary for a deep understanding of statistical analysis and hypothesis testing. Each term plays a crucial role in the methodology and interpretation of statistical results.