Statistics

Statistics

8.3 Basic Terms

• Null hypothesis (H 0 ): Is associated with a contradiction to an assumption to be tested. • Alternative hypothesis (H 1 ): Is associated to an assumption to be tested. • Region of acceptance: The values of the test which fail to reject the null hypothesis. • Critical region: The values of the test which the null hypothesis is rejected. • Critical value: The threshold value containing the boundaries of the regions in which the hypothesis will be accepted or rejected. • Power (1 - β): The probability of correctly rejecting the null hypothesis. The symbol β represents the false negative, or incorrectly rejecting the null hypothesis. The power test determines the sensitivity of the statistical test. • Significance level (α): The probability of incorrectly rejecting the null hypothesis. The symbol (α) represents the false positive (1 – α). • Statistical significance: Results are considered statistically significant the tested sample is inconsistent with the (null) hypothesis.

8.4 Common Statistical Tests

• One-sample test: Compare the sample to the population from which the hypothesis is drawn. • Two-sample test: Compare two samples, typically experimental and control samples. • Paired test: Compare two samples where it is impossible to control all variables that may influence the results. • Z-test: Compare the means of the data where normality and standard deviation are known; these are more tightly controlled statistical conditions. • T-test: Compare the means of the data where normality and standard deviation may not be known; these are more relaxed statistical conditions. • F-test: Also referred to the analysis of variance (ANOVA). F-tests are used to determine whether groupings of data by category are meaningful.

8.5 Types of Hypothesis Errors

• Type I error: Occurs when the null hypothesis is rejected when, in fact, it is true. o The probability of committing a Type I error is called the significance level, which is often shown with the alpha symbol, denoted by α. • Type II error: Occurs when one fails to reject a null hypothesis, when it in fact, is false. o The probability of not committing a Type II error is called the power of the test; this is often shown with the symbol Beta, denoted by β.

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