Statistics Essentials for BIOL 3000 Flashcards

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Statistical analysis

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Process of estimating how a quantity changes, quantifying the uncertainty in that estimate, and assessing how likely you would obtain a similar result if the study were repeated. It provides a framework for drawing inferences from data while emphasizing biological interpretation. It relies on components like effect size, precision, and consistency to reach conclusions.

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P-value

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The probability of obtaining results at least as extreme as observed, assuming the null hypothesis is true: p = P(observed or more extreme | H0). A very small p-value suggests the observed outcome is unlikely under H0. The American Statistical Association notes that p-values do not measure the probability that a hypothesis is true, nor do they alone determine scientific conclusions; results should be reported with context and transparency.

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Confidence Interval

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A range of values calculated from sample data that likely contains the true population parameter (for example the mean) with a specified confidence level (such as 95%). It reflects the precision of the estimate and depends on the standard error. The 68 percent interval spans the middle 68 percent of the sampling distribution (within 1 standard error), while the 95 percent interval spans the middle 95 percent (within 1.96 standard errors).

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Standard Error

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The standard error is the standard deviation of the sampling distribution of a statistic, commonly the mean. It equals the sample standard deviation divided by the square root of the sample size: SE = \frac{s}{\sqrt{n}}. Roughly 68 percent of sample means fall within 1 SE of the observed mean, and about 95 percent within 1.96 SE for normal distributions.

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Test statistic

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A test statistic is a numeric measure such as t, F, or chi-squared that summarizes how well the observed data fit a null model. It captures the strength of evidence against the null hypothesis. Larger absolute values indicate greater inconsistency with the null.

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Type I error

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Type I error is the false positive, meaning the null hypothesis is rejected when it is true. It is controlled by the significance level alpha, commonly 0.05. In practice, lowering alpha reduces false positives but may reduce power to detect real effects.

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Type II error

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Type II error is the false negative, meaning failing to reject a false null hypothesis. The power of a test is defined as 1 minus beta, where beta is the probability of a Type II error. Increasing sample size or the true effect size increases power and reduces beta.

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Effect size

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Effect size measures the magnitude of an observed effect independent of sample size. It complements p-values by indicating practical importance. Common measures include Cohen's d, correlation coefficient r, and odds ratio (OR), depending on study design: d, r, OR.

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Hypotheses

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Hypotheses are plausible explanations for why an observed pattern exists. They guide the design of tests and predictions and should be developed from existing literature. For each hypothesis, generate at least one test to evaluate support for it.

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Predictions

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Predictions are expected outcomes of a test under a hypothesis, specifying the direction of relationships or outcomes. They enable researchers to determine whether data align with a hypothesis and to plan appropriate tests.

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Null hypothesis

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Null hypothesis H0 states that there is no effect or no difference. Statistical tests assess whether data provide enough evidence to reject H0 in favor of an alternative. The p-value quantifies the incompatibility of the data with H0 given a model.

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Alternative hypothesis

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Alternative hypothesis Ha posits that an effect exists or that relationships differ from zero. Tests aim to provide evidence against H0 in favor of Ha, with directionality depending on one-tailed or two-tailed predictions.

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Fisher

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Sir Ronald Aylmer Fisher helped inaugurate modern statistical thinking. He described the p-value as a convenient threshold for deciding what to ignore, emphasizing that significance should not be treated as proof and that replication matters. His work provides historical context for significance testing.

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ASA statements

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American Statistical Association statements describe that p-values indicate incompatibility with a model but do not measure the probability that a hypothesis is true, and that conclusions should not rely solely on crossing a threshold. They advocate full reporting and transparency.

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Observed pattern

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An observed pattern is the empirical relationship or trend in data that motivates hypotheses. It guides hypothesis generation and the selection of tests to explain it, often by translating statistical results into biological meaning.

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Study design steps

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Study design involves: 1) proposing hypotheses, 2) listing potential tests for each hypothesis, 3) making predictions for each test, 4) determining which tests can distinguish among hypotheses, and 5) consulting literature for supporting studies. This iterative process aims to clarify explanations before data collection.

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Direction

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Direction refers to the expected sign or slope of an effect (positive or negative). Predictions should specify the direction so tests can discern whether the data align with the proposed hypothesis.

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Precision

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Precision describes how tightly an estimate is known, reflected in the width of confidence intervals and the size of standard errors. Greater precision means narrower intervals and more reliable estimates.

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Evidence of consistency

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Evidence of consistency is the degree to which results agree across tests, data subsets, or replications. Consistency strengthens conclusions by reducing the likelihood that findings arise from random variation.

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Confidence Level

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The confidence level is the probability that the interval method would capture the true parameter if repeated many times, e.g., 95%. Higher levels yield wider intervals, trading precision for a broader claim about containing the true value. CI calculations use this level to interpret results.