Experimental Biology: Inferential Statistics and Hypothesis Testing

This set of vocabulary flashcards covers the fundamental concepts of inferential statistics, hypothesis testing, error types, and experimental controls as presented in the Experimental Biology lecture.

Statistics

A branch of mathematics dealing with the collection, analysis, interpretation, and presentation of numerical data.

Descriptive Statistics

The branch of statistics that collects, organises, and describes data from a target population.

Inferential Statistics

The practice of using sampled data to draw conclusions, make predictions, or infer something about a larger population.

Inferential Framework

A series of logical steps and tests used to build knowledge, including observations, models, hypotheses, null hypotheses, experimental design, and interpretation.

Hypothesis

An idea or explanation that is tested through study, experimentation, and analysis of data via statistics.

Null Hypothesis ($H_0$)

A statement proposing that no difference or statistical significance exists between two or more populations; it is the hypothesis put to the test for potential rejection.

Alternative Hypothesis ($H_1$ or $H_a$)

A statement proposing that a phenomenon is occurring due to non-random causes; it is accepted if the Null Hypothesis is rejected.

Falsifiability

The logical possibility that an assertion, hypothesis, or theory can be shown to be false by an observation or experiment.

Type I Error

A 'false positive' occurring when the null hypothesis is actually true, but the statistical test indicates it should be rejected.

Type II Error

A 'false negative' occurring when the null hypothesis is actually false, but the test fails to determine it to be significant.

P-value

The probability value that determines the likelihood that the null hypothesis is true; typically a cut-off of $< 0.05$ is used for rejection.

Probability

A quantitative description of the likelihood associated with various outcomes, represented as a number between $0$ (impossibility) and $1$ (certainty).

Probabilistic Reasoning

The process of knowing the population characteristics and predicting the likelihood of a specific sample outcome.

Statistical Reasoning

The process of observing a random sample to estimate the proportions or characteristics of the whole population.

Expectation

The probability-weighted sum of all possible values in a random variable's support, representing the average of many independent samples.

Variance (\text{\sigma}^2)

A measurement of the spread or degree of dispersion of data points around the sample mean.

Biological Variation

Variance in data caused by natural phenomena such as genetics or environmental factors.

Systematic Error

A consistent difference, also known as bias, between the recorded value and the true value.

Control Group

A population examined in parallel to the treatment group to remove the effects of all factors except the specific variable being investigated.

Experimental Controls

Any environmental factors (e.g., light, temperature) fixed by the experimenter to isolate the effect of the manipulated variable.

Procedural Controls

A group treated exactly like the experimental group, including dummy treatments like placebos, to control for the effect of the experimental process itself.

Statistical Controls

An alternative to fixing environmental factors where researchers measure biotic and abiotic variables to extract and remove their effects during data analysis.

Historical Controls

A control group derived from previously collected data when only one physical experimental group currently exists.

Sample Variance Formula

The formula used to estimate population variance from a sample: \text{\sigma}^2 = \frac{\sum (x_i - ar{x})^2}{n - 1}.