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Probability

The likelihood or chance that a specific event will occur in a given trial.

P(E)

Denotes the probability of event E, always satisfies 0 ≤ P(E) ≤ 1.

Complement Rule

If two events, E1 and E2, are complements, then P(E1) = 1 – P(E2).

Additive Rule of Probability

Used for mutually exclusive events. P(E1 or E2) = P(E1) + P(E2).

Multiplicative Rule

For independent events, P(A and B) = P(A) * P(B).

Joint Probability

The probability of two events occurring together.

Marginal Probability

The probability of an event irrespective of the outcome of other events.

Conditional Probability

The probability of an event given that another event has occurred.

Type I Error

Rejecting the null hypothesis when it is actually true (false positive).

Type II Error

Failing to reject the null hypothesis when it is actually false (false negative).

Alpha Level (α)

Threshold p value for rejecting the null hypothesis; commonly set at 0.05.

p Value

The probability of observing a test statistic as extreme as the one obtained, given that the null hypothesis is true.

ANOVA

Analysis of variance; a statistical method to compare means among different groups.

t-test

A statistical test used to compare the means of two groups.

Correlation

A statistical measure that expresses the extent to which two variables are linearly related.

Regression

A statistical process for estimating relationships among variables.

Spearman Correlation

A non-parametric measure of rank correlation, assessing how well the relationship between two variables can be described.

Pearson Correlation

A measure of the linear correlation between two continuous variables.

Homoscedasticity

A condition in which the variance of the errors is constant across all levels of the independent variable.

Normality

An assumption that the data is normally distributed.

Independent Samples t-test

Used to compare the means of two unrelated groups.

Paired Samples t-test

Used to compare means from the same group at different times.

One-Way ANOVA

Used to compare means among three or more unrelated groups.

Repeated Measures ANOVA

Used to compare means across multiple measurements taken from the same group.

Standard Deviation

A measure of the amount of variation or dispersion in a set of values.

Confidence Interval (CI)

A range of values that is likely to contain the population parameter with a certain level of confidence.

Effect Size

A quantitative measure of the magnitude of a phenomenon.

Null Hypothesis (H0)

The hypothesis that there is no effect or difference; it is what we seek to test against.

Alternative Hypothesis (HA)

The hypothesis that there is an effect or difference; it is what we seek to find evidence for.

Statistical Power

The probability that a test will correctly reject a false null hypothesis.

Sampling Variation

The natural variation among estimates due to the randomness of the sample.