statistics

Null Hypothesis ($H_0$)

States that no statistical significance or difference exists between two or more populations.

Alternative Hypothesis ($H_1$)

States that a phenomenon is likely occurring due to non-random causes.

P-value

The probability of observing data as extreme as, or more extreme than, the actual results, assuming that the null hypothesis ($H_0$) is true.

Continuous Variables

Variables measured on a continuous scale where any numerical value is possible.

Discrete Variables

Variables that have a limited number of prefixed values and cannot be ordered by magnitude.

Descriptive Statistics

Provide basic information about the collected data, specifically regarding position (mean/median) and dispersion (variability).

Inferential Statistics

Uses data from a sample to make inferences about a larger population.

Standard Deviation ($SD$)

A measurement used to quantify the dispersion or variability of data points relative to their mean.

Confidence Interval ($CI$)

The range in which the true mean of a population lies with a certain probability, derived from a sample set.

ANOVA (Analysis of Variance)

A statistical method used to compare means across three or more groups.

Type I Error

False positive; occurs when the null hypothesis is true, but the test incorrectly indicates a difference exists.

Type II Error

False negative; occurs when the null hypothesis is false, but the test fails to determine the difference as significant.

Mann-Whitney U Test

A non-parametric equivalent to the unpaired t-test, used for comparing two independent groups.

Chi-Square Test ($\chi^2$)

A non-parametric test used to determine if there is a relationship between two categorical variables.

Standard Error ($SE$)

Measures how accurately the sample mean represents the true population mean.

Effect Size

A quantitative measure of the magnitude of a phenomenon; often used to indicate the strength of a relationship.

Skewness

Measures the asymmetry of a distribution; data can be skewed either to the left or the right.

Kurtosis

Measures the 'flatness' or peakedness of a distribution.

Leptokurtic Distribution

A distribution with more observations concentrated close to the mean.

Platykurtic Distribution

A distribution with more observations spread toward the extremes.

Post-Hoc Tests

Used after an ANOVA to determine exactly which specific groups differ from each other.