Testing Normality and Distribution in Data Analysis

Gaussian Distribution

A symmetric probability distribution defined by mean and standard deviation.

Karl Friedrich Gauss

Mathematician known for contributions to statistics.

Normal Curve

Bell-shaped curve representing normal distribution.

Mean (μ)

Average value of a dataset, central point.

Standard Deviation (σ)

Measure of data dispersion around the mean.

Mode

Value that appears most frequently in a dataset.

Inflection Points

Points where the curve changes concavity at μ ± σ.

Asymptotic Behavior

Curve approaches horizontal axis but never touches.

Total Area Under Curve

Equal to 1, representing total probability.

Standardized Normal Distribution

Normal distribution with mean 0 and standard deviation 1.

Z-Score

Standardized score indicating how many standard deviations from the mean.

Central Limit Theorem

Distribution of sample means approaches normality as sample size increases.

Histogram

Graphical representation of frequency distribution of data.

Normal Q-Q Plot

Graph comparing quantiles of data against a normal distribution.

Kolmogorov Smirnov Test

Statistical test for comparing a sample with a reference probability distribution.

Lilliefors Test

Test for normality when mean and variance are unknown.

Anderson-Darling Test

Test assessing if a sample comes from a specified distribution.

Shapiro-Wilk Test

Test for normality based on sample data.

Non-Normal Distribution

Distribution that does not follow a normal curve.

Positively Skewed Distribution

Distribution with a tail extending towards higher values.

Negatively Skewed Distribution

Distribution with a tail extending towards lower values.

Homogeneity of Variances

Assumption that different groups have equal variances.

Levene's Test

Test assessing equality of variances across groups.

Data Transformation

Process of modifying data to meet statistical assumptions.

Square-root Transformation

Used for moderate skewness in data.

Log Transformation

Applied for data with greater skewness.

Inverse Transformation

Used for severe skewness in data.