MATLAB Statistical Analysis

Descriptive Statistics

Descriptive statistics are numerical and graphical methods used to summarize and describe the important characteristics of observed data.

Data Distribution

A data distribution describes how observed values are spread across their possible values, including their center, variability, and overall shape.

Normal Distribution

The normal distribution is a continuous, symmetric, bell-shaped probability distribution characterized by its mean and standard deviation.

Probability Density Function (PDF)

A probability density function describes the relative likelihood of values for a continuous random variable. Probabilities are obtained from areas under the density curve over intervals.

normpdf

normpdf evaluates the probability density function of a normal distribution at specified values.

Cumulative Distribution Function (CDF)

A cumulative distribution function gives the probability that a random variable is less than or equal to a specified value.

normcdf

normcdf evaluates the cumulative distribution function of a normal distribution at specified values.

Quantile

A quantile is a value that divides an ordered probability distribution or dataset so that a specified proportion of observations lies at or below that value.

quantile

quantile returns specified quantiles of data, such as quartiles or other percentile-based locations.

Histogram

A histogram displays the distribution of numerical data by dividing values into intervals and showing the number of observations in each interval.

histogram

histogram creates a histogram of numerical data in MATLAB for visualizing its distribution.

Box Plot

A box plot summarizes a dataset using its median, quartiles, spread, and potential outliers.

boxchart

boxchart creates box plots in MATLAB for visually comparing the distributions of numerical data.

Hypothesis Test

A hypothesis test uses sample data to evaluate evidence about a claim concerning a population or probability distribution.

Null Hypothesis

The null hypothesis (H₀) is the baseline statistical claim tested using sample data and is rejected only when sufficient evidence exists against it.

Alternative Hypothesis

The alternative hypothesis (H₁ or Hₐ) represents the competing claim supported when sufficient evidence exists to reject the null hypothesis.

Significance Level

The significance level (α) is the predetermined probability threshold used to decide whether evidence against the null hypothesis is statistically significant.

p-Value

A p-value is the probability, assuming the null hypothesis is true, of obtaining a test statistic at least as extreme as the observed result.

Statistical Significance

A result is statistically significant when its p-value satisfies the chosen significance criterion, commonly p ≤ α.

h Test Decision

In MATLAB hypothesis-testing functions, h commonly represents the test decision: h = 1 indicates rejection of the null hypothesis, while h = 0 indicates failure to reject it at the chosen significance level.

ttest

ttest performs a one-sample t-test or paired-sample t-test, depending on the supplied inputs, to evaluate a hypothesis about a population mean or paired mean difference.

ttest2

ttest2 performs a two-sample t-test for comparing the means of two independent populations.

Normality Assessment

Normality assessment evaluates whether observed data are reasonably consistent with a normal distribution.

Probability Plot

A probability plot compares observed data with a theoretical probability distribution to visually assess how well the distribution describes the data.

probplot

probplot creates a probability plot for comparing sample data with a specified theoretical probability distribution.