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Sample Size Calculation01:19

Sample Size Calculation

Knowledge of the sample size is the first requirement to conduct random sampling or an experiment. The sample size is the total number of units, observations, or groups (in some cases) used to get the data to estimate a population parameter. As the name suggests, the sample size is that of the sample drawn from the population and differs from the population size.
The sample size for the given experiment or sampling effort is fundamental to any study design. Sample size decides the number of...
Systematic Error: Methodological and Sampling Errors01:15

Systematic Error: Methodological and Sampling Errors

In the case of systematic errors, the sources can be identified, and the errors can be subsequently minimized by addressing these sources. According to the source, systematic errors can be divided into sampling, instrumental, methodological, and personal errors.
Sampling errors originate from improper sampling methods or the wrong sample population. These errors can be minimized by refining the sampling strategy. Defective instruments or faulty calibrations are the sources of instrumental...
Classification of Signals01:30

Classification of Signals

In signal processing, signals are classified based on various characteristics: continuous-time versus discrete-time, periodic versus aperiodic, analog versus digital, and causal versus noncausal. Each category highlights distinct properties crucial for understanding and manipulating signals.
A continuous-time signal holds a value at every instant in time, representing information seamlessly. In contrast, a discrete-time signal holds values only at specific moments, often denoted as x(n), where...
Classification of Systems-I01:26

Classification of Systems-I

Linearity is a system property characterized by a direct input-output relationship, combining homogeneity and additivity.
Homogeneity dictates that if an input x(t) is multiplied by a constant c, the output y(t) is multiplied by the same constant. Mathematically, this is expressed as:
How Data are Classified: Categorical Data01:11

How Data are Classified: Categorical Data

A variable, usually notated by capital letters such as X and Y, is a characteristic or measurement that can be determined for each member of a population. Data are the actual values of variables. They may be numbers, or they may be words. Datum is a single value.
Data are classified based on whether they are measurable or not. Categorical data cannot be measured; instead, it can be divided into categories. For example, if Y denotes a person's party affiliation, some examples of Y include...
Classification of Systems-II01:31

Classification of Systems-II

Continuous-time systems have continuous input and output signals, with time measured continuously. These systems are generally defined by differential or algebraic equations. For instance, in an RC circuit, the relationship between input and output voltage is expressed through a differential equation derived from Ohm's law and the capacitor relation,

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Related Experiment Video

Updated: May 29, 2026

Image Recognition and Parameter Analysis of Concrete Vibration State Based on Support Vector Machine
08:27

Image Recognition and Parameter Analysis of Concrete Vibration State Based on Support Vector Machine

Published on: January 5, 2024

On dimensionality, sample size, classification error, and complexity of classification algorithm in pattern

S Raudys1, V Pikelis

  • 1Lietuvos RSR Moksly, Adademiha, Lenino, U.S.S.R.

IEEE Transactions on Pattern Analysis and Machine Intelligence
|August 27, 2011
PubMed
Summary
This summary is machine-generated.

This study compares four discriminant functions for classifying individuals into two populations. The findings help estimate sample sizes and select optimal classification algorithms, especially with limited data.

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Area of Science:

  • Multivariate statistics
  • Statistical classification

Background:

  • Discriminant functions (DFs) are crucial for classifying individuals into populations.
  • Assumptions about covariance matrix structures influence DF performance.
  • Bayes rule provides a foundation for deriving DFs for normal populations.

Purpose of the Study:

  • To compare the performance of four discriminant functions.
  • To analyze the impact of covariance matrix structure on classification accuracy.
  • To provide guidance on sample size estimation and algorithm selection.

Main Methods:

  • Derivation of DFs using Bayes rule for normal populations.
  • Analytical derivation of expected probability of misclassification (EPN).
  • Analysis of classification error (EPN) based on algorithm structure, asymptotic error (P¿), and sample size to dimensionality ratio (N/p or N²/p).

Main Results:

  • Classification error (EPN) is dependent on algorithm structure, P¿, and N/p ratios.
  • Formulas derived for linear and quadratic DFs.
  • Tables presented for learning quantity (H = EPN/P¿) based on P¿, N, and p.

Conclusions:

  • The derived formulas and tables aid in estimating learning sample size.
  • Optimal feature selection can be guided by the analysis.
  • Informed choices of classification algorithms are possible with limited sample sizes.