Mathematics · Statistics
Kish Effective Sample Size from Weight Sums Calculator
Calculate kish effective sample size from sum of survey weights and square root of summed squared weights.
Inputs and results stay in this browser. Change one value at a time to explore the relationship.
Calculation steps
- Use c=(a/b)² with sum of survey weights=1000 and square root of summed squared weights=50.
- Kish effective sample size=400.
Understand Kish Effective Sample Size from Weight Sums
One idea, three depths
Choose how deeply to explain Kish Effective Sample Size from Weight Sums
Kish Effective Sample Size from Weight Sums: Calculate kish effective sample size from sum of survey weights and square root of summed squared weights.
Age 5Explain it to a 5-year-oldStart with a picture
Imagine using Kish Effective Sample Size from Weight Sums to answer this question: calculate kish effective sample size from sum of survey weights and square root of summed squared weights? Enter sum of survey weights and square root of summed squared weights; the calculator shows Kish effective sample size. For example: sum of survey weights=1000 and square root of summed squared weights=50 produce Kish effective sample size=400. The answer tells you Kish effective sample size.
Age 15Explain it to a 15-year-oldConnect it to the formula
Kish effective sample size is squared total weight divided by the sum of squared weights. This page evaluates the relationship directly. The rule is c=(a/b)². Its input values are sum of survey weights, square root of summed squared weights, and the main result is Kish effective sample size. For example: sum of survey weights=1000 and square root of summed squared weights=50 produce Kish effective sample size=400.
CollegeExplain it at college levelState the model precisely
This calculator evaluates the stated kish effective sample size from weight sums relation over the valid real-number domain stated below. The implemented relation is c=(a/b)², evaluated from sum of survey weights, square root of summed squared weights to produce Kish effective sample size. Kish effective sample size is squared total weight divided by the sum of squared weights. This page evaluates the relationship directly. The second input is the square root of the summed squared weights so the reversible square-ratio form applies.
Inputs and valid domain
- sum of survey weights must be a finite real number.
- square root of summed squared weights must be a finite real number.
Important boundary: The second input is the square root of the summed squared weights so the reversible square-ratio form applies.
The formula
c=(a/b)²
How the calculator works through it
It substitutes sum of survey weights, square root of summed squared weights into the formula and exposes every numerical step above. The main output is Kish effective sample size.
Read the result correctly
The Kish effective sample size is the direct answer to “calculate kish effective sample size from sum of survey weights and square root of summed squared weights.” Read it with the units shown beside the inputs; a sign, angle, percentage or rate changes what the number means.
A worked check
sum of survey weights=1000 and square root of summed squared weights=50 produce Kish effective sample size=400.
Where this model stops being reliable
The second input is the square root of the summed squared weights so the reversible square-ratio form applies.
Learn it by changing one value
Begin with the worked example, then change one value while keeping the others fixed. Compare the new result and calculation steps to identify which part of the formula changed.
Dictionary terms behind this calculator
Before studying the codeWhat you should know firstUse the calculator immediately, or check the foundations before reading the implementation.
These foundations help you understand why Kish Effective Sample Size from Weight Sums works. They never block the calculator, and “optional” means useful context rather than a hidden requirement.
Hard requirements
- Reading formulas and substituting values
Kish Effective Sample Size from Weight Sums uses c=(a/b)². You need to recognise what each side represents before substituting the stated inputs or rearranging the relationship.
Review this foundation about 4 min
Strong support
- Averages and representative values
Representative values help you judge what the Kish Effective Sample Size from Weight Sums inputs summarise and what the result can legitimately describe.
Review this foundation about 5 min
Optional enrichment
- Spread and measurement variation
Variation is not always part of the Kish Effective Sample Size from Weight Sums formula, but it helps you judge how stable a reported result may be.
Review this foundation about 6 min
Mathematics → algorithm → program
Implement this calculation in code
These are direct reference implementations of the calculator's principal relationship and first output. They run locally and include a small known-answer check where the language supports it.
Algorithm
- Read sum of survey weights, square root of summed squared weights.
- Evaluate the principal relationship: c=(a/b)².
- Return Kish effective sample size and check the domain conditions described above.
Python
from math import *
def kish_effective_sample_size_calculator(a, b) -> float:
return ((a / b) * (a / b))
assert abs(kish_effective_sample_size_calculator(1000, 50) - 400) < 1e-6 * max(1.0, abs(400))
C
#include <assert.h>
#include <math.h>
double kish_effective_sample_size_calculator(double a, double b) {
return ((a / b) * (a / b));
}
int main(void) {
const double expected = 400;
const double actual = kish_effective_sample_size_calculator(1000, 50);
assert(fabs(actual - expected) < 1e-6 * fmax(1.0, fabs(expected)));
}
C++
#include <cassert>
#include <cmath>
#include <numbers>
double kish_effective_sample_size_calculator(double a, double b) {
return ((a / b) * (a / b));
}
int main() {
constexpr double expected = 400;
const double actual = kish_effective_sample_size_calculator(1000, 50);
assert(std::fabs(actual - expected) < 1e-6 * std::fmax(1.0, std::fabs(expected)));
}
Linux x86-64 assembly
x86-64 NASM · System V ABI · Linux · SSE2 with libm where required
; double kish_effective_sample_size_calculator(double a, double b)
; Linux x86-64 NASM · System V ABI · first eight doubles in xmm0–xmm7
global kish_effective_sample_size_calculator
section .text
kish_effective_sample_size_calculator:
push rbp
mov rbp, rsp
sub rsp, 48
movsd [rbp-8], xmm0
movsd [rbp-16], xmm1
movsd xmm0, [rbp-8]
divsd xmm0, [rbp-16]
movsd [rbp-32], xmm0
movsd xmm0, [rbp-8]
divsd xmm0, [rbp-16]
movsd [rbp-40], xmm0
movsd xmm0, [rbp-32]
mulsd xmm0, [rbp-40]
movsd [rbp-24], xmm0
movsd xmm0, [rbp-24]
leave
ret
MATLAB
function result = kish_effective_sample_size_calculator(a, b)
result = ((a / b) * (a / b));
end
Wolfram Language
ClearAll[mwCalculate];
mwCalculate[a_, b_] := ((a / b) * (a / b));
Continue in mathematical software
The downloaded file includes your current inputs and first calculated result. It is created locally.
Floating-point answers can differ slightly by language, compiler and processor. Compare within a suitable tolerance rather than assuming every decimal representation will be identical.
Supporting sourcesAcademic referencesPrimary standards, textbooks and complete citations
Standards, reading and academic references
Use the calculator as the worked interaction, then consult the primary standards and academic textbooks listed below. MW SysArc links to the original sources; the explanation on this page is original and does not reproduce them.
Introductory Statistics 2e
Read the free OpenStax statistics textbookCite this book
- APA 7
- Illowsky, B., & Dean, S. (2023). Introductory statistics 2e. OpenStax. https://openstax.org/books/introductory-statistics-2e/pages/1-introduction
- MLA 9
- Illowsky, Barbara, and Susan Dean. Introductory Statistics 2e. OpenStax, 2023, https://openstax.org/books/introductory-statistics-2e/pages/1-introduction.
- Chicago author-date
- Illowsky, Barbara, and Susan Dean. 2023. Introductory Statistics 2e. Houston, TX: OpenStax. https://openstax.org/books/introductory-statistics-2e/pages/1-introduction.
OpenStax entries are free to read online. Follow the licence shown on each linked source before redistributing or adapting its content.
Reuse the page responsiblyCite this pageAPA, MLA, Chicago, Harvard, BibTeX and RIS
These formats cite this calculator page itself. They are separate from the academic references above, which support the mathematical method and terminology.
APA 7
MW SysArc. (2026, July 21). Kish Effective Sample Size from Weight Sums Calculator. MW SysArc Tools. https://math.mwsysarc.com/statistics/kish-effective-sample-size-calculator
MLA 9
MW SysArc. “Kish Effective Sample Size from Weight Sums Calculator.” MW SysArc Tools, 21 July 2026, https://math.mwsysarc.com/statistics/kish-effective-sample-size-calculator. Accessed 31 Aug. 2026.
Chicago 17
MW SysArc. “Kish Effective Sample Size from Weight Sums Calculator.” MW SysArc Tools. Published July 21, 2026. Accessed August 31, 2026. https://math.mwsysarc.com/statistics/kish-effective-sample-size-calculator.
Harvard
MW SysArc (2026) ‘Kish Effective Sample Size from Weight Sums Calculator’, MW SysArc Tools. Published 21 July 2026. Available at: https://math.mwsysarc.com/statistics/kish-effective-sample-size-calculator (Accessed: 31 August 2026).
BibTeX and RIS records
BibTeX
@misc{mwsysarc_kish_effective_sample_size_calculator_2026,
author = {{MW SysArc}},
title = {Kish Effective Sample Size from Weight Sums Calculator},
howpublished = {MW SysArc Tools},
year = {2026},
url = {https://math.mwsysarc.com/statistics/kish-effective-sample-size-calculator},
note = {Published July 21, 2026; accessed August 31, 2026}
}RIS
TY - ELEC
AU - MW SysArc
TI - Kish Effective Sample Size from Weight Sums Calculator
T2 - MW SysArc Tools
PY - 2026
DA - 2026-07-21
Y2 - 2026-08-31
UR - https://math.mwsysarc.com/statistics/kish-effective-sample-size-calculator
N1 - Published July 21, 2026
ER -Clear answers
Frequently asked questions
What does the Kish Effective Sample Size from Weight Sums do?
Calculate kish effective sample size from sum of survey weights and square root of summed squared weights.
How does the Kish Effective Sample Size from Weight Sums work?
The calculator applies c=(a/b)². Kish effective sample size is squared total weight divided by the sum of squared weights. This page evaluates the relationship directly.
What can I learn from the Kish Effective Sample Size from Weight Sums?
It connects the mathematical rule to your chosen numbers and shows each calculation step. Change one input at a time to see how the result responds.
Does MW SysArc receive or store what I enter?
No. The calculation runs locally in your browser. MW SysArc does not receive or store your calculation inputs.
How should I use the result?
Use the steps to understand the method, then verify important school or professional work using the notation and rounding rules required in your setting.
Last reviewed . Calculations tested .