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SDCalc
PertengahanAplikasi·11 min

Membina Selang Keyakinan dengan Sisihan Piawai

Pelajari cara membina selang keyakinan menggunakan sisihan piawai. Fahami maksud aras keyakinan dan cara mentafsir CI dalam senario dunia sebenar.

Apakah Selang Keyakinan?

Selang keyakinan (CI) ialah julat nilai yang berkemungkinan mengandungi parameter populasi sebenar. Berbeza daripada memberikan satu anggaran titik, CI mengakui ketidakpastian dengan menyediakan satu julat.

“Kami 95% yakin min sebenar jatuh antara 48.2 dan 51.8”

95% CI: [48.2, 51.8]

Formula

Selang keyakinan untuk min populasi ialah:

Formula Selang Keyakinan

CI = x̄ ± z* × (σ / √n)
  • x̄ = min sampel
  • z* = nilai genting (1.96 untuk 95% CI)
  • σ = sisihan piawai
  • n = saiz sampel
  • σ/√n = ralat piawai
Aras KeyakinanNilai z*
90%1.645
95%1.960
99%2.576

Tafsiran yang Betul

Salah Faham Lazim

95% CI TIDAK bermaksud “terdapat 95% kebarangkalian min sebenar berada dalam selang ini.” Min sebenar sama ada berada atau tidak berada dalam selang—ia tetap.

Tafsiran yang Betul

“Jika kita mengulangi proses persampelan ini berkali-kali, 95% daripada selang yang dikira akan mengandungi min populasi sebenar.”

Contoh Penyelesaian

Contoh: Kepuasan Pelanggan

Anda meninjau 100 pelanggan dan mendapati skor kepuasan min 7.5 dengan sisihan piawai 1.5. Kira 95% CI.
1

Cari ralat piawai

SE = 1.5 / √100 = 0.15
2

Kira margin ralat

ME = 1.96 × 0.15 = 0.294
3

Bina selang

CI = 7.5 ± 0.294 = [7.21, 7.79]

Tafsiran: Kami 95% yakin min kepuasan pelanggan sebenar berada antara 7.21 dan 7.79.

Apa yang Mempengaruhi Lebar CI?

Saiz Sampel (n)

n lebih besar = CI lebih sempit Lebih banyak data = lebih tepat

Sisihan Piawai (σ)

σ lebih besar = CI lebih lebar Lebih banyak kebolehubahan = kurang pasti

Aras Keyakinan

Keyakinan lebih tinggi = CI lebih lebar 99% CI lebih lebar daripada 95% CI

Further Reading

← Pusat Pembelajaran

How to Read This Article

A statistics tutorial is a practical interpretation guide, not just a formula dump. It refers to the assumptions, notation, and reporting language that analysts need when they explain a result to a teacher, manager, client, or reviewer. The article body covers the specific topic, while the sections below create a common interpretation frame that readers can reuse across related metrics.

Reading goalWhat to focus onCommon mistake
DefinitionWhat the metric is and what quantity it summarizesTreating the formula as self-explanatory
Formula choiceSample versus population assumptions and notationUsing n when n-1 is required or vice versa
InterpretationWhether the result indicates concentration, spread, or riskCalling a large value good or bad without context

Frequently Asked Questions

How should I interpret a high standard deviation?

A high standard deviation means the observations are spread farther from the mean on average. Whether that spread is acceptable depends on the context: wide dispersion might signal risk in finance, instability in manufacturing, or genuine natural variation in scientific data.

Why do some articles mention n while others mention n-1?

The denominator reflects the difference between population and sample formulas. Population variance and population standard deviation use N because the full dataset is known. Sample variance and sample standard deviation often use n-1 because Bessel’s correction reduces bias when estimating population spread from a sample.

What is a statistical interpretation guide?

A statistical interpretation guide is a page that moves beyond arithmetic and explains meaning. It tells you what a metric is, when the formula applies, and how to describe the result in plain English without overstating certainty.

Can I cite this article in a report?

You should cite the underlying authoritative reference for formal work whenever possible. This page is best used as an explanatory bridge that helps you understand the concept before quoting the original standard or handbook.

Why include direct citations on every article page?

Direct citations give readers a route to verify the definition, notation, and assumptions. That improves trust and reduces the chance that a simplified explanation is mistaken for the entire technical standard.

Authoritative References

These sources define the concepts referenced most often across our articles. Bessel's correction is a sample adjustment, variance is a squared measure of spread, and standard deviation is the square root of variance expressed in the same units as the data.