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LanjutanLanjutan·14 min

Ujian Hipotesis dengan Sisihan Piawai

Pelajari bagaimana sisihan piawai digunakan dalam ujian hipotesis. Fahami ujian-t, ujian-z, dan cara menentukan keertian statistik.

Gambaran Keseluruhan

Ujian hipotesis ialah kaedah statistik untuk membuat keputusan tentang populasi berdasarkan data sampel. Sisihan piawai memainkan peranan penting dalam menentukan sama ada perbezaan yang diperhatikan adalah signifikan secara statistik atau hanya disebabkan oleh kebetulan rawak.

1

Nyatakan Hipotesis

Nyatakan hipotesis nol (H₀) dan hipotesis alternatif (H₁)
2

Pilih Aras Keertian

Pilih aras keertian (α), biasanya 0.05
3

Kira Statistik Ujian

Kira statistik ujian menggunakan sisihan piawai
4

Bandingkan dengan Nilai Genting

Bandingkan dengan nilai genting atau kira nilai-p
5

Buat Keputusan

Buat keputusan: tolak atau gagal menolak H₀

Ujian-Z

Gunakan ujian-Z apabila anda mengetahui sisihan piawai populasi (σ) dan mempunyai saiz sampel yang besar (n ≥ 30).

Statistik Ujian-Z

z = (x̄ - μ₀) / (σ / √n)

Contoh

Pengilang mendakwa bateri tahan 100 jam secara purata (μ₀ = 100). Anda menguji 36 bateri dan mendapati x̄ = 98 jam. Jika σ = 12 jam: z = (98 - 100) / (12 / √36) = -2 / 2 = -1 Dengan z = -1 dan α = 0.05 (dua ekor), kita gagal menolak H₀. Perbezaan ini tidak signifikan secara statistik.

Ujian-T

Gunakan ujian-t apabila anda tidak mengetahui sisihan piawai populasi dan perlu menganggarkannya daripada sampel (menggunakan s dan bukan σ).

Statistik Ujian-T

t = (x̄ - μ₀) / (s / √n)

Bila Menggunakan Ujian-T vs Ujian-Z

- Ujian-Z: σ diketahui, n ≥ 30 - Ujian-T: σ tidak diketahui (gunakan s), sebarang saiz sampel Dalam amalan, ujian-t jauh lebih lazim kerana kita jarang mengetahui σ populasi sebenar.

Ralat Piawai

Ralat piawai (SE) mengukur sejauh mana min sampel berbeza daripada min populasi. Ia adalah penghubung utama antara sisihan piawai dan ujian hipotesis.

Ralat Piawai Min

SE = σ / √n (atau s / √n apabila menggunakan SD sampel)

Ralat piawai berkurang apabila saiz sampel meningkat. Sampel yang lebih besar memberikan anggaran yang lebih tepat dan memudahkan pengesanan perbezaan sebenar.

Keertian Statistik

Sesuatu keputusan adalah signifikan secara statistik apabila kebarangkalian memerhatikannya secara kebetulan (nilai-p) berada di bawah ambang yang anda pilih (α).

Jika nilai-p < α

Tolak H₀. Keputusan adalah signifikan secara statistik.

Jika nilai-p ≥ α

Gagal menolak H₀. Keputusan mungkin disebabkan oleh kebetulan.

Keertian Statistik vs Keertian Praktikal

Keputusan yang signifikan secara statistik tidak semestinya penting secara praktikal. Dengan sampel yang sangat besar, perbezaan kecil boleh menjadi “signifikan” tetapi tidak bermakna dalam amalan. Sentiasa pertimbangkan saiz kesan bersama-sama nilai-p.

Further Reading

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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.