ᕉᓚᑦ: ᖃᐅᔨᓴᕐᕕᒃ · ᖃᐅᔨᓴᕐᕕᒃ · ᓈᓴᐅᑎᓕᕆᓂᖅ · 8 ᒥᓂᑦ

ᑲᐃ-ᔅᑯᐃᐅ ᖃᐅᔨᓴᕈᑎ

ᐱᐅᓯᐅᔪᖅ ᖃᐅᔨᓴᕈᑎ ᐊᐱᖅᑯᑎᒧᑦ “ᑕᒪᒃᑯᐊ 37 ᓈᓴᐅᑏᑦ ᓈᒻᒪᒃᑐᒥᑦ ᐊᒃᓴᓗᐊᕐᒥᑦ ᓴᖅᑭᑕᐅᔪᓐᓇᖅᐸᑦ?”

ᓇᐃᑦᑐᖅ ᑭᐅᔾᔪᑎ

χ² = Σ (ᑕᑯᔭᐅᓯᒪᔪᖅ − ᓂᕆᐅᒋᔭᐅᔪᖅ)² / ᓂᕆᐅᒋᔭᐅᔪᖅ 37 ᐃᓂᓂ ᑕᒪᐃᓐᓂ. ᑲᐃ-ᔅᑯᐃᐅ ᐊᕕᒃᓯᒪᓂᖏᓐᓄᑦ 36 ᐃᒻᒥᓂᖅᑐᑦ ᐊᒥᓲᓂᖏᓐᓄᑦ ᓇᓪᓕᒋᓗᒍ p ᐊᑭᖓ ᓇᓂᓯᓂᐊᕐᓗᒍ.

ᓈᓴᐅᑎᖓ
Σ (O−E)²/E
df
36
ᑭᒡᓕᐊ 5%-ᒥ
51.0
ᑭᒡᓕᐊ 1%-ᒥ
58.6

ᓈᓴᐃᓂᖅ

ᐃᓂᐊᑐᖅᑕᐅᔪᑦᐃᓂᑲᐃᕙᖅᑐᒥ 37 ᓈᓴᐅᑎᓕᑦ ᐃᓂᑦ ᐊᑕᐅᓯᖓ. ᐊᓯᐊᓂ ᐊᑎᖏᑦ: ᐃᓂᒋᐊᖅ, ᖃᓪᓗᐊᖅ.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → ᑕᒪᑐᒪ ᓂᕆᐅᒋᔭᐅᔪᖅ ᓈᓴᐅᑎᖓ n/37. ᐃᓂ ᑕᒪᑐᒪ, ᑕᑯᔭᐅᓯᒪᔪᑉ ᓂᕆᐅᒋᔭᐅᔪᓪᓗ ᐊᔾᔨᒌᙱᓐᓂᖓ ᐃᒻᒥᓂᒃ ᐊᐱᕐᓗᒍ ᓂᕆᐅᒋᔭᐅᔪᒧᓪᓗ ᐊᕕᒃᓗᒍ; 37 ᐃᓚᖏᑦ ᑲᑎᑦᓗᒋᑦ. ᓈᒻᒪᒃᑐᖅ ᐊᒃᓴᓗᐊᖅ ᐊᔾᔨᒌᒃᑎᓪᓗᒋᑦ ᐊᒡᒐᖓ 36-ᒥᒃ ᑐᓂᓯᕙᒃᑐᖅ (ᐃᒻᒥᓂᖅᑐᑦ ᐊᒥᓲᓂᖏᑦᖃᐅᔨᓴᕐᕕᒃᐃᒻᒥᓂᖅᑐᑦ ᐊᒥᓲᓂᖏᑦᓈᓴᐃᓂᒃᑯᑦ ᓈᓴᐅᑎᒥ ᐃᒻᒥᓂᖅᑐᑦ ᐊᑭᐅᔪᑦ ᐊᒥᓲᓂᖏᑦ. 37 ᐃᓂᓂ ᑲᐃ-ᔅᑯᐃᐅ ᖃᐅᔨᓴᕈᑎᒥ 36, ᓈᓴᐅᑏᑦ ᑲᑎᓪᓗᒋᑦ ᐃᓘᓐᓇᖓᓂᒃ ᐊᔾᔨᖃᕆᐊᖃᕐᒪᑕ.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ →), ᐊᔾᔨᒌᙱᓐᓂᐅᑉ ᐊᑦᔨᐅᑎᖓᓈᓴᐃᓂᖅᐊᔾᔨᒌᙱᓐᓂᐅᑉ ᐊᑦᔨᐅᑎᖓᐊᔾᔨᒌᙱᓐᓂᐅᑉ ᓯᑭᐊᖅᑐᓂᖓ (√); ᐱᓐᓂᐅᑉ ᓂᕆᐅᒋᔭᐅᔪᒥᑦ ᐊᑐᐃᓐᓇᐅᒐᔪᒃᑐᖅ ᐅᖓᓯᑦᑎᒋᓂᖓ.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → ᐊᒡᒐᖓ 8.5. 51.0 ᖁᓛᓂ 5%-ᒥ ᐱᒻᒪᕆᐅᔪᖅ; 58.6 ᖁᓛᓂ 1%-ᒥ. ᐊᒃᓴᓗᐊᑉ ᓴᖑᓯᒪᓂᖓᓂᒃ ᖃᐅᔨᓴᕈᑎ ᓈᓴᐅᑎᖓ ᓱᓕᔪᒥᒡᓗ p ᐊᑭᖓᖃᐅᔨᓴᕐᕕᒃp ᐊᑭᖓᐊᒃᓴᓗᐊᖅ ᓈᒻᒪᒃᐸᑦ ᑕᑯᔭᐅᓯᒪᔪᑐᑦ ᐊᖏᑎᒋᔪᒥᒃ ᐅᕝᕙᓘᓐᓃᑦ ᐊᖏᓂᖅᓴᒥᒃ ᐊᔾᔨᒌᙱᓐᓂᕐᒥᒃ ᑕᑯᓂᕐᒧᑦ ᐱᔪᓐᓇᕐᓂᖅ.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → ᓈᓴᖅᑕᖏᒃ ᐋᖅᑭᒃᓯᒪᔪᒥᑦ ᐃᓱᓕᑦᑐᙱᑦᑐᒥᑦ ᒐᒪ ᓈᓴᐅᑎᓕᐅᕈᑎᒥᑦ.

n ᑲᐃᕙᕐᓃᑦᓂᕆᐅᒋᔭᐅᔪᖅ ᐃᓂᒧᑦσ ᐃᓂᒧᑦᐃᓂ +2σ-ᒥᐃᓂ +3σ-ᒥ
370103.11619
1,000275.13742
3,7001009.9120130
10,00027016.2303319
37,0001,00031.21,0621,094
σ ≈ √(n·p·(1−p)) p = 1/37-ᒥ. 1,000 ᑲᐃᕙᕐᓂᓂ ᐃᓂ 37-ᒥ ᐊᒃᑐᖅᑕᐅᓂᓕᒃ ᐊᓯᖏᓐᓂᑦ ᐊᔾᔨᒋᙱᑦᑐᖅ; 42-ᒥ ᑕᑯᔭᐅᓯᒪᔪᓂᒃ ᑐᒡᓕᐊᓂᒃ ᐱᔭᕆᐊᖃᖅᑐᖅ.

ᐆᑦᑑᑎ ᐱᓕᕆᐊᖑᓯᒪᔪᖅ

1,000 ᑲᐃᕙᕐᓃᑦ. ᐃᓂᑦ ᐱᖓᓱᑦ ᖁᓕᑦ ᐱᖓᓲᔪᖅᑐᓪᓗ 20-ᒥᑦ 34-ᒧᑦ ᐊᒃᑐᖅᑕᐅᓂᖃᖅᑐᑦ; ᐃᓂ 8 41-ᓂᒃ. ᓂᕆᐅᒋᔭᐅᔪᖅ 27.03. ᐃᓂ 8-ᐅᑉ ᐃᓚᖓ ᑭᓯᐊᓂ (41 − 27.03)²/27.03 = 7.2. ᐊᓯᖏᑦ 36 ᐃᓚᖏᑦ 38-ᒧᑦ ᑲᑎᑦᑐᑦ ᐃᓱᒪᒋᓗᒋᑦ (ᐊᒡᒐᖓ). χ² = 45.2 36 df-ᒥ, p ≈ 0.14. ᐱᒻᒪᕆᐅᙱᑦᑐᖅ: ᓈᒻᒪᒃᑐᖅ ᐊᒃᓴᓗᐊᖅ ᑕᒪᑐᒥᖓ ᐱᓕᕆᕙᒃᑐᖅ ᐊᕐᕕᓂᓖᑦ ᐊᑕᐅᓯᕐᓂᑦ ᐊᑕᐅᓯᕐᒥᒃ. ᐃᓂ 8 ᖃᐅᔨᓴᖅᑕᒃᓴᐅᔪᖅ, ᓇᓂᓯᓂᐅᙱᑦᑐᖅ, ᑭᐅᔾᔪᑎᖓᓗ ᐅᓇ: ᑲᐃᕙᕐᓃᑦ ᑕᐅᓴᓐ ᐊᓯᖏᑦ.

ᐃᓱᒪᓕᐅᕈᑏᑦ

ᐃᒻᒥᓂᖅ ᑲᐃᕙᕐᓃᑦᓈᓴᐃᓂᖅᐃᒻᒥᓂᖅ ᑲᐃᕙᕐᓃᑦᑲᐃᕙᕐᓂᖅ ᑕᒪᐃᓐᓂ ᐊᔾᔨᒌᒃᑐᓂᒃ ᐱᔪᓐᓇᕐᓂᓕᒃ, ᓯᕗᓂᖓᓂ ᐱᓯᒪᔪᑦ ᖃᓄᐃᒃᑲᓗᐊᕐᒪᖔᑕ. ᒪᑉᐱᒐᓂ ᐅᕙᓂ ᓈᓴᐅᑎᓕᐅᕈᑏᑦ ᑕᒪᐃᑦ ᑐᙵᕕᖓ.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ →, ᓂᕆᐅᒋᔭᐅᔪᑦ ᓈᓴᐅᑏᓪᓗ ᐃᓂᒧᑦ ᒥᑭᓛᖅ 5, ᑕᒪᓐᓇ ᑐᑭᖃᖅᑐᖅ n ≥ 185 ᖃᐅᔨᓴᕈᑎ ᐊᑐᓐᓇᕐᓂᐊᕐᒪᑦ, ᐊᒥᓲᓂᖅᓴᐅᔪᐊᓗᐃᓪᓗ ᐊᑐᓂᖃᕐᓂᐊᕐᒪᑦ. ᐊᒃᓴᓗᐊᓂᑦ ᐊᔾᔨᒌᙱᑦᑐᓂᑦ ᑲᐃᕙᕐᓂᓂᒃ ᑲᑎᑦᓯᓂᖅ ᓯᕗᓪᓕᖅᐹᖅ ᐃᓱᒪᓕᐅᕈᑎ ᐱᔾᔪᑎᖓᒍᑦ ᓯᖁᒥᑦᑎᔪᖅ (ᐊᒃᓴᓗᐊᕐᒥᒃ ᐱᓇᓂ ᐊᒃᑐᕈᓯᒥᒃ ᖃᐅᔨᓴᖅᑐᑎᑦ). ᐱᙳᐊᖅᑎᑦᓯᔨᐅᑉ ᐃᓕᖁᓯᖓ ᓱᓕᓪᓚᕆᒃᑐᒥᒃ ᓯᖁᒥᑦᑎᓂᐊᖅᑐᖅ, χ²-ᓗ ᐊᖏᒡᓕᒋᐊᖅᑎᓪᓗᒍ ᐃᓂ ᓇᓪᓕᐊᑐᐃᓐᓇᖅ ᐊᒃᓴᓗᐊᑉ ᓴᓇᓯᒪᓂᖓᒍᑦ ᐱᐅᒋᔭᐅᓂᖅᓴᐅᙱᑉᐸᓪᓘᓐᓃᑦ.

ᕉᓚᑦ: ᐱᙳᐊᖅᑎᑦᓯᔨᐅᑉ ᐃᓕᖁᓯᖓᕉᓚᑦᒥ ᐃᒻᒥᓂᖅ ᑲᐃᕙᕐᓃᑦ

ᐱᐊᓴᓐ ᒪᓐᑎ ᑳᓗᓗ

ᑳᓪ ᐱᐊᓴᓐ (Karl Pearson) ᖃᐅᔨᓴᕈᑎ ᓴᖅᑭᑎᓚᐅᖅᑕᖓ 1900-ᒥ, ᓯᕗᓪᓕᖅᐹᓂᓗ ᐆᑦᑑᑎᖏᓐᓂ ᐊᑕᐅᓯᖅ 26,306 ᒪᓐᑎ ᑳᓗᒥ ᑎᑎᕋᖅᑕᐅᓯᒪᔪᑦ ᕉᓚᑦ ᑲᐃᕙᕐᓃᑦ, ᓇᓂᓯᓚᐅᖅᑐᖅ ᐊᔾᔨᒌᙱᓗᐊᐸᓗᒃᑐᓂᒃ ᐱᔪᓐᓇᕐᓂᒃᑯᑦ ᐊᓯᑦᑐᕐᓂᐅᔪᓐᓇᙱᑦᑐᓂᒃ, ᐅᖃᓚᐅᖅᓗᓂᓗ “ᒪᓐᑎ ᑳᓗᒥ ᕉᓚᑦ… ᐱᔪᓐᓇᕐᓂᒃᑯᑦ ᐱᙳᐊᕐᓂᐅᙱᑦᑐᖅ”. ᑭᖑᓂᐊᒍᑦ ᑎᑎᕋᖅᑏᑦ ᐃᓱᒪᓕᐅᓚᐅᖅᑐᑦ ᐱᐅᓯᐅᖅᑎᓄᑦ ᑐᓴᒐᒃᓴᓕᐅᖅᑎᐅᓪᓗᑎᒃ ᑲᐃᕙᕐᓂᓂᒃ ᑎᑎᕋᖅᓯᒪᔪᑦ ᐊᒥᓱᓂᒃ ᓴᓇᓚᐅᖅᓯᒪᓂᖏᓐᓂᒃ, ᑕᒪᓐᓇᓗ ᑎᑎᕋᖅᓯᒪᔪᑦ ᓇᑭᙶᕐᓂᖏᓐᓂᒃ ᐃᓕᓐᓂᐊᕈᑕᐅᔪᖅ.

ᖃᐅᔨᓴᕈᑎ ᐊᒃᓴᓗᐊᕐᓗ
1900

ᐱᐊᓴᓐ ᑲᐃ-ᔅᑯᐃᐅ ᓈᒻᒪᒃᑐᒥᒃ ᖃᐅᔨᓴᕈᑎ ᓴᖅᑭᑎᑦᑕᖓ, ᒪᓐᑎ ᑳᓗᒥ ᑲᐃᕙᕐᓂᓂᒃ ᐆᑦᑑᑎᖃᖅᓗᓂ.

1900-ᖏᓐᓂ

ᑲᐃᕙᕐᓃᑦ ᑎᑎᕋᖅᓯᒪᔪᑦ ᐊᐱᖅᑯᑕᐅᓕᖅᑐᑦ; ᑎᑎᕋᖅᑏᑦ ᑐᓪᓕᖅᑐᓂᒃ ᓴᓇᓯᒪᓇᔭᖅᑐᑦ.

1920-ᖏᓐᓂ

ᕕᔅᓱ (Fisher) ᐃᒻᒥᓂᖅᑐᑦ ᐊᒥᓲᓂᖏᓐᓂᒃ ᒪᓕᒐᓕᐅᖅᑐᖅ; 5% ᐱᐅᓯᐅᓕᖅᑐᖅ.

1940–50-ᖏᓐᓂ

ᓈᓴᐅᑎᓕᕆᔩᑦ ᕉᓚᑦ ᑲᐃᕙᕐᓂᖏᓐᓂᒃ ᐃᓕᓐᓂᐊᕈᑎ ᑎᑎᕋᖅᓯᒪᔪᑐᑦ ᐊᑐᖅᐸᒃᑐᑦ ᐊᔾᔨᒌᒃᑐᓂᒃ ᖃᐅᔨᓴᕈᑎᓄᑦ.

1990-ᖏᓐᓂ

ᒑᓯᐊ-ᐱᓛᔪ (García-Pelayo) ᐃᓚᒌᑦ ᐱᓕᕆᔾᔪᓯᖓ ᐊᑐᖅᑕᖏᑦ ᓱᓕᔪᓂᒃ ᑎᑎᕋᖅᓯᒪᔪᓂᒃ ᒫᑦᕆᑦᒥᓗ ᐊᔪᒐᖅᓗᑎᒃ.

ᒫᓐᓇ

ᑳᓯᓄᐃᑦ ᐊᔾᔨᒌᒃᑐᒥᒃ ᖃᐅᔨᓴᕈᑎᒥᒃ ᐃᒻᒥᓂᒃ ᐊᒃᓴᓗᐊᖏᓐᓂ ᐊᑐᖅᐸᒃᑐᑦ ᐋᖅᑭᒃᓯᒪᑦᑎᐊᕐᓂᖏᓐᓄᑦ.

ᐱᐊᓴᓐ 1900-ᒥ ᖃᐅᔨᓴᕈᑎᖓ ᒪᓐᑎ ᑳᓗᒥ ᑲᐃᕙᕐᓃᑦ ᐊᔾᔨᒌᙱᓗᐊᐸᓗᒃᑐᓂᒃ ᓇᓂᓯᓚᐅᖅᑐᖅ; ᐱᐅᓯᐅᖅᑎᓄᑦ ᑎᑎᕋᖅᑏᑦ ᐊᒥᓱᓂᒃ ᓴᓇᓚᐅᖅᓯᒪᔪᑦ.

ᒪᓐᑎ ᑳᓗ ᕉᓚᑦ

ᓱᓕᔪᖅ ᖃᐅᔨᓴᕐᓂᖅ: ᓛᔅ ᕖᒐᔅᒥ ᐃᒻᒥᓂᒃ ᐊᐅᓚᔪᑦ ᐊᒃᓴᓗᐊᑦ

ᐱᙳᐊᖅᑏᑦ ᐃᓱᒪᒋᕙᒃᑕᖏᑦ ᐃᒻᒥᓂᒃ ᐊᐅᓚᔪᖅ ᐊᒃᓴᓗᐊᖅ ᐊᖅᓴᖅᐊᑐᖅᑕᐅᔪᑦᐊᖅᓴᖅᒥᑭᔪᖅ ᐊᖅᓴᖅ ᐊᖁᑎᖓᓂ ᑲᐃᕙᖅᑐᑉ ᐊᑉᐱᖓᓄᑦ ᐃᒋᑕᐅᔪᖅ. ᒫᓐᓇᐅᔪᖅ ᐊᖅᓵᑦ ᐃᕗᕆᓐ ᐅᕝᕙᓘᓐᓃᑦ ᑎᕙᓚᓐ, 18–21 mm.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → ᐊᖏᔪᓂᑦ ᐱᙳᐊᕈᑎᓂᑦ ᐊᓯᐊᓄᑦ ᐊᐅᓚᑦᑎᓂᖓᓂᒃ. 2017-ᒥ ᖃᐅᔨᓴᕐᓂᖅ ᑕᒪᓐᓇ ᐃᓱᒪᒋᔭᖅ ᖃᐅᔨᓴᓚᐅᖅᑕᖓ ᐃᓐᑐᐳᓗᒃ (Interblock) ᐱᙳᐊᖅᑎᑦᓯᔨᖃᙱᑦᑐᓂ ᒪᕐᕉᒃ ᓯᕉᐊᒃᓴᓗᐊᖅᓯᕉᐊᑕᐅᓯᖅ ᐅᔾᔪᐊᕌᔭᒃ ᐃᓂ ᐊᔾᔨᒌᒃᑐᒥᒃ ᐊᑭᓕᐅᑎᓕᖕᓄᑦ, ᑕᓴᓐᓄᑦ ᓇᑉᐸᖅᑐᓄᓪᓘᓐᓃᑦ ᐱᙳᐊᕈᑏᑦ ᐃᓚᐅᑎᙱᑕᖓ; ᑳᓯᓅᑉ ᐃᓚᖓᑕ ᐱᓇᓪᓗᑎᖓ. ᐊᓯᐊᓂ ᐊᑎᖏᑦ: ᐊᑕᐅᓯᖅ ᓯᕉ, 0.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → ᐊᒃᓴᓗᐊᓂ ᓛᔅ ᕖᒐᔅᒥ, ᐊᒃᓴᓗᐊᑉ ᐃᓚᖓᓄᑦ ᑕᓪᓕᒪᓄᑦ ᓴᓂᓕᐅᑎᒌᒃᑐᓄᑦ ᓈᓴᐅᑎᓄᑦ ᐱᙳᐊᕈᑎᓕᐅᖅᓗᓂ, ᐊᒃᓴᓗᐊᕐᒥᒃ ᐊᑯᓂᐅᓂᖓᒍᑦ ᓈᓴᐃᔨᐅᑉ ᐱᙳᐊᕈᑎᓕᐅᕐᓂᖓᑐᑦ. 299 ᑲᐃᕙᕐᓂᓂ ᐊᒃᓴᓗᐊᑉ ᐃᓚᖓ 29-ᓂᒃ ᐊᔪᒐᓚᐅᖅᑐᖅ 39.3 ᓂᕆᐅᒋᔭᐅᓪᓗᓂ, ᑕᒪᑐᒥᖓ ᐃᓚᐃᓐᓂᖅ ᓈᒻᒪᒃᑐᖅ ᐊᒃᓴᓗᐊᖅ ᓴᖅᑭᑎᑦᑎᕙᒃᑐᖅ ᐊᒡᒐᖓ 4%-ᒥ. ᑲᐃ-ᔅᑯᐃᐅ 38 ᐃᓂᓂ ᑕᒪᐃᓐᓂ 45.29 37 ᐃᒻᒥᓂᖅᑐᑦ ᐊᒥᓲᓂᖏᓐᓂ: p = 16.5%. ᑕᑯᔭᐅᓯᒪᔪᑦ ᑐᒡᓕᐊᑦ 1,204 ᑲᐃᕙᕐᓃᑦ ᐱᖓᓱᓐᓂ ᐊᒃᓴᓗᐊᓂ χ² = 34.79, p = 57% ᑐᓂᓯᓚᐅᖅᑐᑦ, ᐊᒃᓴᓗᐊᑉᓗ ᐃᓚᖓ ᓇᓪᓕᐊᑐᐃᓐᓇᖅ ᖃᐅᔨᓴᖅᑕᐅᓯᒪᔪᖅ ᐱᒻᒪᕆᐅᓚᐅᙱᑦᑐᖅ. ᒪᕐᕉᒃ ᑕᑯᔭᐅᓯᒪᔪᑦ ᑲᑎᓪᓗᒋᑦ, 1,503 ᑲᐃᕙᕐᓃᑦ, χ² = 41.75, p = 27% ᑐᓂᓯᓚᐅᖅᑐᑦ. ᐃᓱᓕᑦᑕᐅᑎ ᐅᓇ: ᐊᐅᓚᑦᑎᓂᕐᒥᒃ ᓇᓗᓇᐃᖅᓯᔪᖃᙱᑦᑐᖅ. ᓯᕗᓪᓕᖅᐹᑦ ᑕᑯᔭᐅᓯᒪᔪᑦ ᑭᓯᒪᓂᖏᓐᓂ ᐃᓱᒪᒋᓇᖅᑐᓂᒃ ᐊᔾᔨᖃᓚᐅᖅᑐᑦ; ᑐᒡᓕᐊᑦ ᐃᓱᓕᑦᑎᓚᐅᖅᑕᖏᑦ.

ᑕᑯᔭᐅᓯᒪᔪᑦᑲᐃᕙᕐᓃᑦχ²dfp
ᓯᕗᓪᓕᖅᐹᑦ29945.293716.5%
ᑐᒡᓕᐊᑦ, ᐱᖓᓱᑦ ᐊᒃᓴᓗᐊᑦ1,20434.793757%
ᒪᕐᕉᒃ1,50341.753727%
ᓈᓴᐅᑏᑦ 2017-ᒥ ᖃᐅᔨᓴᕐᓂᕐᒥᑦ; p ᐊᑭᖓ ᑕᒪᑐᒪ χ²-ᒥᓂᑦ ᓴᖅᑭᔪᖅ. ᒪᕐᕉᒃ ᓯᕉ ᐊᒃᓴᓗᐊᖅ 38 ᐃᓂᓕᒃ, ᑕᐃᒪᐃᒻᒪᑦ 37 ᐃᒻᒥᓂᖅᑐᑦ ᐊᒥᓲᓂᖏᑦ.

ᑲᐃ-ᔅᑯᐃᐅ ᐅᖓᑖᓂ

ᐃᓂᒧᑦ ᐊᑕᐅᓯᕐᒧᑦ ᐃᓱᒪᒋᔭᐅᔪᒧᑦ ᒪᕐᕉᓄᑦ ᐊᕕᒃᑐᖅᓯᒪᔪᖅ ᖃᐅᔨᓴᕈᑎ (binomial) ᓴᙱᓂᖅᓴᐅᔪᖅ. ᐊᒃᓴᓗᐊᑉ ᐃᓚᖓᓄᑦ ᐃᓱᒪᒋᔭᐅᔪᒧᑦ, ᐊᒃᓴᓗᐊᑉ ᐃᓚᖓᓄᑦᐊᒃᓴᓗᐊᖅᐊᒃᓴᓗᐊᑉ ᐃᓚᖓᐊᒃᓴᓗᐊᕐᒥ ᐃᓂᑦ ᓴᓂᓕᐅᑎᒌᒃᑐᑦ ᑲᑎᑦᑐᑦ, ᐱᙳᐊᕈᑎᓕᕆᕝᕕᖕᒥ ᑲᑎᑦᑐᓂᑦ ᐊᔾᔨᒋᙱᑦᑐᑦ.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → z ᖃᐅᔨᓴᕈᑎ ᐊᒃᓴᓗᐊᑉ ᐃᓚᖏᓐᓂᒃ ᖃᐅᔨᓴᕐᓂᕐᒥᒃ ᒪᑉᐱᒐᕐᒥ. ᑲᐃ-ᔅᑯᐃᐅ ᑕᒪᐃᓐᓄᑦ ᖃᐅᔨᓴᕈᑎ: ᓱᓇ ᓈᒻᒪᙱᓐᓂᖓᓂᒃ ᐅᖃᐅᑎᔪᖅ ᓱᓇᐅᓂᖓᓂᒃ ᐅᖃᐅᓯᖃᙱᑦᑐᖅ. ᓯᕗᓪᓕᐅᓪᓗᓂ ᐊᑐᕐᓗᒍ, ᑕᐃᒪ ᑕᑯᓗᑎᑦ.

ᐊᒃᓴᓗᐊᑉ ᐃᓚᖏᓐᓂᒃ ᖃᐅᔨᓴᕐᓂᖅ

ᓈᓴᐅᑎᓕᐅᕈᑎ

χ² = Σᵢ (Oᵢ − Eᵢ)² / Eᵢ
Eᵢ = n / 37 · df = 36
ᑭᒡᓕᐊ ᓈᓴᐅᑏᑦ: 51.0 (5%) · 58.6 (1%)

ᐊᐱᖅᑯᑏᑦ

ᓱᖕᒪᑦ 36 ᐃᒻᒥᓂᖅᑐᑦ ᐊᒥᓲᓂᖏᑦ, 37 ᐱᓇᓂ?

37 ᓈᓴᐅᑏᑦ n-ᒧᑦ ᑲᑎᑦᑐᒃᓴᐅᒻᒪᑕ, ᑕᐃᒪᐃᒻᒪᑦ 36 ᑕᐃᒃᑯᐊᖑᓪᓗᐊᑕᖅ ᐃᒻᒥᓂᖅ ᐊᓯᑦᑐᕈᓐᓇᖅᑐᑦ.

ᓴᖑᓯᒪᔪᐊᓗᒃ ᐊᒃᓴᓗᐊᖅ ᖃᓄᐃᑦᑐᒥᒃ χ²-ᒥᒃ ᑕᑯᑎᑦᑎᓂᐊᖅᐸ?

ᐊᒃᓴᓗᐊᖅ ᐃᓂᒥᒃ ᐊᑕᐅᓯᕐᒥᒃ 1/25-ᒥ ᐃᓂᓕᒃ 10,000 ᑲᐃᕙᕐᓂᓂ ᐃᓂᐅᑉ ᐃᓚᖓᓂᒃ ᑭᓯᒪᓂᖓᓂ ᐊᒡᒐᖓ 60-ᒥᒃ ᑐᓂᓯᓂᐊᖅᑐᖅ; χ² ᐊᒡᒐᖓ 100, p ᐊᒡᒐᖓ ᓯᕉ.

200 ᑲᐃᕙᕐᓂᓂ ᐊᑐᕈᓐᓇᖅᐱᖓ?

ᒪᓕᒐᒃᑯᑦ ᐄ, ᓂᕆᐅᒋᔭᐅᔪᖅ 5.4 ᐃᓂᒧᑦ. ᓱᓇᒥᒃ ᖃᐅᔨᓂᐊᙱᑦᑐᖅ ᐃᓂ ᓂᐳᒃᑎᑕᐅᓪᓗᓂ ᒪᑐᔭᐅᓯᒪᙱᑉᐸᑦ.

ᐃᓪᓗᕐᓇᖅᑐᖅ ᐊᔾᔨᓕᐊᖅ

ᑕᑯᔭᐅᓗᐊᙱᑦᑐᑦ ᐃᒻᒥᓂᒃ ᐊᐱᖅᑕᐅᓯᒪᔪᑦ ᑲᑎᑦᓗᒋᑦ. 51.0-ᒧᑦ ᓇᓪᓕᒋᓗᒍ.

ᑕᑯᔭᐅᓗᐊᙱᑦᑐᑦ ᐃᒻᒥᓂᒃ ᐊᐱᖅᑕᐅᓯᒪᔪᑦ ᑲᑎᑦᓗᒋᑦ. 51.0-ᒧᑦ ᓇᓪᓕᒋᓗᒍ.

ᐱᕝᕕᒋᔭᐅᔪᑦ

  1. Pearson, K. “On the criterion that a given system of deviations from the probable…” Philosophical Magazine 50(302), 1900.
  2. Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1. Wiley, 3-ᖓ ᓴᖅᑭᑕᐅᓂᖓ, 1968. ᐱᙳᐊᕈᑎᒃᓴᐃᑦ ᐃᓘᓐᓇᑎᒃ ᐊᓯᐅᓂᖏᑦ, ᐃᓚᖓ XIV.
  3. Wizard of Odds. “Organic Roulette Experiment.” ᒫᑦᓯ 2017; ᓄᑖᙳᖅᑎᑕᐅᓯᒪᔪᖅ ᐊᐅᒡᒍᓯ 3, 2026.
ᕿᒥᕐᕈᔭᐅᓚᐅᖅᑐᖅ 2026-09-28ᐊᔾᔨᐅᖅᑕᐅᑎ: ᐃᐅᕌᐸ, ᐊᑕᐅᓯᖅ ᓯᕉᖃᓄᖅ ᓈᓴᐃᓂᖅ ↗ᐱᕝᕕᒋᔭᐅᔪᑦ ↗