Level 1 - Quantitative Method - Hypothesis Testing

Hypothesis Testing

Null and Alternative Hypothesis

- Null (Ho): 希望被推翻的立論

- Alternative (H_A): 希望成立的立論

 

General Process of Testing

1.      Define one or two tail test:

-          Two tail : H₀: x = 0, H_A: x ≠ 0

-          One tail : H₀: x >= 0, H_A: x < 0

2.      決定test statistics:

假設要test的是population mean是否等於0

è Test statistics = (sample value – hypothesized value)/S.D. or S.E.

3.      決定level of significance and its critical value (normal distribution)

Level of significance	One tail	Two tail
1%	2.33	2.58
5%	1.65	1.96
10%	1.28	1.65

 4.      比較 test statistics及critical value決定是否能reject null hypothesis

Error and Power of Test

Type 1 Error:

錯誤地 reject 了真的 null hypothesis，level of significance愈大，錯的機會愈大

Type 2 Error:

Reject 不到錯的 null hypothesis

Power of Test:

正確地 reject 了錯的 null hypothesis 的機會率

P value:

Level of significant 要達到幾大，才可將 reject到 null hypothesis, e.g.:

In a two tail test, the observation is 1 S.D. from the mean, critical value indicates there’s 68% chance在 ± 1 S.D.中，所以 level of significance 要 32% 或以上才可 reject 到 null hypothesis

Typical test in exam

考試主要focus on testing observation (population mean) 是否在某一個range，> 或 < 某數值，然後再用sample size，population variance known or not而決定使用T or Z statistics，最後make decision on reject or not

 

Other tests

考試中，一般都不會問及以下test的計算方法，只要大概知道一下，就可以了

1.      Difference in Mean test

-          Test 兩個 population 的 mean 是否一樣或是否相差一個指定的數值

-          Use T statistics

2.      Paired Comparison test

-          Test 兩個 population 是否 independent

-          Use T statistics

3.      Difference in Variance test

a.      Test sample 與 population 的 variance 是否一樣 à use Chi square (X²) statistics

b.      Test 兩個 population 的 variance 是否一樣 à use F statistics