計量經(jīng)濟(jì)第四章ppt課件(完整版)
【正文】 0: bj = 0 H1: bj ?= 0 c 0 a/2 ?1 ? a? c a/2 TwoSided Alternatives 雙邊替代假設(shè) reject reject fail to reject Example: Student Performance and School Size continued(example ) 例子：學(xué)生表現(xiàn)與學(xué)校規(guī)模 ? We have estimated 我們已經(jīng)得到 ^math10=++ –.0002enroll () () () () ? If the question is: whether the number of teachers has impacts on student performance, we can form hypotheses of: H0: bstaff = 0 , H1: bstaff ?= 0. 如果問題是：教師數(shù)目是否對學(xué)生表現(xiàn)有影響，我們可以檢驗如下假設(shè)： H0: bstaff = 0 , H1: bstaff 不等于 0. ? The calculated t ratio is . The 5% critical value of standard normal is . Since , we fail to reject the null 計算得到的 t值為 。 Computing pvalues for t Tests 計算 t檢驗的 p值 ? An alternative to the classical approach : If the calculated t statistic is used as critical value, what is the smallest significance level at which the null hypothesis would be rejected? 另一種想法：如果將算得的 t 統(tǒng)計量作為臨界值，那么使得零假設(shè)被拒絕的最小顯著水平是多少？ ? This level is known as the pvalue. For a twosided alternative, 這個水平稱為 p 值。對于 95自由度的 t分布， 1%顯著水平下單邊檢驗的臨界值為 ，拒絕零假設(shè)。在此替代假設(shè)下，我們并未規(guī)定 xj 對 y影響的符號。當(dāng)我們用某一特定樣本計算此統(tǒng)計量時，我們得到這個檢驗統(tǒng)計量的一個實現(xiàn)（ t）。 Background Review 背景知識回顧 ? Two kinds of mistakes are possible in hypothesis testing. 在假設(shè)檢驗中存在兩種可能的錯誤。Multiple Regression Analysis: Inference 多元回歸分析：推斷 (1) y = b0 + b1x1 + b2x2 + . . . bkxk + u Lecture Outline 本課提綱 ? CLM assumptions and Sampling Distributions of the OLS Estimators 經(jīng)典假設(shè)與 OLS估計量的樣本分布 ? Background review of hypothesis testing 假設(shè)檢驗的背景知識 ? Onesided and twosided t tests 單邊與雙邊 t檢驗 ? Calculating the p values 計算 p值 Assumption (Normality) 假設(shè) （正態(tài)） ? So far, we know that given the GaussMarkov assumptions, OLS is BLUE, 我們已經(jīng)知道當(dāng) Gauss－ Markov假設(shè)成立時， OLS是最優(yōu)線性無偏估計。 ? Type I error: reject the null hypothesis when it is in fact true. 第一類錯誤：當(dāng)零假設(shè)為真時拒絕零假設(shè)（棄真） ? Type II error: fail to reject the null when it is actually false. 第二類錯誤：當(dāng)零假設(shè)為假時未拒絕零假設(shè)（取偽） Background Review 背景知識回顧 ? Hypothesis testing rules are constructed to make the probability of mitting type I error fairly small. 我們建立一些假設(shè)檢驗的規(guī)則使發(fā)生第一類錯誤的概率非常小。 Theorem t Distribution for the Standardized Estimators 定理 : 標(biāo)準(zhǔn)化估計量的 t分布 ? ?? ?? ?? ?。 ? For a twosided test, we set the critical value based on a/2 and reject H0 if the absolute value of the t statistic c. c is the percentile in the t distribution with nk1 degrees of freedom if a?. 對于雙邊檢驗，我們根據(jù) a/2計算臨界值。 Computing pvalues for t Tests 計算 t檢驗的 p值 ? The steps in classical hypothesis testing: 經(jīng)典假設(shè)檢驗的步驟 ? State the null and the alternative hypothesis 表述零假設(shè)和替代假設(shè) ? Decide a significance level and find the related critical value
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