《計(jì)量經(jīng)濟(jì)第四章》ppt課件(文件)
【正文】 Using a transformation, especially taking the log, often yields a distribution that is closer to normal. 通過變換，特別是通過取自然對(duì)數(shù)，往往可以得到接近于正態(tài)的分布。 ? Type I error: reject the null hypothesis when it is in fact true. 第一類錯(cuò)誤：當(dāng)零假設(shè)為真時(shí)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(cuò)誤：當(dāng)零假設(shè)為假時(shí)未拒絕零假設(shè)（取偽） Background Review 背景知識(shí)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(yàn)的規(guī)則使發(fā)生第一類錯(cuò)誤的概率非常小。 Background Review 背景知識(shí)回顧 ? The critical value of the test statistic is the value of the statistic for which the test just reject the null hypothesis at the given significance level. 檢驗(yàn)統(tǒng)計(jì)量的 臨界值 是使得零假設(shè)剛好在給定顯著性水平上被拒絕的統(tǒng)計(jì)量的值。 Theorem t Distribution for the Standardized Estimators 定理 : 標(biāo)準(zhǔn)化估計(jì)量的 t分布 ? ?? ?? ?? ?。在5％顯著水平下，臨界值位－ ? Because –, we fail to reject the null. 由于 ，我們不能拒絕零假設(shè) Example: Student Performance and School Size 例子：學(xué)生表現(xiàn)與學(xué)校規(guī)模 ? If we are also interested in asking whether betterpaid teachers leads to better student performance, we can test 如果我們同樣感興趣是否高收入的教師會(huì)使學(xué)生表現(xiàn)更好，我們可以檢驗(yàn)： ? H0 :βtotp=0 versus H1 :βtotp0 ? The calculated t statistic equals . Since , therefore rejecting the H0 at 1% level. 計(jì)算得到的 t統(tǒng)計(jì)量為 。 ? 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(duì)于雙邊檢驗(yàn)，我們根據(jù) a/2計(jì)算臨界值。標(biāo)準(zhǔn)正態(tài)分布的在 5%的顯著水平對(duì)應(yīng)的臨界值為 。 Computing pvalues for t Tests 計(jì)算 t檢驗(yàn)的 p值 ? The steps in classical hypothesis testing: 經(jīng)典假設(shè)檢驗(yàn)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 決定顯著水平，找到臨界值 ? Calculate the t statistic based on the sample data 根據(jù)樣本數(shù)據(jù)計(jì)算 t 統(tǒng)計(jì)量 ? Compare the t statistic with the critical value to decide whether to reject the null ? 比較 t 值與臨界值，決定是否拒絕零假設(shè)。對(duì)于雙邊檢驗(yàn) pvalue=P(|T||t|). Computing pvalues for t Tests 計(jì)算 t檢驗(yàn)的 p值 pα/2 pα/2 In the above example, it must be true that 1%p5%. pvalue=P(|T|) =2P(T) =. 。我們是否應(yīng)當(dāng)拒絕零假設(shè)？ ? Committing to a significance level ahead of time can hide useful information about the oute of a hypothesis test. 提前確定顯著水平可能會(huì)隱藏關(guān)于假設(shè)檢驗(yàn)的一些有用信息。 Summary for H0: bj = 0 總結(jié) ? Unless otherwise stated, the alternative is assumed to be twosided 除非特別指出，我們總認(rèn)為替代假設(shè)是雙邊的 ? If we reject the null, we typically say “xj is statistically significant at the a % level” 如果拒絕了零假設(shè)，我們通常說 “ xj 在 a % 水平下顯著 ” ? If we fail to reject the null, we typically say “xj is statistically insignificant at the a % level” 如果不能拒絕零假設(shè)，我們通常說 “ xj 在 a % 水平下
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