計量經(jīng)濟第四章ppt課件-資料下載頁
2025-05-03 07:37本頁面
【正文】 reject the null, we typically say “xj is statistically insignificant at the a % level” 如果不能拒絕零假設，我們通常說 “ xj 在 a % 水平下不顯著 ” Testing other hypotheses 其他假設檢驗 ? A more general form of the t statistic recognizes that we may want to test something like H0: bj = aj 如果我們想對形如 H0: bj = aj 的假設進行檢驗，需要更一般的 t統(tǒng)計量 ? In this case, the appropriate t statistic is 此時，恰當?shù)? t 統(tǒng)計量是 ? ?? ?0 t e s ts t a n d a r d f o r t h e 0 w h e r e,??????jjjjjaaseat當進行標準檢驗時bbExample: Campus Crime and Enrollment 例子：校園犯罪與錄取 ? Question: Will 1% increase in enrollment increase campus crime by more than 1%? 問題：錄取量提高 1%是否會導致校園犯罪增加超過 1%? ? Suppose total number of crimes is determined by 假設犯罪總數(shù)由下式?jīng)Q定 crime=exp(b0 )enrollb1exp(u). ? One can estimate 可以估計 log(crime)=b0 + b1 log(enroll)+u Example: Campus Crime and Enrollment 例子：校園犯罪與錄取 ? And test H0: b1 = 1 H1: b1 1. ? Using data from the FBI’s uniform Crime reports (97 observations), the estimated equation is ? 利用 FBI犯罪報告（ 97個觀察值）的數(shù)據(jù)，估計得到方程 ^log(crime)=+(enroll) () () () The correct t ratio=()/=. The 1% onesided critical value for a t distribution with 95 degrees of freedom is . Therefore reject the null. t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。 Computing pvalues for t Tests 計算 t檢驗的 p值 ? The steps in classical hypothesis testing: 經(jīng)典假設檢驗的步驟 ? State the null and the alternative hypothesis 表述零假設和替代假設 ? 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)計算 t 統(tǒng)計量 ? 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。 Computing pvalues for t Tests 計算 t檢驗的 p值 ? Suppose at 40 degrees of freedom, a calculated t ratio is , the related 5% and 1% critical values are and , respectively. Should we reject or not to reject the null? 假設自由度為 40，算得 t 值為 ，對應 5%和1%的臨界值分別為 和 。我們是否應當拒絕零假設？ ? 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隱藏關于假設檢驗的一些有用信息。 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。對于雙邊檢驗 pvalue=P(|T||t|). Computing pvalues for t Tests 計算 t檢驗的 p值 pα/2 pα/2 In the above example, it must be true that 1%p5%. pvalue=P(|T|) =2P(T) =
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