1.0 Hypothesis Testing

Transcription

1 .0 Hypothesis Testing The Six Steps of Hypothesis Testing Rejecting or Accepting the Null Samples and Data. Parametric Tests for Comparing Two Populations Testing Equality of Population Means (T Test! " # ± & '.'*,,-. / Independent Samples with Unequal Population Variances Independent Samples and Equal Population Variances Dependent Samples Matched Pairs Testing Equality of Population Variances (F Distribution or F Test ( / ( /!, 7 8\,,,-. 7.-:,,-. Testing the Equality of Population Proportions [< ± > '.'*?< ( < /. Test for Whether A Series Is Normally Distributed Test for Normal Distribution (Jarque-Bera Test D(" E AB = F G D(" EH B = F H IAJ = AAJ K IAD = AAD K.3 Parametric Test for Comparing Two Or More Populations Analysis of Variance (ANOVA.4 Nonparametric Tests for Comparing Two Populations Testing Location with Independent Samples (Wilcoxon Rank Sum Test > = J. D(J. ~O(0, F LM Testing Location with Dependent Variables Matched Pairs (Sign Test.5 Nonparametric Test for Comparing Two Or More Populations Kruskal-Wallis Test.6 Correlation Correlation for Quantitative Data (Pearson Correlation Coefficient Correlation for Ordinal Data (Spearman Rank Correlation Coefficient

2 .0 Regression. Simple Regression Model Least squares estimators Time-Series Data Cross-Section Data Constant Error Variance/Homoscedasticity QRS(T U = F Hypothesis Result Maximum Sampling Error with Probability (V W &:,,- /Y(Z [ \ V]](V W% interval estimate/confidence interval for _` az[ \ ± &:,,- /YbZ [ \ cd Log Linear Equation Log-Log Equation. Multiple Regression Model Checking for Heteroskedasticity Goodness of Fit Y U = e U ef U = e U bz[ ' + Z[. ".U + Z[ " U + + Z[ iu " i c Testing the Overall Model Quadratic Models e = Z ' + Z. ". + Z ". + Z G " + Z H " + Z * ". " + T je j". = Z. + Z ". + Z * " + T Hypothesis Testing & Interval Estimation for functions with more than one coefficient QRS lmbz[, Z[ G cn = o jm p QRSbZ[ c + o jm p QRSbZ[ G c + o jm p o jm p qrqbz[, Z[ G c jz[ j Z[ G jz[ jz[ G!o Z [ p ± & (,-i-. /Yo Z [ p Z[ G Z[ G Dummy Variables Testing Joint Null Hypothesis (Wald F-Test Prediction/Forecasting QRSbe ' ef ' c = QRSbZ[ ' c + " ' QRSbZ[. c + " ' qrqbz[ ', Z[. c + QRS(T ' QRSbe ' ef ' c = QRS(T ' = F /Ybe ' ef ' c = sqrs t be ' ef ' c [ef ' ± & ('.'*,,-i-. /Y(e ' ef ', ] Model Choice Issues

3 3.0 Binary Choice Models Linear Probability Model Probit Model Z \ v w(x U Logit Model Z \ v o exp{ x U} ( + exp{x U } p 4.0 Time Series Regression Features of Time Series Regressions Autocorrelations ~ = qrq(e Ä, e Ä- QRS(e Ä Significance of an Autocorrelation Correlograms Time-Series Regression Models Forecasting From an AR( Model ef LÅ. = Ç[ + Éf. e L ef LÅ\ = Ç[ + Éfef LÅ\-. Ñef LÅ\ ± & '.'*,L- /YbÖ \ cü AR( Model with Trend e E á = É. be Ä-. E á c + T Ä e Ä = e Ä E á Estimation Strategy e Ä = Ç + äe Ä-. + T Ä e Ä = Ç + äe Ä-. É e Ä-. + T Ä Two Non-Stationary Models e Ä = Ç + e Ä-. + T Ä Multiplier Analysis e = ã + Z ' " Ä + Z. " Ä-. + Z " Ä- + + Q Ä je Ä = Z j" ' = Ç[ Ä Ä je Ä = je ÄÅ = Éf j" Ä- j". Ç[ Ä v je Ä j" Ä- = v Z = Ç[ ' + Ç[. + Ç[ v je Ä j" Ä-\ = v Z \ = Ç [ ' Éf.

4 .0 Hypothesis Testing Explain the general framework for using data to make inferences about population parameters The Six Steps of Hypothesis Testing. Set up null and alternative hypotheses. Test statistic and sampling distribution 3. Specify significance level 4. Define decision rule 5. Collect sample, compute or p-vale 6. Make decision and conclude Rejecting the null there is not enough evidence to accept the null. Rejecting or Accepting the Null Accepting the null never state the null is true, simply it is not false there is not enough evidence to reject the null or the evidence from the sample is not compatible with the null Explain the general framework for using data to make inferences about population parameters Samples and Data To learn about parameters like E or <, you use a sample to make sample statistics " or < probability distributions show how good the samples are as estimates

5 . Parametric Tests for Comparing Two Populations Apply the six hypothesis testing steps to testing a population mean µ Test hypotheses for the difference between two means using samples of independent quantitative data Testing Equality of Population Means (T Test ç ' : E. = E ç è : E. E rs E. < E rs E. > E when ç è : E. E, the test is two-tailed p-values on EViews are always for -tail test, must be halved for -tail reject null when & > critical value reject null when p < significance population variances are always known 95% interval estimate! " # ± & '.'*,,-. / Two t tests for using independent samples of quantitative (continuous data to test the equality of population means. One test assumes equal variances; the other does not Independent Samples with Unequal Population Variances & = (" #. "# (E. E ~&(Q ì /. + /. degrees of freedom a /. + / jö =. d î /. / ï î.. + ï Independent Samples and Equal Population Variances & = (" #. "# (E. E s/ ñ l. + n ~&,M Å, ó -

6 Estimates common population variance F = F. = F pooled variance estimate / ñ = (. /. + ( /. + degrees of freedom Q =. + Explain the difference between testing for the equality of means with independent samples and testing for the equality of means with matched pairs Test the equality of two means using a sample of matched pairs data Dependent Samples Matched Pairs ç ' : E ò = 0 ç è : E ò 0 rs E ò < 0 E ò > 0 matched pairs is better than independent samples as the variance is smaller & = " # ò / ò ~& :,,-. ôhysy õ = ". " p-value <S ú&, > " # ò / ù ò 0 Apply the six hypothesis testing steps to testing a population variance s Test the equality of two population variances Testing Equality of Population Variances (F Distribution or F Test ç ' : F. = F ç. : F. F rs F. < F rs F. > F Tests whether population variances are equal or vary samples are independent Explain how the F-distribution is obtained from two independent chi-square distributions or f statstic û = /. /F. /. /F. ~û, M -.,, ó - The ratio of two independent chi-square random variables, each divided by its degrees of freedom, is an F random variable or F distribution degrees of freedom parameters are and. reject ç ' if û.- ü ó,, M-.,, ó - > M ó / ó M ó M / ó > ûü M ó,, M-.,, ó - confidence interval

7 ( / ( /!, 7 8\,,,-. 7.-:,,-. critical values û :.-, = M, ó û:, ó, M lower critical values can be obtained from upper critical values alternatively, the larger sample variance can be placed in the numerator. Apply the six hypothesis testing steps to testing the equality of two population proportions, ç: <. = < Testing the Equality of Population Proportions ç ' : <. = < ç. : <. < rs <. < < rs <. > < Variables are intendent and binomially distributed categorical either or 0 the Satterthwait-Welche t-test on EViews <. < > =?< ( < l + ~O(0,. n pooled estimate < =.< + <. + 95% interval estimate [< ± > '.'*?< ( < /