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1、【复旦大学首批FIST项目传播学研究方法讲义】3_统计推断和t-检验-方差分析 导读：就爱阅读网友为您分享以下“【复旦大学首批FIST项目传播学研究方法讲义】3_统计推断和t-检验-方差分析”的资讯，希望对您有所帮助，感谢您对的支持!3、统计推断、卡方检验、t检验和方差分析 复旦大学2013年FIST课程 传播研究方法 Winson Peng 彭泰权 Outline ?Inferential Statistics Significance Test Crosstabulation/Chi-square Test t-Test F-Test/ANOVA I. What Does Bivariat
2、e Analysis Do? 1.Estimate and test the significance of the difference in an interval DV between/among groups (Compare means based on t-test or F-test) 2.Estimate and test the significance of the difference in a nominal DV between/among groups 2(Crosstabulations based on ? test) 3.Estimate and test t
3、he significance of the correlations between an interval IV and an interval DV (Correlation or Regression based on t-test or F-test) 3 Statistical Techniques for Bivariate Analysis IV DV Dichotomous Multinomial Continuous Dichotomous Logistic ?2 Test of Regression Multinomial Crosstabulation Analysis
4、 Multinomial Logistic Regression Continuous t-Test ANOVA (F-Correlation Test) /OLS Regression 4 Statistical Techniques for Multi-IVs and Single DV IVs DV Dichotomous Multinomial Continuous Mixed Dichotomous Logistic Regression Log-linear Modeling Multinomial Multinomial Logistic Regression Continuou
5、s ANOVA OLS Regression /ANCOVA 5 Statistical Techniques for Multi-IVs and Multi-DVs IVs DVs Dichotomous Multinomial Continuous Mixed Dichotomous Not available; convert Latent Categorical continuous IVs to Multinomial Analysis (LCA) categorical and then use LCA Continuous General Linear Modeling MANC
6、OVA (GLM) /MANCOVA /Structural Equation Modeling (SEM) 6 Probability Theory, Sampling Distributions, and Estimates of Sampling Error ?Sampling Distribution oSingle most important concept in inferential statistics oDefinition: The theoretical, probabilistic distribution of a statistic for all possibl
7、e samples of a given size (N). oThe sampling distribution is a theoretical distribution. ?Every application of inferential statistics involves three different distributions. ?Information from sample is linked to population via sampling distribution oPopulation: empirical; unknown oSampling Distribut
8、ion: theoretical; known oSample: empirical; known Figure 7.4 ?The Sampling Distribution of Ten Cases Figures 7.5 & 7.6 Figure 7.7 Sampling Distribution: Properties 1.Normal in shape. 2.Has a mean equal to the population mean. 3.Has a standard deviation (standard error) equal to the population standa
9、rd deviation divided by the square root of N. Central Limit Theorem: Key ?If repeated random samples of size N are drawn from any population with mean and standard deviation , then, as N becomes large, the sampling distribution of sample means will approach normality, with a mean ?/Nand standard dev
10、iation of oFor any trait or variable, even those that are not normally distributed in the population, as sample size grows larger, the sampling distribution of sample means will become normal in shape. ?Importance of Central Limit Theorem: removes constraint of normality in the population. Steps in
11、Significance Test 1.Formulate null and alternative hypotheses ooo?1?2Null hypothesis (H0): Alternative hypothesis (Ha): ?1?2One-tailed vs. two-tailed tests 2.Choose appropriate test statistic: z, t, F, or ?2 3.Specify significance level and critical value: oo Significance level: ? = .05 (or .01, .00
12、1) Critical value: specific Z-, t-, F-, or ?2 value corresponding to the chosen ?-level 13 Steps in Significance Test (2) Estimate the chosen test statistic, e.g., , or x1?x2x1?x2z?t?sex1?x2sex1?x2 5.Compare the estimated statistic against the specified critical value (?) to decide if the evidence i
13、s strong evidence to reject H0, e.g.,: 4.oif z ? Za, accept H0; oif z Za, reject H0. 14 Significance Level (?) & Critical Value (Za) 1?Region of ?2Rejection Region of Acceptance ?2Region of Rejection -Za/2 ?Za/2 15 Significance Level (?) vs. Probability Level (p) ? is a critical value (commonly as .
14、05, .01, or .001) for sampling distribution prescribed in advance; ?p is an observed probability based on the sample data; ?if p 16 Type I vs. Type II Errors ?Type I Error: reject a null hypothesis when it is in fact true. ?Type II Error: accept a null hypothesis when it is actually false. ?Since it
15、 is impossible/impractical to know if the null hypothesis is true or false, rejection of an H0 always involves making a Type I Error whereas acceptance of an H0 always runs the risk of a Type II Error. 17 Errors in Significance Test H0 is actually Decision True False Reject H0 Type I Error Correct Decision Accept H0 Correct Decision Type II Error 18 Calculation of Type I & II Errors ?Probability (Type I Error) = ? ?Probability (Type II Error) = b ?Power of Test = 1 - b 19
