【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

【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
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-T est
F-Test/ANOVA
I. What Does Bivariate 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
(Crosstabulations based on 2 test)
3.Estimate and test the significance of the correlations
between an interval IV and an interval DV
(Correlation or Regression based on t-test or F-test)
Statistical Techniques for Bivariate Analysis
IV
DV Dichotomous Multinomial Continuous
Dichotomous
2 Test of
Crosstabulation Analysis
Logistic Regression
Multinomial Multinomial Logistic Regression
Continuous t-Test ANOVA (F-
Test)
Correlation
/OLS Regression
IVs
DV
Dichotomous
Multinomial
Continuous
Mixed
Dichotomous
Log-linear Modeling
Logistic Regression Multinomial Multinomial Logistic
Regression Continuous
ANOVA
OLS Regression /ANCOVA
IVs
DVs Dichotomous Multinomial Continuous Mixed
Dichotomous
Latent Categorical
Analysis (LCA) Not available; convert continuous IVs to categorical and then
use LCA
Multinomial
Continuous General Linear Modeling
(GLM) /MANCOVA
MANCOVA
/Structural Equation
Modeling (SEM)
Probability Theory, Sampling Distributions, and Estimates of Sampling Error
Sampling Distribution
o Single most important concept in inferential statistics
o Definition: The theoretical, probabilistic distribution of a
statistic for all possible samples of a given size (N).
o The sampling distribution is a theoretical distribution.
Every application of inferential statistics involves three different distributions.
o Population: empirical; unknown
o Sampling Distribution: theoretical; known
o Sample: empirical; known
Information from sample is linked to population via sampling distribution
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 standard 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 μ and standard deviation σ, then, as N
becomes large, the sampling distribution of sample means will approach normality, with a mean μ
and standard deviation of
o For 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.
/N
Steps in Significance Test
1.Formulate null and alternative hypotheses
o Null hypothesis (H 0):
o Alternative hypothesis (H a ): o
One-tailed vs. two-tailed tests
2.Choose appropriate test statistic: z , t , F , or χ2
3.Specify significance level and critical value:
o Significance level: α = .05 (or .01, .001) o
Critical value: specific Z -, t -, F -, or χ2 value corresponding to the chosen α-level
21μμ=21μμ≠
Steps in Significance Test (2)
4.
Estimate the chosen test statistic, e.g., , or
pare the estimated statistic against the
specified critical value (α) to decide if the evidence is strong evidence to reject H 0, e.g.,:
o if z ≤ Z a , accept H 0; o if z > Z a , reject H 0.
2121x x se x x z --=212
1x x se x x t --=
2α2αα
-1μ
Z a/2
-Z a/2
Region of
Rejection
Region of Rejection
Region of Acceptance
Significance Level (α) & Critical Value (Z a )
Significance Level (α) vs. Probability Level (p)
α is a c ritical value (commonly as .05, .01, or .001) for sampling distribution prescribed in advance;
p is an observed probability based on the sample data; ?if p < α, H0 is rejected; otherwise, H0 cannot be rejected.
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 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.
Errors in Significance Test
H0 is actually
Decision True False Reject H0Type I Error Correct Decision Accept H0Correct Decision Type II Error
Calculation of Type I & II Errors ?Probability (Type I Error) = α
Probability (Type II Error) = b
Power of Test = 1 - b。