effect sizes总结及操作指南-zhaomf
阅读时间-小学六年级毕业试卷
EFFECT SIZES
效应量的选用与分析
参考文献：
Cohen J (1988)“Statistical power analysis for
the behavioral sciences” . New Jersey:
Lawrenced Erlbaum Associates, Inc. Publishers.
pp 283-286
Durlak, J. A. (2009). How to
select, calculate, and interpret effect sizes.
Journal of
pediatric psychology, jsp004.
Levine, T. R., & Hullett, C. R. (2002). Eta
squared, partial eta squared, and
misreporting
of effect size in communication research. Human
Communication
Research, 28(4), 612-625.
Thompson, B. (2007). Effect sizes, confidence
intervals, and confidence intervals for
effect
sizes. Psychology in the Schools, 44, 423–432.
Lakens, D. (2013). Calculating and reporting
effect sizes to facilitate cumulative
science:
a practical primer for t-tests and ANOVAs.
Frontiers in psychology, 4.
郑昊敏, 温忠麟, & 吴艳.
(2011). 心理学常用效应量的选用与分析.
心理科学进
展
,
19(012), 1868-1878
1
.
Effect Size
20141113 minfang_zhao@ ZhaoMF
What are effect sizes？
There
are many different types of ESs but those
discussed here provide information about the
magnitude and direction of the difference
between
two groups or the relationship between
two variables.
An ES can be a difference
between means, a
percentage, or a correlation
(Vacha-Hasse &
Thompson, 2004).
It allows
us to move beyond the simplistic ‗Does it
work or not?‘ to the far more sophisticated
‘
How
well does it work in a range of
contexts
？’
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Types of Effect Sizes
Mean
Differences between Groups
– Cohen‘s d
–
Hedges‘ g
CorrelationRegression
–Pearson‘s r and R
2
–Cohen‘s f
2
Contingency tables
–Odds Ratio
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Types of Effect Sizes
ANOVA
or GLMs
–Eta-squared
–Omega squared
–Intraclass correlation (rater equality)
Chi-square tests
–Phi(2 binary
variables)
–Cramer‘s Phi or V (categorical
variables)
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Cohen’s d
– Standardizes ES of the difference between
two means
– d ranges from -∞to +∞
–
interpretation: the difference between the mean
values
is ―d‖ standard deviations, Cohen
(1988)
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Cohen’s d
d值总是作为一种标准的平均数差异的估计,与当前样
本无关。
(Cohen, 1992)
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Hedge’s g &
Glass’s ∆
Correction
Special Cases
positively biased
estimators of an ES when
– For small sample sizes use Hedge‘s g
sample sizes are small.
Practically
speaking, the
correction amounts to a
4% reduction in effect
when the total
sample
size is 20 and around 2%
when
N=50
(Hedges & Olkin, 1985).
– For
unequal group variances, use Glass‘s ∆
• uses
sample SD of the control group only so that effect
sizes would not differ under equal means and
unequal
variances(Rosenthal, 1991).
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校正部分，不同的研究可能使用的
校正部分不一样，可以参考相关领
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Size 20141113 ZhaoMF
域研究的校正方式。
Pearson’s r
– used in the context of
correlation…measuring association
between 2
continuous variables.
– Interpretation: For
every 1-unit standard deviation change
in x,
there is a ―r-unit‖ standard deviation change in
y.
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Odds Ratio
–
Used in the context of binarycategorical outcomes
– Odds of being in one group (eg. success)
relative to the
odds of being in a different
group (eg. failure)
– OR ranges from 0 to ∞
– OR>1 indicates an increase in odds relative
to the
reference group
– OR < 1 indicates
a decrease in odds relative to the
reference
group
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Phi
– Used
for crosstabs or for chi-square tests (equality of
proportions or tests of independence between 2
binary
variables)… = 0 indicates
independence
– Phi are related to correlation
and Cohen‘s d (for 2 binary
variables)
–
Interpreted like Pearson‘s r and R
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Size 20141113 ZhaoMF
Cramer’s Phi or V
–
Cramer‘s Phi (Cramer‘s V) can be used with
categorical
variables with more than 2
categories (m >2 ) (R x C tables)
– measures
the inter-correlation of the variables, but is
biased since it increases with the number of
cells. Increase
in R and C will indicate a
strong association, which is just an
artifact
of the type of variable used.
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2
Pearson’s R
– used in
the context of regression…measuring how well a
regression line fits to a given data
regression line fits to a
given data
– R
: linear association between 2 continuous
variables
– R
2
:(Coefficient of
Determination) –proportion of shared
variability between 2 or more variables
–
Interpretation: ―R
2
*100%‖ is percent
variance of the
outcome y that can be
explained by the linear regression
model
(i.e. indicates how well the linear regression
line fits
the data)
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2
Cohen’s f
– Used in
multiple linear regression,
– Standardized
effect size is the proportion of explained
variance over unexplained variance
–
Estimate is biased and overestimates the effect
size for
ANOVA (unbiased estimate is Omega-
Squared)
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2
Eta Squared(η)
and
partial Eta Squared(η
p
2
)
– Used with ANOVA family and GLMs
– Measures the degree of association in the
sample
– Partial eta-squared is the proportion
of the total variability
attributable to a
given factor.
– Interpretation:
―η
2
*100%‖ is percent of the variance in y
explained by the variance in x (similar to the
R
2
interpretation for
linear
regression (Dattalo,2008))
– η
2
is
biased and on average overestimates the variance
explained in the population, but decreases as
the sample size gets
larger.
– Caution!:
SPSS show ONLY η
p
2
(偏eta 方)
关于两者区别参考：Levine, T. R., & Hullett, C. R.
(2002). Eta squared, partial eta squared, and
misreporting of effect size in communication
research. Human Communication Research, 28(4),
612-625.
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Omega
Squared
– Used with ANOVA
family and GLMs (small sample size)
–
Estimates the proportion of variance in the
population
that is explained by the treatment
.
– is always smaller than η
2
or
η
p
2
, since measures
the
population variance and Eta measures the sample
variance.
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Table of
interpretation for different
effect
sizes(Judging ES in Context！)
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Cohen (1988)
Reporting
Guidelines and Trends
What to report (APA,
2010):
– Type of effect size
– Value of
the effect size
– Interpretation of the effect
size
– Practical significance of the effect
size
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Software
Calculate
effect size
– online calculator
http:
http:ct_#anova
–
Statistical softwares SPSS
show a example
tutorial on how calculate Cohen's d and Partial
Eta Squared using SPSS
https:ch?v=UVK1P7HthzU
—
G-power（可以计算预实验后计算可能需要的样本量）
http:
— Power
and Sample Size Programs
http:
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常用设计的效应量使用参考指南
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双因素重复测量设计
击选
Measures>命令。
在<
Repeated Measures Define Factor(s)>对话框中，在
按钮。(两个以上被试内因素，同理，add)
单击
序，如A1B2与其后的[1,2]一致）。（若有被试间
因素此处可以
将该因素指定为Between-subjects factors）
单击
据需要选取。单击按钮
单击
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SPSS输出结果
输出为偏eta方，根据需要根据公式计算eta方
效应量参考0.01(small),0.06(med),0.14(large)
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单因素多水平设计
SPSS在One way ANOVA选项中没有效应量
估计，因此如
果想计算效应量要击选
因变量指定到
单击
标根据需要选取。单击按钮
单因素多水平设计偏eta方以及independent t test
计算cohen‘s d
参考视频教学： https:ch?v=UVK1P7HthzU
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配对组内设计Paired-Samples T test
被试内的单因素双水平设计--SPSS选择Paired-Samples T
test；SPSS运行结果中找到t值；
利用t值以及样本量n计算dz效应值
Rosenthal (1991)
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