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Cohen's d
Cohen's D is a method of estimating effect size in a ttest based on means or distances between/among means.
Learning Objective

Justify Cohen's D as a method for estimating effect size in a ttest
Key Points

An effect size is a measure of the strength of a phenomenon (for example, the relationship between two variables in a statistical population) or a samplebased estimate of that quantity.

An effect size calculated from data is a descriptive statistic that conveys the estimated magnitude of a relationship without making any statement about whether the apparent relationship in the data reflects a true relationship in the population.

Cohen's D is an example of a standardized measure of effect, which are used when the metrics of variables do not have intrinsic meaning, results from multiple studies are being combined, the studies use different scales, or when effect size is conveyed relative to the variability in the population.

As in any statistical setting, effect sizes are estimated with error, and may be biased unless the effect size estimator that is used is appropriate for the manner in which the data were sampled and the manner in which the measurements were made.

Cohen's D is defined as the difference between two means divided by a standard deviation for the data:
$D=\frac { { \bar { x } }_{ 1 }{ \bar { x } }_{ 2 } }{ \sigma }$ .
Terms

Cohen's D
A measure of effect size indicating the amount of different between two groups on a construct of interest in standard deviation units.

pvalue
The probability of obtaining a test statistic at least as extreme as the one that was actually observed, assuming that the null hypothesis is true.
Full Text
Cohen's D is a method of estimating effect size in a ttest based on means or distances between/among means . An effect size is a measure of the strength of a phenomenon—for example, the relationship between two variables in a statistical population (or a samplebased estimate of that quantity). An effect size calculated from data is a descriptive statistic that conveys the estimated magnitude of a relationship without making any statement about whether the apparent relationship in the data reflects a true relationship in the population. In that way, effect sizes complement inferential statistics such as pvalues. Among other uses, effect size measures play an important role in metaanalysis studies that summarize findings from a specific area of research, and in statistical power analyses.
The concept of effect size already appears in everyday language. For example, a weight loss program may boast that it leads to an average weight loss of 30 pounds. In this case, 30 pounds is an indicator of the claimed effect size. Another example is that a tutoring program may claim that it raises school performance by one letter grade. This grade increase is the claimed effect size of the program. These are both examples of "absolute effect sizes," meaning that they convey the average difference between two groups without any discussion of the variability within the groups.
Reporting effect sizes is considered good practice when presenting empirical research findings in many fields. The reporting of effect sizes facilitates the interpretation of the substantive, as opposed to the statistical, significance of a research result. Effect sizes are particularly prominent in social and medical research.
Cohen's D is an example of a standardized measure of effect. Standardized effect size measures are typically used when the metrics of variables being studied do not have intrinsic meaning (e.g., a score on a personality test on an arbitrary scale), when results from multiple studies are being combined, when some or all of the studies use different scales, or when it is desired to convey the size of an effect relative to the variability in the population. In metaanalysis, standardized effect sizes are used as a common measure that can be calculated for different studies and then combined into an overall summary.
As in any statistical setting, effect sizes are estimated with error, and may be biased unless the effect size estimator that is used is appropriate for the manner in which the data were sampled and the manner in which the measurements were made. An example of this is publication bias, which occurs when scientists only report results when the estimated effect sizes are large or are statistically significant. As a result, if many researchers are carrying out studies under low statistical power, the reported results are biased to be stronger than true effects, if any.
Relationship to Test Statistics
Samplebased effect sizes are distinguished from test statistics used in hypothesis testing in that they estimate the strength of an apparent relationship, rather than assigning a significance level reflecting whether the relationship could be due to chance. The effect size does not determine the significance level, or viceversa. Given a sufficiently large sample size, a statistical comparison will always show a significant difference unless the population effect size is exactly zero. For example, a sample Pearson correlation coefficient of 0.1 is strongly statistically significant if the sample size is 1,000. Reporting only the significant pvalue from this analysis could be misleading if a correlation of 0.1 is too small to be of interest in a particular application.
Cohen's D
Cohen's D is defined as the difference between two means divided by a standard deviation for the data:
Cohen's D is frequently used in estimating sample sizes. A lower Cohen's D indicates a necessity of larger sample sizes, and vice versa, as can subsequently be determined together with the additional parameters of desired significance level and statistical power.
The precise definition of the standard deviation s was not originally made explicit by Jacob Cohen; he defined it (using the symbol σ) as "the standard deviation of either population" (since they are assumed equal). Other authors make the computation of the standard deviation more explicit with the following definition for a pooled standard deviation with two independent samples .
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Key Term Reference
 average
 Appears in this related concepts: Mean: The Average, Physics and Engeineering: Center of Mass, and Average Value of a Function
 bias
 Appears in this related concepts: Distorting the Truth with Descriptive Statistics, Interpreting Distributions Constructed by Others, and Chance Error and Bias
 correlation
 Appears in this related concepts: Benefits of Globalization, Controlling for a Variable, and Descriptive and Correlational Statistics
 correlation coefficient
 Appears in this related concepts: Coefficient of Determination, Inferences of Correlation and Regression, and Overview of How to Assess StandAlone Risk
 datum
 Appears in this related concepts: Change of Scale, Comparing Nested Models, and Using a Statistical Calculator
 descriptive statistics
 Appears in this related concepts: Applications of Statistics, Graphs of Qualitative Data, and Descriptive or Inferential Statistics?
 deviation
 Appears in this related concepts: Standard Error, Variance, and Degrees of Freedom
 empirical
 Appears in this related concepts: What Is Statistics?, Other Topics in M&A, and The Impact of Culture on an Organization
 error
 Appears in this related concepts: Estimating the Accuracy of an Average, Estimation, and Precise Definition of a Limit
 independent
 Appears in this related concepts: Regression Analysis for Forecast Improvement, The Rise of Independents, and Unions and Intersections
 independent sample
 Appears in this related concepts: Comparing Two Independent Population Means, Comparing Two Independent Population Proportions, and Wilcoxon tTest
 inferential statistics
 Appears in this related concepts: Inferential Statistics, What Is a Sampling Distribution?, and Properties of Sampling Distributions
 level
 Appears in this related concepts: Randomized Design: SingleFactor, Factorial Experiments: Two Factors, and Statistical Controls
 mean
 Appears in this related concepts: Mean, Variance, and Standard Deviation of the Binomial Distribution, The Mean Value Theorem, Rolle's Theorem, and Monotonicity, and Understanding Statistics
 population
 Appears in this related concepts: Samples, Random Sampling, and Organismal Ecology and Population Ecology
 sample
 Appears in this related concepts: Sampling, Defining the Sample and Collecting Data, and Identifying Product Benefits
 significance level
 Appears in this related concepts: Using the Model for Estimation and Prediction, Elements of a Hypothesis Test, and Choosing a significance level
 standard deviation
 Appears in this related concepts: Expected Value and Standard Error, Using the Normal Curve, and Interpreting the Standard Deviation
 statistical power
 Appears in this related concepts: Two Regression Lines, Models with Both Quantitative and Qualitative Variables, and tTest for Two Samples: Paired
 statistical significance
 Appears in this related concepts: Tests of Significance, Was the Result Significant?, and Was the Result Important?
 statistics
 Appears in this related concepts: Misleading Graphs, Communicating Statistics, and Population Demography
 ttest
 Appears in this related concepts: The tTest, Assumptions, and tTest for One Sample
 variable
 Appears in this related concepts: Related Rates, Calculating the NPV, and Fundamentals of Statistics
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Cite This Source
Source: Boundless. “Cohen's d.” Boundless Statistics. Boundless, 02 Jul. 2014. Retrieved 21 May. 2015 from https://www.boundless.com/statistics/textbooks/boundlessstatisticstextbook/otherhypothesistests13/thettest60/cohensd2982755/