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Guidelines on calculation and interpretation of effect size

# Guidelines on calculation and interpretation of effect size...

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Statistics 101A Effect Size Professor Esfandiari What does effect size mean conceptually? The concept of effect size 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. For example, if the weight loss program results in an average loss of 30 pounds, we do not know if every participant loses exactly 30 pounds, or if half the participants lose 60 pounds and half the participants lose no weight at all. In inferential statistics, an effect size helps to determine whether a statistically significant difference is a difference of practical concern. Given a sufficiently large sample size, a statistical comparison will always show a significant difference unless the difference in the population from which the data are sampled is exactly zero. The effect size conveys whether an observed difference is substantively important. This is in contrast to a statistical significance test, which assesses whether a relationship could be due to chance, regardless of the strength of the apparent relationship in the data . In meta- analysis, effect sizes are used as a common measure that can be calculated for different studies and then combined into an overall summary. Reporting effect sizes is considered good practice when presenting empirical research findings in many fields [1][2]. Effect sizes are particularly prominent in social and medical research. Relative and absolute measures of effect size convey different information, and can be used complementarily. Reported measures of effect size Pearson r correlation Pearson's correlation, often denoted r and introduced by Karl Pearson, is widely used as an effect size when paired quantitative data are available; for instance if one were studying the relationship between birth weight and longevity. The correlation coefficient can also be used when the data are binary. Pearson's r can vary in magnitude from 1 to 1, with 1 indicating a perfect negative linear relation, 1 indicating a perfect positive linear relation, and 0 indicating no linear relation between two variables.

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