In medical parlance how will we differentiate between sample size and effect size?
SAMPLE SIZE: A segment or portion of a population drawn from the pool under a particular sampling method, i.e. random or nonrandom, for purposes of making a generalization about the population. When studying the population in detail, i.e. census, is not feasible or impracticable, sample is used. The size of the sample drawn is called sample size. The size of which the finding and conclusion reach is representative (non-biased) of the population or from which a generalization may be made is called minimum sample sample size. Sample size calculation may be of two types: (i) finite population where the population N is known or (ii) the population N is unknown. Below are two common sample size calculation methods:
(1) nYamane = N / (1 + N(e2))
... where n = sample size; N = population size; and e = error level, i.e. 0.05 for 0.95 confidence interval. This population proportion method is called the Yamane method. The second method for unknown population size is given by:
(2) nnonfinite = (Z2σ2) / E2
... where nnonfinite = sample size for non-finite N case; Z = standard score from the Z-table; σ = estimated population variance (sigma2); and E = σ / sqrt(ntest). Under this second method, one needs to take a test sample (ntest) in order to obtain descriptive statistics and proceed to inferential statistics.
EFFECT SIZE: Effect size is defined as the measure of the strength of the phenomenon. There are various measurement tools for measurement effect size; these methods include:
1. Pearson correlation coefficient
2. R squared: R2
3. Eta squared: η2
4. Omega squared: ω2
5. Choen’s f2
6. Cohen’s q
7. Cohen’s d
8. Glass’ delta: Δ
9. Heges’ g
10. Root mean squared: ψ
11. Phi: Φ
12. Cramer’s V
13. Cohen’s W
14. Odd’s ratio
15. Choen’s h
It is considered good practice to report effect size. See Wilkinson (1999) and Nakagawa et al. (2007). I hope this is helpful. Cheers.
REFERENCES: See below for basic materials on effect size.
[1] Cohen, J (1992). "A power primer". Psychological Bulletin 112 (1): 155–159.
[2] Jacob Cohen (1988). Statistical Power Analysis for the Behavioral Sciences (second ed.). Lawrence Erlbaum Associates.
[3] Kelley, Ken; Preacher, Kristopher J. (2012). "On Effect Size". Psychological Methods 17 (2): 137–152.
[4] Nakagawa, Shinichi; Cuthill, Innes C (2007). "Effect size, confidence interval and statistical significance: a practical guide for biologists". Biological Reviews Cambridge Philosophical Society 82 (4): 591–605.
[5] Wilkinson, Leland; APA Task Force on Statistical Inference (1999). "Statistical methods in psychology journals: Guidelines and explanations". American Psychologist 54 (8): 594–604.
http://www.clintools.com/victims/resources/software/effectsize/effect_size_generator.html
http://www.mdp.edu.ar/psicologia/vista/vista.htm
http://www.uv.es/~friasnav/EffectSizeBecker.pdf
SAMPLE SIZE: A segment or portion of a population drawn from the pool under a particular sampling method, i.e. random or nonrandom, for purposes of making a generalization about the population. When studying the population in detail, i.e. census, is not feasible or impracticable, sample is used. The size of the sample drawn is called sample size. The size of which the finding and conclusion reach is representative (non-biased) of the population or from which a generalization may be made is called minimum sample sample size. Sample size calculation may be of two types: (i) finite population where the population N is known or (ii) the population N is unknown. Below are two common sample size calculation methods:
(1) nYamane = N / (1 + N(e2))
... where n = sample size; N = population size; and e = error level, i.e. 0.05 for 0.95 confidence interval. This population proportion method is called the Yamane method. The second method for unknown population size is given by:
(2) nnonfinite = (Z2σ2) / E2
... where nnonfinite = sample size for non-finite N case; Z = standard score from the Z-table; σ = estimated population variance (sigma2); and E = σ / sqrt(ntest). Under this second method, one needs to take a test sample (ntest) in order to obtain descriptive statistics and proceed to inferential statistics.
EFFECT SIZE: Effect size is defined as the measure of the strength of the phenomenon. There are various measurement tools for measurement effect size; these methods include:
1. Pearson correlation coefficient
2. R squared: R2
3. Eta squared: η2
4. Omega squared: ω2
5. Choen’s f2
6. Cohen’s q
7. Cohen’s d
8. Glass’ delta: Δ
9. Heges’ g
10. Root mean squared: ψ
11. Phi: Φ
12. Cramer’s V
13. Cohen’s W
14. Odd’s ratio
15. Choen’s h
It is considered good practice to report effect size. See Wilkinson (1999) and Nakagawa et al. (2007). I hope this is helpful. Cheers.
REFERENCES: See below for basic materials on effect size.
[1] Cohen, J (1992). "A power primer". Psychological Bulletin 112 (1): 155–159.
[2] Jacob Cohen (1988). Statistical Power Analysis for the Behavioral Sciences (second ed.). Lawrence Erlbaum Associates.
[3] Kelley, Ken; Preacher, Kristopher J. (2012). "On Effect Size". Psychological Methods 17 (2): 137–152.
[4] Nakagawa, Shinichi; Cuthill, Innes C (2007). "Effect size, confidence interval and statistical significance: a practical guide for biologists". Biological Reviews Cambridge Philosophical Society 82 (4): 591–605.
[5] Wilkinson, Leland; APA Task Force on Statistical Inference (1999). "Statistical methods in psychology journals: Guidelines and explanations". American Psychologist 54 (8): 594–604.
http://www.clintools.com/victims/resources/software/effectsize/effect_size_generator.html
http://www.mdp.edu.ar/psicologia/vista/vista.htm
http://www.uv.es/~friasnav/EffectSizeBecker.pdf
HI,
An Effect Size is the strength or magnitude of the difference between two sets of data.
The sample size is an important feature of any empirical study in which the goal is to make inferences about a population from a sample. It is a subset of the desired population. It is a part of the population.
Sample size is the number of observations from the population of interest. There are usually at least two populations of interest: treatment and control. If I take 500 lab rats and treat 100 with some drug, then my sample size is 400 for the control and 100 for the treatment.
The effect size is the difference between the treatment and the control. If there are multiple treatments then there are many different effect sizes: one for each possible pairwise comparison. A better approach would be to say that the effect size is the 95% confidence interval for the difference between any two treatments (the control is a treatment where you do nothing). So drug A results in 10% reduction in blood pressure, while drug B results in a 50% reduction. Drug B has a larger effect, but what if also say that the standard deviation for drug A is 0.007 while for drug B it is 23.8. Drug A is considered ok, but not great. Drug B is adored by some and reviled by others. Which is the larger effect?
Maybe I have one drug and I want to do a dose response trial with 5 doses from 1 mg/kg to 50 mg/kg. Now the "effect size" could be defined as the slope of the regression line. However, you also need to consider error. If slope is effect size, then I could have a very steep slope, but have a low R-squared (the regression explains very little of the variability in the data). Alternatively, if R-squared is the "effect size" then I can have an R-squared of 0.99945 for drug 1 and note that increasing dose reduces symptoms (ranked 1 to 10) by 0.05 for each 10 mg/kg increase in concentration while drug 2 had an R-Squared of 0.8932 but reduced symptoms by 1.4 for each 10 mg/kg increase in concentration.
Say you have an experimental study on non-Hodgkin's Lymphoma in rats and try to correlate incidence based on pesticide exposure, strain, gender, and diet. In this case there is no simple statistic that can be used to measure the distance between groups. So I note that 2,4-D + White coat + male + high fat had more NHL than female rats with brown coats and low fat diets. What are the units for a measure between these groups? One option is to use Mahalanobis distance which has no units. The Mahalanobis distance would be the effect size for a multivariate study using variables with mixed units. There may be other measures, but this is the only one that I know. The Mahalanobis distance is useful to compare treatments within a study but useless to compare my results from a new study against previously published results. As with the regression example, error can cause problems. So I get a Mahalanobis distance of 9.8 between the two groups, but I correctly determine the outcome (cancer or not) 65% of the time. In a different study: I might get a Mahalanobis distance of 1.7 as the largest distance between any two groups but get 99% accuracy.
Of course all of this assumes that the models fit in all other respects. The "effect size" no matter how you define it is irrelevant if the model used for analysis is inappropriate.
I will confess that I am not familiar with all the statistics that Paul listed, so I have a bit of homework too.
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