CALCULATE

CALCULATE

** Effect Size calculator** calculates the value of effect size correlation and the Cohen's-D using the means and

- Enter means and standard deviations of two groups in the boxes. These values must be real numbers;
- Press the
**"CALCULATE"**button to make the computation; - Effect size calculator will find the Cohen's-D and the effect size for two groups.

__An effect size__ is a measure of the magnitude of a phenomenon. For instance, the correlation between two variables, the regression coefficient in a regression, the mean difference, are examples of effect size. The effect size is independent of sample sizes. In other words, it measures a treatment effect and it is independent of the sizes of samples. In meta analysis, in addition to the statistical hypothesis, we consider also effect sizes. The standard error of the effect size is of great importance.
The effect size can be measured in the following ways:

- as the standardized difference between two means;
- as the correlation between the independent variable and the dependent variable.

Cohen's D is the ratio of the difference between the means and the pooled standard deviation: $$d=\frac{\bar X-\bar Y}{s}$$ where $s=\sqrt{\frac{s_X^2+s_Y^2}{2}}$. Cohen's d better works for sample sizes largen than $50$. If the sample sizes smaler than $50$, it tends to over-inflate results.

The effect size can be found from Cohen's D in the following way $$r=\frac{d}{\sqrt{d^2+4}}$$ The effect size for t-Test indicates whether or not the difference between two means is statistically significant. The effect size and Cohen's D from t-Test and df values are determined by the formulas: $$r^2 = {\frac{t^2}{t^2+df}},\quad d=\frac{2t}{\sqrt{df}}$$ where $t$ is the t-Test value and $df$ is the degrees of freedom.

The effect size calculator work with steps shows the complete step-by-step calculation for finding the effect size and Cohen's-D for two groups with the means of $\bar X=12$ and $\bar Y=8$ and standard deviations of $s_X=0.3468$ and $s_Y=1.2876$ using the effect size and Cohen's d formulas. For any other values of means and standard deviations, just supply four real numbers and click on the "CALCULATE" button. The grade school students may use this

The effect size is also used for ANOVA (analysis of variance) and it is determined by measure variability that is accounted for by the treatment effect. The effect size is applicable in social science and in medical sciences (where size of treatment effect is important). The values of effect sizes from different experiments can be compared and combined to give a broader picture. It can interpret results of studies with large samples and show statistical significance for small differences.

**Practice Problem 1:**

In a school, teaches evaluate students knowledge in mathematics. Some of the obtained results were:

mean | standard deviation | |

Trigonometry | 2.56 | 1.09 |

Statistics | 4.56 | 2.54 |

Probability | 3.56 | 1.98 |

A sample of $18$ persons are selected from a population with mean of $89$. After treatment, the sample mean is $85$ with standard deviation of $9$. Find the Cohen's d and the effective size for test with $\alpha=0.05$.

The effect size calculator, formula, work with steps and practice problems would be very useful for grade school students (K-12 education) to understand the concept of the effect size and Cohen's-D. This concept can be of benefit in statistics and probability, especially in meta analysis.