• Education Research
  • Introduction
  • Acknowledgements
  • 1. Groundwork
  • 2. Process
  • 2. Paradigms
  • 3. Learning Theories
  • 4. Methodology
  • 5. Data Collection
  • 5. Methods
  • 7. Reporting
  • Appendix A. Supplements
  • Appendix B. Example Studies
  • Appendix D. Software Examples
  • Appendix C. Historical Readings
  • Download
  • Translations
  • Common Statistical Formulas and Equations

    StatisticsStatistical FormulasEquationsStatistical Equations

    R-Squared

    $$ R^{2}=\frac{N\sum xy-\sum x \sum y}{\sqrt{\left[N\sum x^{2}-\left(\sum x\right)^{2}\right]\left[N\sum y^{2}-\left(\sum y\right)^{2}\right]}} $$

    F Test

    $$ F=\frac{Variance\ of\ set\ 1}{Variance \ of \ set \ 2} = \frac{\sigma _{1}^{2}}{\sigma _{2}^{2}} $$

    See Variance.

    Chi-Square

    $$ \chi ^2 = \sum{\frac{(O-E)^2}{E}} $$

    Population Mean

    $$ \mu = \frac{\sum{X_i}}{N} $$

    Mean

    $$ \overline{x} = \frac{\sum{x}}{n} $$

    Variance

    $$ \sigma ^2 = \frac{\sum{(x-\overline{x})^2}}{n} $$

    Standard Deviation

    $$ S=\sigma=\sqrt{\frac{\sum{(x-\overline{x})^2}}{n}} $$

    Linear Regression

    $$ y=a+bx $$

    Where a (or the intercept) is:

    $$ a =\frac{\sum y \sum x^{2} – \sum x \sum xy} {(\sum x^{2}) – (\sum x)^{2}} $$

    And b (or the slope) is:

    $$ b=\frac{n\sum xy-\left(\sum x\right)\left(\sum y\right)}{n\sum x^{2}-\left(\sum x\right)^{2}} $$

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