Measures of Variation and Statistical Significance

Measures of Variation

• The Standard Deviation:
  • Definition: A measurement of the amount of variation among scores within a normal distribution.
  • Empirical Rule (for Normal Distributions):
    • Approximately $68\%$ of scores will be found within $1$ standard deviation ($1SD$) of the mean.
    • Approximately $95\%$ of scores will be found within $2$ standard deviations ($2SD$) of the mean.
    • Approximately $99.7\%$ of scores will be found within $3$ standard deviations ($3SD$) of the mean.

Statistical Significance

• P-value (Probability Value):
  • Definition: A statistical measure indicating how likely it is that your observed data would have occurred purely by random chance.
  • Threshold for Significance: A P-value less than $0.05$ ($5\%$) is conventionally considered statistically significant. This implies that the observed result is unlikely to be attributable to random variation alone, suggesting a true effect or relationship.