Statistical Analysis: The CSI Framework and Comparing Medians

CSI Statistical Analysis Framework

• The CSI acronym represents the core components of the analysis section in a report:

  • C (Center): Describing the center of the distribution.

  • S (Shift, Spread, Shape, and Special Features): Identifying these four specific components.

  • I (Inference): Making conclusions about the population in context.

• Context involves discussing features with reference back to the population involved in the situation.

Comparing Centers (Medians)

• To compare centers, calculate the difference between the medians of two groups by subtracting the smaller value from the larger value.

• Rugby Players Weights Example:

  • Median weight of Backs: $92\,\text{kg}$.

  • Median weight of Forwards: $110.5\,\text{kg}$.

  • Difference: $110.5\,\text{kg} - 92\,\text{kg} = 18.5\,\text{kg}$.

Grading Criteria for Statistical Interpretation

• Achieved: Write a sentence identifying which group has a larger median and state the difference ($18.5\,\text{kg}$ in the rugby sample).

• Merit: Justify the statement with specific numerical evidence from the data for both groups ($110.5\,\text{kg}$ for Forwards and $92\,\text{kg}$ for Backs).

• Excellence: Provide contextual reasoning ("tell the story") using external research to explain the results.

  • Contextual Example: Forwards are heavier players ($110.5\,\text{kg}$) because their role requires size and strength for tackles. Backs are lighter ($92\,\text{kg}$) to facilitate speed, agility, and evasiveness.