Spearmans Rho

Research Question

  • Relationship between age at first arrest and number of days incarcerated.

Hypotheses

  • Null Hypothesis (H0): No relationship between age at first arrest and days incarcerated.

  • Alternative Hypothesis (Ha): There is a relationship between age at first arrest and days incarcerated.

Assumptions

  1. Related paired variables: Each prisoner has an age at first arrest correlated with their incarceration duration.

  2. Continuous variables:

    • Variable 1: Age at First Arrest (in years)

    • Variable 2: Number of Days Incarcerated

  3. Normal distribution: Variables should be normally distributed.

Spearman's Rho

  • Correlation coefficient measuring monotonic relationships in ranked data.

  • Spearman’s correlation assesses the strength and direction of association between two ranked variables.

  • Calculation: Transforming data into ranks before analysis is essential.

Calculation Steps

  1. Calculate Spearman's rho for the dataset: Determine if the correlation is positive or negative and assess strength (weak, moderate, strong).

    • Example coefficient: -0.55 (moderate negative).

  2. Compute t-statistic from correlation coefficient: (t=r⋅n−21−r2)(t = \frac{r \cdot \sqrt{n-2}}{\sqrt{1-r^2}})

  3. Use Excel to find p-value (p) from t-statistic.

Results Interpretation

  • Spearman’s rank correlation: rs(23) = -0.55, p = 0.006.

  • Indication: As age at first arrest increases, the number of days incarcerated tends to decrease.

Summary of Analysis Processes

  1. Check assumptions for data analysis.

  2. Transform variable data into ranks.

  3. Calculate Spearman’s rank coefficient.

  4. Interpret results for conclusion drawing.