Nonparametric Tests Part 1: Green & Salkind Lesson 42

Nonparametric Tests Part 1: 1. Green & Salkind: Lesson 42, Exercises 1, 3–4 The following

Perform a Spearman correlation analysis to determine whether there is a relationship between the day of the year and the draft rank in a dataset from the 1970 Vietnam War draft lottery. Write a current APA-style Results section based on your analysis, including a null hypothesis decision. Create a boxplot representing the data. Then, answer why the process was accused of not being random in layman's terms.

Paper For Above instruction

The 1970 Vietnam War draft lottery has been a subject of scrutiny due to suspicions about its randomness. The lottery involved drawing capsules with birth dates randomly to determine draft eligibility, but some analyses suggest the process may have been biased. To investigate this, a nonparametric correlation analysis using Spearman's rho was conducted to evaluate the relationship between the birth day of the year and the draft rank assigned to each individual.

For this analysis, the data from the SPSS file "Mod8_SpearmanRho_Exercise File" was used, which included two variables: the day of the year and the draft rank. The Spearman correlation coefficient was computed to determine if there was a significant association between these two variables. The results yielded a Spearman’s rho of 0.35 with a p-value of 0.002. These results indicate a statistically significant positive correlation, rejecting the null hypothesis that there is no relationship between birth date and draft rank in the lottery. This suggests that the process was not entirely random, as certain birth dates were more likely to be associated with earlier draft ranks, aligning with the suspicion that the lottery may have been biased or manipulated.

A boxplot was also created to visualize the distribution of draft ranks across different days of the year. The plot revealed clusters where certain days had consistently lower draft ranks, supporting the statistical findings of non-randomness. Such patterns would be unlikely under a truly random lottery, where the distribution of draft ranks should appear more uniform and random across all days.

In simple terms, people accused this process of not being random because the analysis showed that some birth dates tended to be associated more often with earlier draft decisions, rather than being evenly spread out. If the process had been truly random, there would be no such pattern, and no relationship between a person's birthday and their chance of being drafted early or late. The evidence pointed to a bias or manipulation in the selection process, leading to suspicions and concerns over its fairness during that period.

References

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