The Journal Of Professional Nursing Article Titled The Gradu

The Journal Of Professional Nursing Article Titled The Graduate Recor The Journal of Professional Nursing article titled “The Graduate Record Examination as an Admission Requirement for the Graduate Nursing Program” reported a significant correlation between undergraduate grade point average (GPA) and GPA at graduation from a graduate nursing program. The following data were collected on 10 nursing students who graduated from a graduate nursing program. Undergrad GPA 3.5 3.1 2.7 3.7 2.5 3.3 3.0 2.9 3.8 3.2 GPA at Graduation 3.4 3.2 3.0 3.6 3.1 3.4 3.0 3.4 3.7 3.8 Compute the Spearman rank coefficient and test the null hypothesis of no relationship versus a positive relationship.

Use a level of significance equal to 0.05.

Paper For Above instruction Introduction The relationship between undergraduate GPA and graduate GPA has significant implications for admissions policies in nursing education. Understanding whether a monotonic relationship exists can guide educators in selecting candidates who are more likely to succeed academically. The Spearman rank correlation coefficient is a non-parametric measure that assesses the strength and direction of the association between two ranked variables, making it suitable for such analysis with small sample sizes or non-normal data distributions (Siegel & Castellan, 1988). This paper aims to compute the Spearman rank coefficient based on the provided data, test the null hypothesis of no relationship, and determine whether a positive association exists at the 0.05 significance level.

Methodology The data provided consist of undergraduate GPAs and corresponding graduate GPAs for ten students. The steps involved include ranking these data points, calculating the difference between ranks, applying the Spearman rank correlation formula, and conducting a hypothesis test.

The data are as follows: | Student | Undergrad GPA | Graduation GPA | |-----------|--------------|----------------| | 1 | 3.5 | 3.4 | | 2 | 3.1 | 3.2 |

| 3 | 2.7 | 3.0 | | 4 | 3.7 | 3.6 | | 5 | 2.5 | 3.1 | | 6 | 3.3 | 3.4 | | 7 | 3.0 | 3.0 | | 8 | 2.9 | 3.4 | | 9 | 3.8 | 3.7 | | 10 | 3.2 | 3.8 | ### Ranking the Data First, rank the undergraduate GPAs, assigning rank 1 to the smallest value: - 2.5: Rank 1 - 2.7: Rank 2 - 2.9: Rank 3 - 3.0: Rank 4 (tie between 3rd and 4th, assign average rank 4.5) - 3.1: Rank 6 - 3.2: Rank 7 - 3.3: Rank 8 - 3.5: Rank 9 - 3.7: Rank 10 - 3.8: Rank 11 Similarly, for graduation GPAs: - 3.0: Rank 1 - 3.1: Rank 2

- 3.2: Rank 3 - 3.4: Rank 4. 5.

- 3.4: Rank 4.5 (tie) - 3.4: Rank 4.5 - 3.6: Rank 7 - 3.7: Rank 8 - 3.8: Rank 9 - 3.8: Rank 9.5 (tie) ### Calculating Rank Differences and Squared Differences Next, compute the difference between the rank of undergraduate GPA and GPA at graduation, then square these differences: | Student | Undergrad Rank | Graduation Rank | Difference (d) | d² | |-----------|----------------|-------------------|----------------|-----| | 1 | 9 | 4 | 5 | 25 | | 2 | 6 | 2 | 4 | 16 | |3|2|1|1|1| | 4 | 10 | 8 | 2 | 4 | | 5 | 1 | 3 | -2 | 4 | | 6 | 8 | 4.5 | 3.5 | 12.25| |7|4|1|3|9| | 8 | 3 | 4.5 | -1.5 | 2.25| | 9 | 11 | 8 | 3 | 9 | | 10 | 7 | 9.5 | -2.5 | 6.25|

### Computing Spearman's Rank Correlation Coefficient (ρ) The formula for Spearman's rank correlation coefficient: \[ ρ = 1 - \frac{6 \sum d^2}{n(n^2 - 1)} \] where \( n = 10 \).

Sum of \( d^2 \): \[ \sum d^2 = 25 + 16 + 1 + 4 + 4 + 12.25 + 9 + 2.25 + 9 + 6.25 = 88 \] Plugging in the values: \[ ρ = 1 - \frac{6 \times 88}{10 \times (10^2 - 1)} = 1 - \frac{528}{10 \times 99} = 1 - \frac{528}{990} \approx 1 - 0.533 = 0.467 \] ### Hypothesis Testing Null hypothesis (\(H_0\)): There is no correlation between undergraduate GPA and graduate GPA (\( ρ = 0 \)).

Alternative hypothesis (\(H_1\)): There is a positive correlation (\( ρ > 0 \)).

Calculating the test statistic: \[ t = ρ \sqrt{\frac{n-2}{1-ρ^2}} = 0.467 \sqrt{\frac{8}{1 - 0.467^2}} = 0.467 \sqrt{\frac{8}{1 - 0.218}} = 0.467 \sqrt{\frac{8}{0.782}} \]

\[ t \approx 0.467 \times \sqrt{10.23} \approx 0.467 \times 3.198 \approx 1.493 \] Degrees of freedom (\(df = n - 2 = 8\)).

Using a t-distribution table at \( \alpha = 0.05 \), the critical t-value for a one-tailed test with 8 df is approximately 1.860.

Since \( t = 1.493 < 1.860 \), we fail to reject the null hypothesis at the 0.05 significance level. ### Conclusion The computed Spearman rank correlation coefficient (\( ρ = 0.467 \)) suggests a moderate positive correlation between undergraduate GPA and GPA at graduation. However, the hypothesis test indicates that this correlation is not statistically significant at the 0.05 level, as the calculated t-value does not exceed the critical threshold. Therefore, there is insufficient evidence to conclude a positive relationship exists between undergraduate GPA and graduate GPA in this sample.

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