Learning to Love Data by Scott Massey & Helen Martin

Author:Scott Massey & Helen Martin [Massey, Scott]
Language: eng
Format: mobi
Published: 2021-02-13T16:00:00+00:00

Variable

Correlation Coefficient with PANCE Scores

p value

Admission GPA

-0.03

0.85

Clinical Medicine

0.29

0.12

Emergency Medicine

0.37

0.04

End of Rotation Exam (Surgery)

0.62

0.0003

PACKRAT

0.70

0.00002

Working with a conventional statistical significance level of 5%, admission GPA is not a statistic significantly correlated with PANCE scores since p value associated with its correlation coefficient is greater than 0.05. In other words, the observed correlation coefficient between admission GPA and PANCE score is highly likely by chance alone. Similarly, Clinical Medicine is not statistically significant correlated with PANCE scores since the p value is greater than 0.05.

All other variables are statistically significant correlated with PANCE scores at the 5% significance level since p values associated with correlation coefficients for these variables are less than 0.05. In other words, there is less than 5% probability that the observed correlation coefficients are by chance only. If a more conservative significance level of 1% (alpha=0.01) was chosen, Emergency Medicine would be deemed to be not statistically significantly correlated with PANCE scores since the p value associated with its coefficient is larger than 0.01 (p=0.04).

Based on Cohen’s guidelines (Cohen, 1988; Cohen, 1992), End of Rotation Exam (Surgery) (r=0.62) and PACKRAT (r=0.70) have large-sized relationship (r>0.5) with PANCE scores, and Emergency Medicine has a medium-sized relationship with PANCE scores (r=0.37). PACKRAT (r=0.70) is the strongest predictor of PANCE scores followed by End of Rotation Surgery (r=0.63). While Clinical Medicine has a medium sized relationship with PANCE scores (r=0.27), its correlation coefficient is not statistically significant (p=0.12). Admissions GPA has a negligible relationship with PANCE scores (r=-0.03).

In the example presented here, actual p values are reported even for very small values. Usually, these are reported up to two or three decimal places only. For example, the p value for PACKRAT (p=0.00002) would usually be reported as p<0.001 or p<0.01.

What is Regression?

Regression is a statistical technique to identify predictor variable(s) that can be useful in predicting an outcome variable. Predictor variables are also referred to as independent variables and the outcome/predicted variable is also referred to as the dependent variable. The regression model quantifies the relationship between the predictor and the predicted variables and yields an equation that can be used to estimate the outcome variable value given the value(s) of predictor variable(s). For example, the regression equation is represented as a solid line in the Scatter Plot with Regression Line below. This is the same plot as in the Scatter Plot Demonstrating Positive Correlation above with the addition of the regression line. For any value of variable A on the X axis, the predicted PANCE score is the corresponding value on the Y axis. For instance, the predicted PANCE score for a value of 170 on variable A is approximately 525.

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