PerfectCustomPapers | Introduction to Probability and Statistics

Introduction to Probability and Statistics

A correlation measures and describes the linear relationship between two variables. The relationship is described using a +/- and a numerical value. Define what each indicates about the relationship. Give an example of two variables that seem to be related, and thus have a correlation, but have nothing to do with each other.

Find an empirical study that made an association claim. What type of correlation analysis did they use (Pearson r, biserial, etc.)? Report their findings in APA and interpret them in two to three sentences.

Sample Answer

1. Understanding Correlation

Correlation is a statistical measure that quantifies the strength and direction of the linear relationship between two variables. This relationship is expressed using a correlation coefficient, which typically ranges from -1 to 1.

+/- sign:
- Positive (+): When the correlation coefficient is positive, it indicates a direct relationship between the two variables. As one variable increases, the other also tends to increase. For example, there’s a positive correlation between height and weight in humans.
- Negative (-): A negative correlation coefficient indicates an inverse relationship. As one variable increases, the other tends to decrease. For example, there’s a negative correlation between hours of sleep and perceived stress levels.

Full Answer Section

Numerical value:

- The absolute value of the correlation coefficient indicates the strength of the relationship:
  - Closer to 1: A stronger relationship.
  - Closer to 0: A weaker relationship.

Example of a Spurious Correlation:

While it might appear that there’s a correlation between the number of pirates and global temperature, there’s no causal relationship between these two variables. This is an example of a spurious correlation, where a seemingly strong relationship is actually coincidental or due to other underlying factors.

2. Empirical Study and Correlation Analysis

Note: To provide a specific example, I’d need access to recent research databases. However, I can illustrate the process using a hypothetical study.

Hypothetical Study:

Research Question: Is there a correlation between hours of studying and exam scores?
Correlation Analysis: Pearson correlation coefficient (r) would be appropriate for this study as both variables (hours of studying and exam scores) are continuous.

APA-style Reporting:

“A Pearson correlation analysis revealed a significant positive correlation between hours of studying and exam scores, r(100) = .75, p < .01. This indicates that students who study more hours tend to achieve higher exam scores.”

Interpretation:

The positive correlation coefficient of .75 suggests a moderately strong relationship between studying hours and exam scores. This means that students who study more are likely to perform better on exams, but other factors might also influence their performance.

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