A connection between caffeine and headaches

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Is there a connection between caffeine and headaches? Is there an association between hospital wait times and patient care? Is there a relationship between antibiotic use and weight gain?
Correlation statistics all begin with a research question, and these research questions all seek to determine relationships between variables. Correlational analysis clarifies relationships, but there are many ways to formulate a correlation. Therefore, the strength of a correlation relies on the variables used and the interpretation of the results that may signify a statistically relevant association or relationship.
For this Assignment, you will examine how to interpret results obtained through a correlational analysis. You will evaluate the correlation results provided in the Week 6 Correlations Exercises SPSS output and will reflect on the meaning of the results for the variables examined.

1. What is the strongest correlation in the matrix? (Provide the correlation value and the names of variables)
2. What is the weakest correlation in the matrix? (Provide the correlation value and the names of variables)
3. How many original correlations are present on the matrix?
4. What does the entry of 1.00 indicate on the diagonal of the matrix?
5. Indicate the strength and direction of the relationship between body mass index (BMI) and physical health component subscale.
6. Which variable is most strongly correlated with BMI? What is the correlational coefficient? What is the sample size for this relationship?
7. What is the mean and standard deviation for BMI and doctor visits?
8. What is the mean and standard deviation for weight and BMI?
9. Describe the strength and direction of the relationship between weight and BMI.
10. Describe the scatterplot. What information does it provide to a researcher?

 

Sample Solution

  1. Strongest Correlation:

Examine the correlation matrix and identify the highest correlation coefficient (absolute value, between -1 and 1). This value indicates the strongest relationship (positive or negative) between two variables. For example, if the strongest correlation is 0.8 between BMI and physical activity level, this signifies a strong positive association.

  1. Weakest Correlation:

Similarly, find the lowest correlation coefficient (absolute value). This indicates the weakest relationship between two variables. For example, a value of 0.1 between sleep quality and doctor visits might suggest a weak positive or negative association.

  1. Original Correlations:

The number of original correlations on the matrix will be the total number of variables (excluding duplicates). If there are six variables (A, B, C, D, E, F), there will be 6 x 5 / 2 = 15 original correlations (each variable correlates with five others). The diagonal (1.00 entries) reflects the correlation of a variable with itself (perfect positive correlation).

  1. Diagonal Entry (1.00):

The entries along the diagonal of the correlation matrix will all be 1.00. This signifies a perfect positive correlation between a variable and itself. For instance, the correlation between BMI and BMI will always be 1.00.

  1. BMI and Physical Health:

Look at the correlation coefficient between BMI and the physical health component subscale. A positive coefficient indicates a relationship where higher BMI scores are associated with poorer physical health scores. A negative coefficient suggests the opposite. The strength of the association depends on the absolute value closer to 0 (weak) or 1 (strong).

  1. Strongest Correlation with BMI:

Identify the variable with the highest correlation coefficient (absolute value) compared to BMI. Report the coefficient, variable name, and sample size for that specific correlation.

  1. Means and Standard Deviations:

The SPSS output should provide descriptive statistics for each variable. Locate the mean (average) and standard deviation (spread) for BMI and doctor visits. Repeat for weight and BMI.

  1. Weight and BMI Relationship:

Analyze the correlation coefficient between weight and BMI. A positive coefficient indicates a positive correlation (higher weight associated with higher BMI). A negative coefficient suggests the opposite. The strength of the association depends on the absolute value closer to 0 (weak) or 1 (strong).

  1. Scatterplot Interpretation:

The scatterplot visually represents the relationship between two variables. Look for patterns in the data points. A positive correlation shows a general upward trend, while a negative correlation shows a downward trend. A stronger correlation will have a tighter clustering of points around the trendline. The scatterplot can reveal outliers or non-linear relationships not captured by the correlation coefficient.

By following these steps and referencing the correlation matrix and descriptive statistics, you can interpret the results of your correlational analysis and understand the relationships between the variables you examined.

 

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