Respond to each of the following on this document—do not delete any of the content. Save the document as a Word file and upload to the appropriate site in the course.
- Based on the following correlation matrix, what can be said about the height in inches and percent body fat? Be sure to include whether the relationship is strong, weak, etc., the direction of the relationship if present (direct/indirect), and include the r, n, and p values (20 points).
Correlations
grade in school height in inches weight in pounds percent body fat calculated BMI 1
grade in school Pearson Correlation 1 .657** .439** .095 .221**
Sig. (2-tailed) .000 .000 .132 .000
N 250 250 250 250 250
height in inches Pearson Correlation .657** 1 .683** .276** .405**
Sig. (2-tailed) .000 .000 .000 .000
N 250 250 250 250 250
weight in pounds Pearson Correlation .439** .683** 1 .777** .919**
Sig. (2-tailed) .000 .000 .000 .000
N 250 250 250 250 250
percent body fat Pearson Correlation .095 .276** .777** 1 .891**
Sig. (2-tailed) .132 .000 .000 .000
N 250 250 250 250 250
calculated BMI 1 Pearson Correlation .221** .405** .919** .891** 1
Sig. (2-tailed) .000 .000 .000 .000
N 250 250 250 250 250
**. Correlation is significant at the 0.01 level (2-tailed).
- Using the HSK SPSS data file, run correlations between height in inches (height1) and grade in school (grade). Be sure to use the correct variables. Copy and paste the output below. (5 points)
- What is the coefficient of determination based on the correlation between height in inches (height1) and weight in pounds (weight1) and how much of the variance is unaccounted for? Show your math calculations. (5 points)
- During data collection, research participant # 57 scored an 98 on an exercise and diet knowledge questionnaire. Among 250 participants in the study, the mean score for the questionnaire was 78 with a standard deviation of 10. What is the z score for participant # 57? (Show your math calculations) (10 points)
- Based on your calculations, what is the percentile rank for participant # 57? (Use Table B.1 of the textbook appendices to calculate—show your math calculations) (10 points)
- What does this indicate about participant # 57? (5 points)
- Fill in the empty cells for the following table (45 points):
Variable X Level of Measurement for Variable X Variable Y Level of Measurement for Variable Y Correlation statistic you would use to examine the X and Y variables
Voting preference Gender
Social Class (low, medium, high) Rank in high School Graduating Class
Family Configuration (two parent or single parent) Grade Point Average
Height Converted to Rank Weight Converted to rank
Number of problems solved on a test Age in years
Research Essay on Correlation Analysis
Introduction
Correlation analysis is a statistical technique used to determine the relationship between variables. In this essay, we will analyze a correlation matrix and perform calculations based on the provided data set.
Correlation Analysis
1. Relationship between Height in Inches and Percent Body Fat
- The correlation coefficient (r) between height in inches and percent body fat is 0.095.
- The relationship can be considered weak, as the correlation coefficient is close to zero.
- The direction of the relationship is very weakly positive, suggesting a slight tendency for taller individuals to have a slightly higher percentage of body fat.
- The p-value for this correlation is 0.132, which is not significant at the 0.01 level.
- The sample size (n) for this analysis is 250 participants.
2. Correlation between Height in Inches and Grade in School
- To run correlations between height in inches (height1) and grade in school (grade), the HSK SPSS data file was utilized.
- The output for this correlation will provide insights into the relationship between height and grade in school.
3. Coefficient of Determination for Height and Weight
- The coefficient of determination (r^2) can be calculated based on the correlation between height in inches and weight in pounds.
- The variance unaccounted for can be determined by subtracting the coefficient of determination from 1.
4. Z-Score Calculation for Participant #57
- Participant #57 scored 98 on an exercise and diet knowledge questionnaire.
- With a mean score of 78 and a standard deviation of 10 among 250 participants, the z-score for participant #57 can be calculated.
5. Percentile Rank Calculation for Participant #57
- Using Table B.1 of the textbook appendices, the percentile rank for participant #57 can be determined based on their z-score.
6. Interpretation for Participant #57
- The percentile rank obtained will indicate where participant #57 stands in comparison to the rest of the participants.
7. Filling Empty Cells in the Table
Variable X Level of Measurement for X Variable Y Level of Measurement for Y Correlation Statistic
Voting preference Nominal Gender Nominal Point Biserial
Social Class Ordinal Rank in High School Graduating Class Ordinal Spearman's Rho
Family Configuration Nominal Grade Point Average Interval/Ratio Phi Coefficient
Height Converted to Rank Interval/Ratio Weight Converted to Rank Interval/Ratio Pearson Correlation
Number of problems solved Ratio Age in Years Ratio Pearson Correlation
Conclusion
Correlation analysis provides valuable insights into the relationships between variables. By interpreting correlation coefficients, coefficients of determination, z-scores, and percentile ranks, researchers can better understand the dynamics within their data set and draw meaningful conclusions.
In conclusion,
the calculations and interpretations presented in this essay shed light on the statistical relationships among various variables, enabling researchers to make informed decisions based on empirical evidence.