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Correlation

This article explains the concept of correlation, including positive and negative relationships, perfect and zero correlations, and the interpretation of correlations. It also discusses common examples and the limitations of correlation analysis.

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Correlation

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  1. Correlation

  2. Definition Shows the direction and the strength of the relationship between two variables.

  3. Scatter plot for correlational data

  4. Examples of positive and negative relationships

  5. Positive correlation: when a small amount of one variable is associated with a small amount of another variable, and a large amount of one variable is associated with a large amount of the other .

  6. Negative correlation: when a small amount of one variable is associated with alarge amount of another variable, and a large amount of one variable is associated with a small amount of the other. 120 110 100 90 80 PULLUPS 70 140 150 160 170 180 190 200 210 220 WEIGHT

  7. Perfect Correlation As X increases a unit, Y increases a specific increment.

  8. example 100 A perfect correlation David Peter 90 Mark Jim 80 Ken STRENGTH 70 140 150 160 170 180 190 200 WEIGHT

  9. Not always the correlation is perfect. Guess?

  10. 120 110 100 90 80 STRENGTH 70 140 150 160 170 180 190 200 210 220 WEIGHT

  11. Zero correlation: when there is no association between two variables.

  12. Example A zero correlation

  13. 4 120 15 7 8 13 10 17 110 9 5 20 100 19 IQ 2 90 12 1 14 80 6 18 11 16 3 70 140 150 160 170 180 190 200 210 220 WEIGHT

  14. Three degrees of relationship Zero Positive Perfect

  15. Examples of different values for relationships

  16. practice For each pair, tell whether r is high, moderate, low or zero.± 1- The number of cars on different highways and the number of accidents. 2- The height and age of k-12 students. 3- k-12 students’ scores on a math test and a science test 4- k-12 students’ scores on a math test and a PE test 5- The birthrate and social economic level. 6- The length of the base of a square and the length of its diagonal.

  17. Interpreting correlations • Correlation does not demonstrate causation Number of books at home and students’ academic achievement

  18. Example Earlier wake- up times are consistently related to higher GPA. Although the study demonstrates a relationship between the two variables, it does not explain why the relationship exists.

  19. Correlation Confusion • Every time I eat chocolate, it gives me acne. • Most drug use occurs among the poor

  20. Correlation between two variables represents the degree of observed linear association between two variables, not the extent of their causal relationship. Examples: 1- Correlation between math achievement scores and shoe size in K-12 2- Height and intelligence in adult population 3- Crime rate and the number of churches 4- Crime rate and the number of death penalties 5- The academic degree and income

  21. Conclusion If A correlates with B, three possible causal relationship exist A causes B, B causes A, or C causes both A and B/

  22. Restricted range

  23. r =.52 r = -.40 r = .10 Fear of Death Sixth Graders First graders Cognitive Development

  24. Correlation of sample and population

  25. Influence of outlier on correlation

  26. Spearman correlation • Spearman correlation formula is used with data from an ordinal scale (ranks) • Used when both variables are measured on an ordinal scale

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