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Understanding Correlations: Self-Esteem, Academic Achievement, and Illusory Connections

This article explores the complex relationships between self-esteem, academic achievement, and other variables. While it might seem that high self-esteem correlates with academic success, nationwide reports suggest this link is illusory, as intelligence and socioeconomic status play more significant roles. Additionally, the piece examines the correlation between ice cream consumption and crime rates, noting that both are influenced by warmer weather. Finally, we investigate how sample sizes affect predictions about behavior and distribution, using M&M's as a fun example.

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Understanding Correlations: Self-Esteem, Academic Achievement, and Illusory Connections

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  1. Correlations

  2. ? • Children with high self-esteem also tend to have high academic achievement. • Legitimate correlation or illusory correlation?

  3. Illusory • Actually nationwide reports indicate that self-esteem and achievement are not connected. • Instead the connection lies in intelligence and socioeconomic status.

  4. ? • As ice cream consumption increases, the crime rate increases. • Legitimate correlation or illusory correlation?

  5. LEGIT • Both ice cream consumption and crime rate are related to a third variable. • What?

  6. Warm weather! • When it is warm outside, as it is in summer, people enjoy more ice cream and more crimes are committed because it stays light longer, people are outdoors, and windows are kept open.

  7. Sampling

  8. Sampling • From a small sample of a pack of M&M’s can you accurately predict the total distribution of colors in the world’s M&M’s population? • By the way, over 400 million M&M’s are produced each day.

  9. Let’s Find Out!

  10. Create a table like this Final answers should be in percentage form

  11. First, predict the percentage for each color. • Open your bag. DON’T EAT YOUR M&M’s…yet. • Count each color. • Convert raw data into percentages. • Make a simple graph of distribution. • Form a hypothesis about the actual population. • Last, when I say, compare with your seat partners.

  12. Pool class data. • How many total: blue, yellow, brown, red, orange, green.

  13. M&M’s World Population • 13% Brown • 13% Red • 14% Yellow • 24% Blue • 20% Orange • 16% Green

  14. Conclusion • Individual samples vary widely and initial hypotheses are not very accurate. • However, as the sample grows larger, the approximate population can be determined.

  15. Explain • 1. Why do children with bigger feet spell better? • 2. Why in certain counties in the southern U.S., are divorce rates negatively correlated with death rates? • 3. Why do nations that have added fluoride to their water have a higher cancer rate?

  16. In each case, age is the third factor.

  17. Explain • 1. Why do children with bigger feet spell better? (Bigger feet=older children) • 2. Why in certain counties in the southern U.S., are divorce rates negatively correlated with death rates. (Older couples are less likely to divorce, but more likely to die) • 3. Why do nations that have added fluoride to their water have a higher cancer rate? (nations able to afford such for the majority have healthier people which live longer- long enough to develop cancer, largely a disease of old age.

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