Correlations

?

•Children with high self-esteem also tend to have high academic achievement.

•Legitimate correlation or illusory correlation?

Illusory

•Actually nationwide reports indicate that self-esteem and achievement are not connected.

•Instead the connection lies in intelligence and socioeconomic status.

?

•As ice cream consumption increases, the crime rate increases.

•Legitimate correlation or illusory correlation?

LEGIT

•Both ice cream consumption and crime rate are related to a third variable.

•What?

•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.

Sampling

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.

Let’s Find Out!

Create a table like this Blue Brown Green Orange Red Yellow

Predicted Frequency

Observed Frequency

Class Frequency

Actual Frequency

Final answers should be in percentage form

•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.

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

orange, green.

M&M’s World Population

•13% Brown•13% Red•14% Yellow•24% Blue•20% Orange•16% Green

BrownRedYellowBlueOrangeGreen

Conclusion

• Individual samples vary widely and initial hypotheses are not very accurate.

•However, as the sample grows larger, the approximate population can be determined.

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?

•In each case, age is the third factor.

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.