NGPF 9.2 Correlation vs Causation

Complete the chart by choosing Observational Study (Obs), Experiment (Exp), both, or neither for the following statements:

a. Can determine causation between variables ​ ​ (a)  

b. Researcher does not affect the subjects ​ (b)  

c. Researcher affects the subjects ​ (c)  

d. Can show a linear relationship between variables ​ (d)  

e. Requires collection of data ​ (e)  

• Experiment (Exp)
• Neither

• Observational Study (Obs)
• Both

Take a look at this graph showing the relationship between the different states' and territories' average college tuition and graduation rates.

Describe any correlation you see between graduation rate and average tuition amount using vocabulary from this week's lesson.

• Average college tuition and graduation rates are positively correlated.

• Average college tuition and graduation rates are negatively correlated.

• Average college tuition and graduation rates are not correlated.

• Average college tuition and graduation rates are positively causal.

• Average college tuition and graduation rates are negatively causal.

Describe the correlation relationship between these two variables shown in this graph.

• Acceptance rate and graduation rate are strongly positively correlated.

• Acceptance rate and graduation rate are strongly negatively correlated.

• Acceptance rate and graduation rate are weakly positively correlated.

• Acceptance rate and graduation rate are weakly negatively correlated.

• Acceptance rate and graduation rate are not correlated.

What is the approximate correlation coefficient, r, for these two variables?

Round to the nearest thousandth.

(To find r, calculate the square root of R² to find the magnitude of r and then decide if it should be positive or negative based on the data.)

Mathematical Equivalence

ON

Compare these graphs of the same data with just 6 outliers removed, the states or territories with the top 2 and bottom 4 acceptance rates.

What has changed about the correlation now?

• Correlation became more strongly positive.

• Correlation became more weakly positive.

• Correlation became almost zero.

  (graduation rates remained about the same no matter what value the acceptance rate)

• Correlation became more weakly negative.

• Correlation became more strongly negative.

Compare these graphs of the same data with 6 data points removed. The outliers were specifically kept to have the data tell a different story.

What has changed about the correlation now?

• Correlation is more strongly positive.

• Correlation is more weakly positive.

• Correlation did not change.

• Correlation is more weakly negative.

• Correlation is more strongly negative.

After seeing the outlier effect and the sensitivity of the data set comparing college tuition and graduation rates, what can you do to make sure you are interpreting a data set well?

• Be skeptical about statistics you read or hear about

• Assume that if it is on the internet, it must be true

• Wait until the dust settles, delay making an informed opinion

• The truth is out there, investigate

• Check for multiple representations of the data

Describe the relationship between graduation rate and SAT scores using vocabulary from this week's lesson.

• Graduation rate and SAT scores are positively correlated.

• Graduation rate and SAT scores are negatively correlated.

• Graduation rate and SAT scores are not correlated.

• Graduation rate and SAT scores strongly causal.

• Graduation rate and SAT scores are weakly causal.

How could you design an experiment to find out if tuition costs contribute to the graduation rate?

An ​ (a)   with a ​ (b)   group that has ​ (c)   tuition increased could be compared to an ​ (d)   group that has their tuition ​ (e)   , and then graduation rates of each group could be compared.

• experiment
• observational study
• control
• experimental
• no
• all
• increased
• decreased
• sample survey
• some

What is key for both enduring love and sound investing?