1. 1.2 Conclusions and Issues Causal Relationships CAUSE – al not CAS - ual A relationship where change in the value of one variable CAUSES another variable to also change. Example: A change in temperature changes the number of people at the beach. Non - Example: The amount of sunscreen sold does not change the number of people at the beach. Proving that two variables have a causal relationship is very difficult and generally involves an in-depth study well beyond the scope of this course.

2. Correlation A relationship where the values of two (or more) variables change together in a pattern. Examples: As the temperature increases so does the number of people at the beach. As the amount of sunscreen sold increases so does the number of people at the beach. As the number of pirates at the beach increases the number of non-pirates at the beach decreases. Correlations only indicate how variables are changing NOT if they are affecting one another. In this course we will mostly focus on correlations.

3. Example 1 Determine if there is a correlation between gender and the likelihood that students have a drivers licence. Observations: 71 % of students have licences. (20 / 28 = 0.71) 69 % of male students have licences. (9 / 13 = 0.69) 73 % of female students have licences. (11/ 15 = 0.73) 13 males and 15 females were sampled. Approximately equal amounts of both groups. Each student is worth 3.6% of the total. (1 / 28 = 0.036) Conclusion: 73% of females and 69% of males had licences. Therefore there is a correlation between the variables as females are 4% higher than males. OR While 4% more females have licences than males this difference is very small when compared to the side of the sample which is only 28. This makes each student worth for 3.6% of the total, making the difference insignificant. There is not correlation.

4. Example 2 100 pirates were surveyed in 2000, 2005 and 2010. The number of gold pieces they had was recorded. Record your observations. 020406080100 020406080100 020406080100 2000: 2005: 2010:

5. Lowest Bottom Half Median (25%) Median (50%)Top Half Median (75%) Highest 2000010202550 20051020405070 201020305065100 In general pirates got richer. The spread in 2000 was 0 to 50 while in 2010 it was 20 to 100. The richer pirates increases faster than the poorer pirates. The lowest 25% only increased their wealth by between 10 and 20 pieces while the highest 25% by between 30 and 50 pieces. The middle 50% (moderately wealthy pirates) increased faster than the poor pirates but slower than the rich ones. This group increased by between 20 and 30 pieces In 2000, the richest pirates were the most spread out at a spread of 25 pieces while the poorest pirates where the least spread out with a spread of 10 pieces. The spread of the poorest pirates did not change. It remained at 10 pieces while the spread of the richest pirates increased to 30 in 2005 and 35 in 2010. The spread of the moderately wealthy pirates did increase from 15 pieces in 2000 to 35 pieces in 2010. 57% of the increase occurred in the pirates with lower wealth. The poorest pirates had a greater percentage increase in wealth of between 300% and infinity where as the richer pirates only increased their wealth by between 100% and 160%.

6. Important Facts Your homework is: Pg 21 #3-8, 10, 11, 13 It is important to justify your conclusions with numbers and/or calculations Pirates seem to be quite wealthy. Causal relationships are hard to prove. Correlations are not. Often there is no one correct answer. As long as you can support your conclusion with facts it is probably correct. If you cannot support your conclusions with facts, consider making a different conclusion.