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Association example

association

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Association example

  1. 1. PRACTICE PROBLEM CHI-SQUARED FOR ASSOCIATION/INDEPENDENCE
  2. 2. • IN ORDER TO CHECK FOR A RELATIONSHIP BETWEEN HEAD INJURIES AND SOCCER PARTICIPATION, A STUDY ASKED 240 RANDOMLY SELECTED COLLEGE STUDENTS ABOUT HEAD INJURIES AND THEIR ACTIVITIES. THE RESULTS ARE LISTED BELOW. • DO THE DATA SUGGEST THAT THERE IS A RELATIONSHIP BETWEEN THE NUMBER OF CONCUSSIONS AND ACTIVITIES OF COLLEGE STUDENTS? BE SURE TO WRITE YOUR WORK, HYPOTHESIS STATEMENTS, ETC. 0 concussions 1 concussion 2 concussions 3 or more concussions Soccer players 45 25 11 10 Non-soccer players 68 15 8 5 Non- athletes 45 5 3 0
  3. 3. TAKE A FEW MINUTES TO WORK THIS PROBLEM AND THEN CHECK YOURSELF ON THE REMAINING SLIDES!
  4. 4. STATE HYPOTHESES: • HO: THERE IS NO ASSOCIATION BETWEEN NUMBER OF CONCUSSIONS AND ACTIVITIES OF COLLEGE STUDENTS. • HA:THERE IS AN ASSOCIATION BETWEEN NUMBER OF CONCUSSIONS AND ACTIVITIES OF COLLEGE STUDENTS.
  5. 5. CHECK CONDITIONS: • RANDOM – PROBLEM STATED THAT THEY TOOK A RANDOM SAMPLE OF 240 COLLEGE STUDENTS • LARGE SAMPLE SIZE – NEED TO CHECK EXPECTED COUNTS TO BE SURE THAT THEY ARE ALL AT LEAST 5. EXPECTED COUNTS ARE BELOW: • ALL EXPECTED COUNTS ARE NOT AT LEAST 5 – IT DOES NOT MEET THIS CONDITION – PROCEED WITH CAUTION (AND BE ABLE TO DISCUSS PITFALLS WITH THE PROBLEM LATER) 0 concussions 1 concussion 2 concussions 3 or more concussions Soccer players 59.515 17.278 8.4473 5.7595 Non-soccer players 60.823 17.658 8.6329 5.8861 Non- athletes 34.662 10.063 4.9198 3.3544
  6. 6. DO THE MATH: • 𝜒2 = (𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑑−𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑)2 𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑 • 𝜒2 = (45−59.515)2 59.515 + (25−17.278)2 17.278 + ⋯ (0−3.3544)2 3.3544 = 21.485 • DF: (4-1)(3-1)=6 • P-VALUE: 0.0015
  7. 7. CONCLUSION: • SINCE THE P-VALUE IS SO SMALL, WE DO HAVE STATISTICALLY SIGNIFICANT EVIDENCE TO REJECT THE NULL HYPOTHESIS. • THERE IS AN ASSOCIATION BETWEEN NUMBER OF CONCUSSIONS AND ACTIVITIES OF COLLEGE STUDENTS

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