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PRACTICE PROBLEM
CHI-SQUARED FOR ASSOCIATION/INDEPENDENCE
• 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
TAKE A FEW MINUTES TO WORK THIS
PROBLEM AND THEN CHECK YOURSELF ON
THE REMAINING SLIDES!
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.
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
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
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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Association example

  • 1. PRACTICE PROBLEM CHI-SQUARED FOR ASSOCIATION/INDEPENDENCE
  • 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. TAKE A FEW MINUTES TO WORK THIS PROBLEM AND THEN CHECK YOURSELF ON THE REMAINING SLIDES!
  • 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. 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. 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. 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