Chi Squared

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Produced by Michael G, former colleague... A great simple run through of Chi Squared... Complete with handouts...

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Chi Squared

  1. 1. The Chi-Squared ( Χ 2 ) Test A test of association
  2. 2. The Null and Alternative Hypotheses The Null Hypothesis states that there will be no significant relationship between the data sets The Alternative Hypothesis states that there will be a significant relationship between the data sets So if we were to study the relationship between country size and population what would be the null and the alternative hypotheses
  3. 4. The number of buses observed per minute in relation to the distance from the city centre. 2 3 3 2 Σ (O-E) 2 5 1 10 0 (O-E) 2 /E (O-E) Expected frequency (E) No. of buses per min (O) Distance (km)
  4. 5. The relationship between the size of pebbles in a river in relation to the distance from its source. 20 3 20 2 Total (O-E) 2 60 1 100 0 (O-E) 2 /E (O-E) Expected frequency (E) Average Diameter of pebbles (mm) (O) Distance from source (km)
  5. 6. The number of cars observed in relation to the distance from my house. 44 3 51 2 Total (O-E) 2 53 1 52 0 (O-E) 2 /E (O-E) Expected frequency (E) Number of cars seen (O) Distance from house (km)
  6. 7. Interpreting your Chi-Squared Value <ul><li>Buses = 7.6 Pebbles = 88 Cars = 1 </li></ul><ul><li>Calculate degrees of freedom: </li></ul><ul><ul><li>df = n-1 (where n is the no. of categories) </li></ul></ul><ul><ul><li>In this case df = 4-1 = 3 </li></ul></ul><ul><li>Use a critical values table to work out the significance of your result. </li></ul><ul><li>Significance tells us how confidently we can disprove the null hypothesis </li></ul>
  7. 8. Interpreting your Chi-Squared Value <ul><li>Buses = 7.6 Pebbles = 88 Cars = 1 </li></ul><ul><li>3 degrees of freedom. </li></ul><ul><li>Critical values for 3 df are: </li></ul>What do our results mean? 16.27 11.34 7.82 6.25 Critical value 0.001 99.9% 0.01 99% 0.05 95% 0.10 90% Confidence level
  8. 9. When can you use Chi-Squared? <ul><li>When the data is in the form of frequencies. </li></ul><ul><li>When the frequency data has a precise numerical value. </li></ul><ul><li>When the data is organised into categories or groups. </li></ul><ul><li>When the total number of observations is greater than twenty. </li></ul><ul><li>When the expected frequency in any one category is greater than five. </li></ul>
  9. 10. Task Work through the exam paper. Answer every question on the exam sheet. Those that you do not complete now are to be done for homework.
  10. 11. Chi-Squared Quiz!
  11. 12. Question 1 You need a total number of observations greater than 10 to carry out the chi-squared test. True or False
  12. 13. Question 2 What does the numerical value of the frequency data have to be? A: Precise B: Prime C: Square
  13. 14. Question 3 What does the expected frequency in any one category have to be greater than? A: 5 B: 3 C: 7 D: 10
  14. 15. Question 4 The formula for chi-squared is? A B C
  15. 16. Question 5 Expected values will be the same for every category. True or False

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