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- 1. The Chi-Squared ( Χ 2 ) Test A test of association
- 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
- 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)
- 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)
- 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)
- 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>
- 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
- 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>
- 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.
- 11. Chi-Squared Quiz!
- 12. Question 1 You need a total number of observations greater than 10 to carry out the chi-squared test. True or False
- 13. Question 2 What does the numerical value of the frequency data have to be? A: Precise B: Prime C: Square
- 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
- 15. Question 4 The formula for chi-squared is? A B C
- 16. Question 5 Expected values will be the same for every category. True or False

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That is really helpful information on Chi-Squared test. Just wondering if you could add example and explanation like how to interpret the result or data. Please respond.

arvind tirkey