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# 03 The Chi Squared Test

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### 03 The Chi Squared Test

1. 1. The χ 2 (chi-squared) Test χ 2 = ∑ (O – E) 2 E where ∑ = the sum of O = the observed value E = the expected value ALBIO9700/2006JK
2. 2. Questions:• Are the results we get (observed) sufficiently close to the ones we expected that the differences between them have probably just arisen by chance?• Are they so different that something unexpected must be going on? ALBIO9700/2006JK
3. 3. Answers:• The χ2 (chi-squared) test allows us to compare our observed results with the expected results• Decide whether or not there is a significant difference between them ALBIO9700/2006JK
4. 4. Calculations:1. Work out expected results2. Record in table with observed results3. Calculate difference between each set and square it4. Divide each squared difference by the expected value and add up ALBIO9700/2006JK
5. 5. What the value means?• Relate χ2 (chi-squared) value to probabilities in “Table of χ2 values”• The probabilities are the probability that the difference between our expected and observed results are due to chance ALBIO9700/2006JK
6. 6. Table of χ values 2 •Takes into account the no of comparisonsDegrees made Probability greater than of • number of classes of data - 1freedom 0.1 0.05 0.01 0.001 1 2.71 3.84 6.64 10.83 2 4.60 5.99 9.21 13.82 3 6.25 7.82 11.34 16.27 4 7.78 9.49 13.28 18.46 ALBIO9700/2006JK
7. 7. Problem:In an actual cross between heterozygous greyparents with a long tail, the number of eachphenotype obtained in the offspring were:grey, long 54grey, short 4white, long 4white, short 18Use a χ2 test to determine whether or not thedifference between these observed results andthe expected results is significant. ALBIO9700/2006JK