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# 03 The Chi Squared Test

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• 1. The &#x3C7; 2 (chi-squared) Test &#x3C7; 2 = &#x2211; (O &#x2013; E) 2 E where &#x2211; = the sum of O = the observed value E = the expected value ALBIO9700/2006JK
• 2. Questions:&#x2022; Are the results we get (observed) sufficiently close to the ones we expected that the differences between them have probably just arisen by chance?&#x2022; Are they so different that something unexpected must be going on? ALBIO9700/2006JK
• 3. Answers:&#x2022; The &#x3C7;2 (chi-squared) test allows us to compare our observed results with the expected results&#x2022; Decide whether or not there is a significant difference between them ALBIO9700/2006JK
• 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. What the value means?&#x2022; Relate &#x3C7;2 (chi-squared) value to probabilities in &#x201C;Table of &#x3C7;2 values&#x201D;&#x2022; The probabilities are the probability that the difference between our expected and observed results are due to chance ALBIO9700/2006JK
• 6. Table of &#x3C7; values 2 &#x2022;Takes into account the no of comparisonsDegrees made Probability greater than of &#x2022; 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. 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 &#x3C7;2 test to determine whether or not thedifference between these observed results andthe expected results is significant. ALBIO9700/2006JK