Chi Square 117 



The deviation in this problem is 4.25 so that the deviation 

 divided by the standard error is ^•^%.52 or 0.94, which agrees 

 with the result obtained previously. The probability of occur- 

 rence for various ratios of the deviation to the standard error 

 are listed in Table 2. 



The methods of the probable and the standard errors are 

 similar except that the probable error is 0.6745 times the 

 standard error. If the deviation is greater than three times the 

 probable error, the observed ratio is considered not a true ex- 

 ample of the theoretical. The probable error has been used 

 longer than the standard error. Because it requires a further 

 multiplication, there is a tendency today to replace it with the 

 standard error, although many geneticists still use the older 

 method. 



Chi Square 



Still another method of determining whether an observed ratio 

 is a true example of a theoretical ratio is the x^ (chi square) 

 method. It is often used when the ratio includes more than two 

 terms, as explained in Chapter 9, but is also useful when there 

 are only two terms. Chi square is obtained by finding the actual 

 deviations of the observed frequency from the expected fre- 

 quency for each term of the ratio, squaring them, dividing each 

 squared deviation by the expected frequency of that term, sum- 

 mating these values, and finding the probability from the appro- 

 priate place in a prepared table which lists the probabilities for 

 various values of x^- 



If we return to our problem of orange and white flowers in 

 Nemesia strumosa, we recall that a cross between an orange- 

 flowered plant and a white-flowered plant yielded a ratio of 25 

 orange to 17 white. Is this a true example of a testcross ratio? 

 On the basis of a 1 : 1 ratio, we should expect 21 orange- and 21 

 white-flowered plants. Let x^ represent the observed number of 

 orange plants and Xo the observed number of whites. Then let m 

 represent the expected number in each class, which happens to be 

 the same since this is a 1 : 1 ratio. To determine ^, we use the 

 formula : 



(xi - m)^ {x2 - m)^ 

 m m 



