ࡱ> 796c jbjbSS *:11]4444444xxxxx<x^        ,H <hI 4I 44"44 H`4444 H 44 >Ӿxx How close is close enough? When doing experimental work in genetics, we often do many crosses of the genes that we are studying. When we think we see a pattern that we can predict, we make the prediction (hypothesis) with numbers that we hope will be supported by the evidence we collect. In genetics there is often variation between the prediction and the data collected. As scientists, we want to know if our data is close enough to the prediction to support the hypothesis. If some factor other than chance is at work, we would reject the hypothesis. It is possible to reject an hypothesis when we should have accepted it; it is also possible to accept the hypothesis when we should not have. By using the Chi Square values as our guide we are saying that we will make an erroneous decision about rejecting or accepting our hypotheses less than 5% of the time. In our "card simulation" we will have examples of all of the possibilities: 1) Accept an hypothesis when only chance is the cause of the variance (should accept and do accept). 2) Reject an hypothesis when chance was not the cause of the variance and something other than our prediction was at work (should reject and do reject). 3) Accept an hypothesis when we should not have because something other than what we predicted was at work, but we still got good Chi Square values (shouldnt accept and do accept). This will be an example of that small 5% situation. In all three of these situations our work will be correct, but in the last one it will be misleading. Table 4. (2 Values and Probabilities.   Possibility of Chance Occurrence in Percentage (5% or Less Considered Significant)Degrees of Freedom90%80%70% 50% 30%20%10%5%1%(sig.)10.0160.0640.148.455 1.0741.6422.7063.8416.63520.2110.4460.7131.3862.4083.2194.6055.9919.21030.5841.0051.4242.3663.6654.6426.2517.81511.34141.0641.6492.1953.357 4.878 5.9897.7799.48813.277ChiSquare Test A test that is often applied to determine how well observed ratios fit expected statistical ratios is known as the chisquare ((2) test. This test calculates the deviations of observed numbers from expected numbers into a single numerical value called (2 . The difference between the number observed and the number expected for a phenotype is squared and divided by the number expected. This is repeated for each phenotype class. The (2 value consists of the summation of these values for all classes. The formula for (2 (Suzuki, et al., 1986) is: (observed expected)2 (2 = total of ___________________ over all cases expected Associated with each (2 value is a probability that indicates the chance that, in repeated experiments, deviations from the expected would be as large or larger than the ones observed in this experiment. Table 4 lists probabilities and (2 values. In Table 4, note the column "Degrees of Freedom." In an experiment, the degree of freedom is one less than the number of different phenotypes possible. In this experiment we have two possible phenotypes (the normal and the mutant), so there are 2  1 = 1 degree of freedom. If the probability is greater than 5% (0.05), we accept the observed data. Calculate the (2 value for the class data observed in the F2 generation below. Assume complete dominance of red over black and an expected 3:1 ratio, red:black. Example: If, in an F2 population of 100 plants, results are 60 red: 40 black (expected ratio would be 75 red: 25 black), then: (60 75)2 (40 25)2 (2 = ________ + ________ = 3 + 9 = 12.0 75 25 Looking in the (2 table for (2 = 12.0 with 1 degree of freedom, probability = < 0.01; therefore, these results are not supportive of a 3:1 ratio since the probability is less than 5% (0.05). We should reject our hypothesis. *l m & * + . ! # Y \     %&'rstuv>?@lm]^묪CJH*OJQJmH 55CJOJQJmH jCJOJQJUCJH*OJQJmH  jcCJOJQJmH >*CJOJQJmH 6CJOJQJmH CJOJQJmH 56CJ$OJQJmH ?+a & +   $$44#$|$+a & +              ! # ) / 5 ; A G M S Y Z \ b h n t z   I EFt/0R a            D}}$$y$$44 -N &X #`$ ! # ) / 5 ; A G M S Y {$$$$y$$44 -N &X #  Y Z \ b h n t z $$x$$4 -N &X # $$x$$4 -N &X #   I Eztrttt &x$$4 -N &X #$$$$$ EFt/0Rr7 Nhh ( &^pq|}5CJOJQJmH  jcCJOJQJmH CJH*OJQJmH CJOJQJmH Rr7(/ =!"#$%hhm.drn=2505z4z0&Item.Delete.Next=&Item.Delete=&Url.Item.Deleted=&merge=msgitem" ADD_DATE="1118691158" LAST_VISIT="1118691159" VISITATION_COUNT="2" OBJECT_TYPE="LINK">Novell WebAccess
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Tuesday, June 7, 2005

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