Bio 321 F13 lecture 2 v2

# Up the squares you can also calculate the ra5os

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Unformatted text preview: hought of as a “null hypothesis” –  null hypothesis , or H0, can be any hypothesis –  here, H0 is the hypothesis that the trait is being determined by a single Mendelian factor with dominance in a monohybrid cross •  the alterna5ve hypothesis, or H1, is that there is not a Mendelian basis for the phenotypic ra7o that we are measuring Chi- square test of goodness of ﬁt •  Chi- square distribu7on with k degrees of freedom = distribu7on of the sum of squared devia7ons of k independent data points (standard normal random variables) •  how do we determine k, the number of degrees of freedom? •  here we have two types of progeny: tall and short, and 86 total progeny tall short total 66 20 86 for a fixed # of observations (fixed marginal value of a 1 row x 2 column data table (in red) once we fill one of the red cells => we have 1 degree of freedom the other cell is automatically determined (i.e. is not independent of the first cell) in general •  for a list of categories (only 1 column or row) –  # degrees of freedom k = # categories – 1 –  “one- way chi- square test” •  for a table with N rows and C columns –  # degrees of freedom k = –  (N- 1) x (C- 1) –  “two- way chi- square test” calcula7ng chi square tall short total observed 66 20 86 expected =(86)(3/4)= 64.5 =86(1/4) = 21.5 - observed- expected 1.5 1.5 - (obs- exp)^2 2.25 2.25 - (obs- exp)^2/exp 0.035 0.105 0.14 chi-square = 0.14 with 1 degree of freedom in MS Excel type the following into a cell =chidist(0.14,1) returns 0.708, which is the P value what is the P value? •  it is the chance of genng the data that you got, by chance, if the expected ra7o were actually the value in the popula7on you are sampling –  scoring phenotypic/genotypic ra7os of oﬀspring can be thought of as sampling the meio7c output of the parents what does the P value mean? •  conven7on: if P<0.05 •  which means, there is less than a 1 in 20 chance of genng the data by chance if the expected ra7o is the true popula7on ra7o •  if P<0.05, then this is a “sta7s7cally signiﬁcant” result; i.e. something other than the expected ra7o is the actual ra7o in the popula7on –  i.e. something other than a Mendelian mechanism is determining the cross outcome P value in hypothesis tes7ng •  in general, if P < 0.05, we reject the null hypothesis (H0) and accept the alterna7ve hypothesis (H1) coming to a conclusion from our cross data •  •  •  •  66 tall, 20 short (ra7o = 3.3:1) P = 0.708 => we cannot reject the null hypothesis these data are consistent with a single, Mendelian locus with dominance in a monohybrid cross in class exercise 3 •  let’s do a chi- square goodness of ﬁt for a single locus cross with genotype data •  make up some data for –  #DD –  #Dd –  #dd...
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