Analyzing DataAnalyzing Data2 Test….”Chi” Square2 Test….”Chi” Square

Forked-Line Method, F2Forked-Line Method, F2UuDd x UuDdUuDd x UuDd

1/4 UU

1/2 Uu

1/4 uu

1/4 DD1/2 Dd1/4 dd

1/4 DD1/2 Dd1/4 dd

1/4 DD1/2 Dd1/4 dd

1/4 x 1/4 = 1/16 UUDD

1/4 x 1/2 = 1/8 UUDd1/4 x 1/4 = 1/16 UUdd

1/2 x 1/4 = 1/8 UuDD1/2 x 1/2 = 1/4 UuDd1/2 x 1/4 = 1/8 Uudd

1/4 x 1/4 = 1/16 uuDD

1/4 x 1/2 = 1/8 uuDd1/4 x 1/4 = 1/16 uudd

Genotypes U--D--Genotypes U--D--

1/4 UU

1/2 Uu

1/4 DD1/2 Dd

1/4 DD1/2 Dd

1/4 x 1/4 = 1/16 UUDD

1/4 x 1/2 = 1/8 UUDd

1/2 x 1/4 = 1/8 UuDD1/2 x 1/2 = 1/4 UuDd

If you pick wt F2 worms, what will be the proportion of each class in the F3?Work this out in your notebooks, for Thursday.

Chance Chance DeviationDeviation

The outcomes of The outcomes of segregation, segregation, independent independent assortment, and assortment, and fertilization are subject fertilization are subject to random fluctuations to random fluctuations from predicted from predicted occurrences… occurrences… 

… …as a result of as a result of chancechance..

As the sample size As the sample size increases, the average increases, the average deviation from the deviation from the expected fraction or expected fraction or ratio is expected to ratio is expected to decrease.decrease.

Experimental Data Experimental Data

Does it fit Expected Does it fit Expected Values?Values?

MendelMendel

Goodness of FitGoodness of Fit

Null HypothesisNull Hypothesis null hypothesisnull hypothesis: there : there isis nono statistical difference statistical difference

between the observed value and the predicted between the observed value and the predicted value. value. The apparent difference can be attributed to The apparent difference can be attributed to chancechance  

alternative hypothesisalternative hypothesis: there : there isis a a statistical statistical difference difference between the observed value and the predicted value. between the observed value and the predicted value. The The apparent difference can not be attributed to chance alone.apparent difference can not be attributed to chance alone.   

Important: accepting or rejecting the null hypothesis Important: accepting or rejecting the null hypothesis does not prove anything, it only provides a does not prove anything, it only provides a statistical means of measuring the difference statistical means of measuring the difference between the observed and expected results. between the observed and expected results.

Answer Answer these these

questions…questions… what is the total what is the total

number of offspring?  number of offspring?  offspring n = ______ offspring n = ______ 

how many different how many different classes (phenotypes or classes (phenotypes or genotypes) of offspring genotypes) of offspring did you observe?  did you observe?  

classes n = _______ classes n = _______ 

what are the what are the classesclasses, , and how many were and how many were observed for each observed for each class?class?

  based on genotype based on genotype classes, how many of classes, how many of each phenotype do each phenotype do you expect in each you expect in each class in each...class in each...

290 purple; 110 white 290 purple; 110 white flowersflowers

Offspring n = 400Offspring n = 400

Classes n = 2 (purple, Classes n = 2 (purple, white)white)

Observed:Observed:290 purple290 purple110 white110 white

Expected:Expected:300 purple300 purple100 white100 white

Null Null HypothesisHypothesis

The observed 290 purple The observed 290 purple flowers and 110 white flowers and 110 white flowers are statistically no flowers are statistically no different than the expected different than the expected values of 300 purple flowers values of 300 purple flowers and 100 white flowers. and 100 white flowers.

The apparent difference is The apparent difference is due to chance. due to chance.

290 purple; 110 white 290 purple; 110 white flowersflowers

Offspring n = 400Offspring n = 400

Classes n = 2 (purple, Classes n = 2 (purple, white)white)

Observed:Observed:290 purple290 purple110 white110 white

Expected:Expected:300 purple300 purple100 white100 white

The FormulaThe FormulaO: observedO: observed E: expectedE: expected

Observed:Observed: Expected:Expected:290 purple290 purple 300 purple300 purple110 white110 white 100 white100 white

purplewhite

290110

300100 10

10 100100

0.331

1.33

Degree of FreedomDegree of Freedom

What does the What does the 22 value value mean? mean?

Critical values for chi-square are found on Critical values for chi-square are found on tables, sorted by degrees of freedom and tables, sorted by degrees of freedom and probability levels... probability levels...

2 = 1.33

Null HypothesisNull Hypothesis

What does the What does the 22 value value mean? mean?

2 = 1.33

p = ~0.2

One way to think of this, is that if you did this experiment 100 times, you’d get similar results, do to

chance, roughly 20 times.

Null Hypothesis: Null Hypothesis: There is no statistical difference There is no statistical difference between the measured values, and the expected values between the measured values, and the expected values

(with details).(with details).  

Chi Square Analysis:Chi Square Analysis: “ “What is the probability that the What is the probability that the null hypothesis is correct?”null hypothesis is correct?”

  Reject Null Hypothesis: p = < 0.05Reject Null Hypothesis: p = < 0.05

WednesdayWednesday

FridayFridayWormbaseWormbase

EntrezEntrez

Determine Determine phenotype(s) for each phenotype(s) for each mutant (assignment, mutant (assignment, due at start of class due at start of class Friday), and then ID Friday), and then ID worms in class (on worms in class (on

Friday).Friday).

??