BIOL1020 Lecture 15: BIOL Prac 7- What is the Chi square test

Introduction: A Chi-square test is used to compare observed data with expected data according to a hypothesis. For instance, if you were crossbreeding 2 heterozygous pea plants, you would expect to see a 3:1 phenotypic ratio in the offspring. In this case, if you were to breed 400 pea plants, you would expect to see 300 plants showing the dominant trait and 100 showing the recessive trait. But what happens if you observe only 260 plants with the dominant trait and 140 plants with the recessive trait? Does this mean something is wrong with Mendelian genetics or is this difference in expected results just due to chance (random sampling error)? These are the questions that can be answered using Chi-square statistics. The results of this statistical test is used to either reject or accept (fail to reject) the null hypothesis. The null hypothesis states there is no significant difference between the observed results and the expected results. This means that if the null hypothesis is accepted, the difference in observed and expected results was just a matter of chance and so the observed results basically "fit" with what was expected. Degrees of freedom (df) = number of independent outcomes (Y) being compared less 1 df = Y-1 At the 95% confidence interval we are 95% confident that there is a significant difference between the observed and expected results, therefore rejecting the null hypothesis. Probability Value - Is the decimal value determined from the X2 table and is the probability of accepting the null hypothesis. A 0.05 probability value equates to a 95% confidence interval.

The Chi-squared test formula is: Example: If we cross two pea plants that are heterozygous yellow pods, we would expect a 3:1 phenotypic ratio. So let's say we actually did the cross and got 280 plants with green pods and 120 plants with yellow pods. Question: Is this a 3:1 phenotypic ratio? This is the value of Chi-squared Test. We have a total of 400 plants and we expect a 300 green:100 yellow phenotypic ratio If the calculated Chi-squared value is less than the critical value listed in the Chi-squared table, then we accept the null hypothesis. This means that there is no significant difference between the observed and the expected values. Our degrees of freedom (df) = 2 outcomes - 1, or df = 1. Now we go the X2 table below and using the df = 1 and probability value of 0.05, our critical value is 3.84. Since our calculated X2 value is 5.33, and is larger than the critical value, we reject the null hypothesis and can say (at 95% confidence) that there is a significant difference between our observed and expected values.

The parent generation is yellowed podded and green podded pea plants. You cross a yellow podded pea plant with a green podded pea plant and you get 100% yellow podded plants in the F1 Generation (Phenotypic ratio 4 : 0, yellow to green). What will be the expected phenotypic ratio when you allow the F1 generation to reproduce?

Fill out the Punnett square.

If we actually did the cross and got 1150 yellow and 350 green. Would this be a consistent with what was expected?

Learning Outcomes Questions

1. Why would you run a Chi-squared test?

2. Determine the degrees of Freedom of the phenotypic ratio for this genetic cross.

a. 1

b. 2

c. 3

d. 4

e. 5

3. Using the data given, what is the result of your Chi-squared analysis? x2= ___.

4. Using the results of your Chi-squared analysis, do we fail to reject or reject the null hypothesis?

2. Consider two gene loci in the mouse, locus1 and locus 2. Each locus is on a different, nonhomologousautosomal chromosome . Alleles at locus 1 influence fur color.Allele A is for black and allele a is for white.Allele A is completely dominant to allele a . Allelesat locus 2 influence stature; allele B is for tall andallele b is for short. Allele B is completelydominant to allele b.

Mouse 1, genotype Aa Bb, mates withfemale mice , genotype Aa Bb; 100 progeny are produced.

___: What fraction of the gametes from mouse 1is expected to be genotype Ab ?

___: What fraction of the gametes from mouse 1is expected to have allele a ?

___: What fraction of the progeny is expectedto be true-breeding for both stature and black fur?

___: How many progeny are expected to be tallwith white fur? Show your calculations.

___: How many progeny are expected to beheterozygous at both loci? Show yourcalculations.

___: If you randomly choose two progeny mice,one at a time, what is the probability that both mice are tall andwhite? Show your calculations.

3. Using the geneloci, alleles and phenotypes as described in question 2, considerthis mating between Mouse 3, black and tall, and mouse 4, black andtall. That mating produced these progeny: 58 black and short, 165black and tall, 25 white and short, 62 white and tall.

____: what is the expectednumber of progeny of the phenotypic class, black and short?Show your work.

____: What is the Chi-squarevalue for these observed and expected data? Show yourwork.

___: How many degrees offreedom are used for the Chi-square test in thissituation?

______: What is theapproximate Chi-square probability for this Chi-square value anddegrees of freedom?

_____: Mouse 3 mated withmice that had the phenotype short & white, and produced 200progeny. How many progeny are expected to have the phenotype, blackand tall?

____: In addition tothe gene loci, alleles and phenotypes described in question 1,consider a third gene locus with alleles D and d; D for long fur,and d for short fur. D is completely dominant to allele d. Thisgene locus segregates independently of the other two loci. Mouse 5,genotype Aa Bb Dd, mates with mouse 6 of the same genotype.What fraction of the progeny are expected to have the phenotype,black fur, tall & long fur?

I don't need the answers to question #2, justquestion #3. (the hilghted) However question 3 asks for informationfrom question 2, so that is why it is there

Thank you

Choose the corrett answer(s) for questiona 11-16 Please Help

Question 11

A P value represents:

Question 12

Who makes the final decision whether an article will bepublished?

Question 13

Which of the following contain original data produced by theauthors? (Select all correct answers)

Question 13

Which of the following contain original data produced by theauthors? (Select all correct answers)

Question 15

What is a limitation(s) of correlative experiments? (Select allcorrect answers)

Question 16

Which of the following is an example of a good hypothesis?(Select all correct answers)