1. Chi Square Pg 302

2. Why Chi - Squared ▪Biologists and other scientists use relationships they have discovered in the lab to predict events that might happen under more real-life circumstances. ▪These predictions are, at some point, supported by real data. – More often than not, these 2 sets of data, do not always match exactly. ▪The change in the data, or fluctuations, between lab data and real life data are due to a large variety of variables that can’t be accounted for in the lab, or something else that a scientists may have missed. ▪How do we know?? – The most common test used is called the Chi-Squared.

3. Are two genes linked or unlinked? ▪As we have talked about, not all patterns of inheritance follow Mendel’s law of independent assortment. ▪Genes that are found in close proximity on the same chromosome tend to be inherited together, which makes them linked genes. ▪But how do we tell? – You guessed it Chi-Squared!!!

4. How it’s done. ▪If genes are unlinked and assorting independently, then you would expect a phenotypic ratio of 1:1:1:1. ▪If the genes are linked, however this ratio will be more like 1:1:0: 0, where you would expect the offspring to look like either parent. – This means that the gens are NOT assorting independently. ▪The Chi-Square will measure the “goodness of fit”, by comparing observed data to the expected. ▪It should also be noted that the size of the experimental set is important. With small data sets, even if the genes are linked, discrepancies might be small by chance, if the linkage is weak. – *For simplicity we ignore the sample size.

5. The formula

6. Model 1- Calculating Chi-Squared (Let’s Try one) Hypothesis- there is an equal chance of flipping heads or tails on a coin. Coin A Observed Data (o) Expected (e) (o-e)(o-e)^2 Heads108100 Tails92100 Total200

7. Hypothesis- there is an equal chance of flipping heads or tails on a coin. Coin B Observed Data (o) Expected (e) (o-e)(o-e)^2 Heads120100 Tails80100 Total200

8. Now let’s answer a couple questions… ▪1. What is the hypothesis that is being tested in Model 1? ▪2. Describe the experiment being performed in Model 1. ▪3. How many flips of the coin will be conducted in each trail for the experiment in Model 1? ▪4. If you were told that one of the coins used in the experiments in Model 1 was a “trick” coin, which coin would you predict was rigged? Explain your reasoning. ▪Choose the correct phrase to complete the sentence is: – A larger chi-square value means the observed data is very different/ very similar to the expected data.

9. The experiments in model one didn’t give us an expected out come…. Why? ▪Was it due to random chance? ▪Or does the coin being flipped favor head for some reason? ▪Using our Chi-Square data, and knowing that in statistics a “significant” difference means there is less than 5% chance that the variation in that data is due to random events. – So! The variation would mostly likely be due to an environmental factor.

10. Degrees of Freedom ▪To determine if the chi-square value is large enough to be “significant” we used degrees of freedom. ▪If an experiment has five possible outcomes, then in reality there is one result and 4 other possibilities(total of five). ▪Degrees of freedom = number of possible outcomes - 1

11. Degrees of freedom ▪How many outcomes were possible in the coin flip experiments? ▪How many degrees of freedom were there in the coin flip experiment?

12. Applying it to genetics! ▪If 100 heterozygous (Bb) males mate with 100 heterozygous females (Bb). – Predict the number of offspring from the 100 mating pairs that will be each genotype. ▪BB ▪Bb ▪bb

13. Observed vs. Expected Observed (o) Expected (e) (o-e)(o-e)^2 BB28 Bb56 bb16 The sum of:

14. Back to degree’s of freedom ▪How many genotype outcomes were possible? ▪How many degrees of freedom are there?

15. What do we do with all this information??? Use a Chi-Squared Distribution Table! Converts Chi-Square values to probability that the differences in the data are due to chance. Reject hypothesis Accept hypothesis

16. So… back to our problem ▪We had a X 2 value of 4.32 ▪With 2 degrees of freedom ▪Where does that fall on our table? ▪Significant or Not Significant? ▪We have a P value that is 0.2 < p value < 0.1 – NOT SIGNIFICATNT! ▪ But what does that mean???? – It means there is a 20% to 10% change that variability in the data is only due to change. This is not significant.

17. Now, turn to page 302 in your book… ▪Work out that problem for homework.