# Chi Square Analysis - MS. RAGO'S CLASS WEBSITE Chi-Square Analysis AP Biology UNIT 7: MENDELIAN GENETICS CHI SQUARE ANALYSIS AP BIOLOGY CHI SQUARE ANALYSIS: The chi square analysis allows you to use statistics to determine if your data is good or non-biased or if the data is bad or biased If statistics show the data is biased this means that somehow the data is far different from what you expected and something is causing the difference beyond just normal chance occurrences. In the Fly Lab we are using laws of probability to determine possible outcomes for genetic crosses. How will we know if our fruit fly data is good? YOU WILL PERFORM A CHI SQUARE ANALYSIS! CHI SQUARE FORMULA: NULL HYPOTHESIS:

The hypothesis is termed the null hypothesis which states In That there is NO substantial statistical deviation (difference) between observed values and the expected values. other words, the results or differences that do exist between observed and expected are totally random and occurred by chance alone. CHI SQUARE VALUE: If the null hypothesis is supported by analysis The assumption is that mating is random and normal gene segregation and independent assortment occurred. Note: this is the assumption in all genetic crosses! This is normal meiosis occurring and we would expect random segregation and independent assortment.

If the null hypothesis is not supported by analysis The deviation (difference) between what was observed and what the expected values were is very far apartsomething non-random must be occurring. Possible explanations: Genes are not randomly segregating because they are sex-linked or linked on the same chromosome and inherited together. DF VALUE: In order to determine the probability using a chi square chart you need to determine the degrees of freedom (DF) DEGREES OF FREEDOM: is the number of phenotypic possibilities in your cross minus one. DF = # of groups (phenotype classes) 1 Using the DF value, determine the probability or distribution using the Chi Square table If the level of significance read from the table is greater than 0.05 or 5% then the null

hypothesis is accepted and the results are due to chance alone and are unbiased. EXAMPLE: DIHYBRID FRUIT FLY CROSS x Black body eyeless Wild type F1: all wild type F1 CROSS PRODUCED THE FOLLOWING OFFSPRING 5610 1881 Wild type Normal body eyeless 1896 622 Black body eyeless Black body ANALYSIS OF THE RESULTS: Once the total number of offspring in each

class is counted, you have to determine the expected value for this dihybrid cross. What are the expected outcomes of this typical dihybrid cross? (9:3:3:1) 9/16 3/16 3/16 1/16 should should should should be be be be wild type normal body eyeless black body wild eyes black body eyeless. NOW CONDUCT THE ANALYSIS: Phenotype Observed

Wild 5610 Eyeless 1881 Black body 1896 Eyeless, black body 622 Total 10009 Hypothesis To compute the expected value multiply the expected 9/16:3/16:3/16:1/16 ratios by 10,009 CALCULATING EXPECTED VALUES: To calculate the expected value: Multiply the total number of offspring times the expected fraction for each phenotype class TOTAL = 10,009

Wild-type expected value: 9/16 x 10,009 = 5634 Eyeless expected value: 3/16 x 10,009 = 1878 Black body expected value: 3/16 x 10,009 = 1878 Black body & Eyeless expected value: 1/16 x 10,009 = 626 NOW CONDUCT THE ANALYSIS: Phenotype Observed Hypothesis Wild 5610 5634 Eyeless 1881 1878 Black body 1896 1878

Eyeless, black body 622 626 Total 10009 Null hypothesis: The two traits (black body and eyeless) are not linked and therefore randomly segregate & assort independently of each other during gamete formation. The differences between the expected values and observed values are due to chance alone. CALCULATING X2: Using the chi square formula compute the chi square total for this cross: (5610 - 5630)2 / 5630 = 0.07 (1881 - 1877)2 / 1877 = 0.01 (1896 - 1877)2 / 877 = 0.20 (622 - 626)2 / 626 = 0.02 x2 = 0.30 How

many degrees of freedom? 4 phenotype classes 1 = 3 degrees of freedom CHI SQUARE TABLE: REJECT HYPOTHESIS ACCEPT NULL HYPOTHESIS RESULTS ARE NOT RANDOM RESULTS ARE RANDOM Probability (p) Degrees of Freedom 0.95 0.90 0.80 0.70 0.50 0.30 0.20

0.10 0.05 0.01 0.001 1 0.004 0.02 0.06 0.15 0.46 1.07 1.64 2.71 3.84 6.64 10.83 2

0.10 0.21 0.45 0.71 1.39 2.41 3.22 4.60 5.99 9.21 13.82 3 0.35 0.58 1.01 1.42 2.37

3.66 4.64 6.25 7.82 11.34 16.27 4 0.71 1.06 1.65 2.20 3.36 4.88 5.99 7.78 9.49 13.38

18.47 5 1.14 1.61 2.34 3.00 4.35 6.06 7.29 9.24 11.07 15.09 20.52 6 1.63 2.20 3.07

3.83 5.35 7.23 8.56 10.64 12.59 16.81 22.46 7 2.17 2.83 3.82 4.67 6.35 8.38 9.80 12.02

14.07 18.48 24.32 8 2.73 3.49 4.59 5.53 7.34 9.52 11.03 13.36 15.51 20.09 26.12 9 3.32

4.17 5.38 6.39 8.34 10.66 12.24 14.68 16.92 21.67 27.88 10 3.94 4.86 6.18 7.27 9.34 11.78

13.44 15.99 18.31 23.21 29.59 ANALYSIS QUESTIONS: Looking this statistic up on the chi square distribution table tells us the following: The P value read off the table places our chi square number of 0.30 with 3 degrees of freedom closer to 0.95 or 95% This means that greater than 95% of the time when our observed data is this close to our expected data, the deviation from expected value is due to random chance and not something else! We therefore accept our null hypothesis. ANALYSIS QUESTIONS: What is the critical value at which we would reject the null hypothesis?

For three degrees of freedom this value for our chi square is > 7.815 What if our chi square value was 8.0 with 4 degrees of freedom, do we accept or reject the null hypothesis? Accept, since the critical value is >9.48 with 4 degrees of freedom. HOW TO WRITE YOUR RESULTS: When reporting chi square data use the following formula sentence. With _____ degrees of freedom, my chi square value is _____, which gives me a p value between _____% and _____%, I therefore _____ (accept/reject) my null hypothesis. Use this sentence for your results section of your lab write-up. Your explanation of what the significance of this data means goes in your conclusion.