Chi Square SBI3UP

How can you tell if an observed set of offspring counts is legitimately the result of a given underlying simple ratio? For example, you do a cross and see 290 purple flowers and 110 white flowers in the offspring. This is pretty close to a 3/4 : 1/4 ratio, but how do you formally define "pretty close"? What about 250:150? We use a Chi Square test!

Chi Square (X2 ): statistical test to determine “goodness of fit” Why use Chi Square? Compares tallies/counts of categorical data b/t 2+ independent groups (only use actual #’s, do not use %, means, etc.) Compares expected data (hypothesis) to observed data E.g. results of genetic cross with the theoretical distribution Determines whether to accept or reject a null hypothesis

Null hypothesis (H0): hypothesis that a you try to disprove Alternative hypothesis (H1): what you really think is the cause or relationship

Example: H1  plants produce oxygen when provided with water, carbon dioxide and sunlight H0  plants do not produce oxygen when provided with water, carbon dioxide and sunlight A Chi Square test is used to determine the likelihood that the results do not fit the null hypothesis. If 95% or 99% likelihood than the null hypothesis is rejected and alternate is accepted

X2  chi square (X is Greek for Chi) Σ  sum of (Σ is Greek for sigma) o  observed results e  expected results Note: this equation is provided on the AP biology exam.

Match up degrees of freedom with % likelihood To use the table: Match up degrees of freedom with % likelihood Degrees of freedom is one # less than the total number of classes of offspring in a cross E.g. in a monohybrid cross there are 2 classes of offspring based on phenotype, so df is 1 E.g. in a dihybrid cross there are 4 classes of offspring, so df is 3

Be sure to use p = 0.05. If chi-square value > critical value from the table “reject the null hypothesis” If chi-square value < critical value “fail to reject” the null hypothesis Therefore you accept the genetic theory about the expected ratio is correct

Example 1: You flip a coin 50 times Example 1: You flip a coin 50 times. You end up with head 31 times and tails 19 times. Come up with your hypotheses. H0 = there is no significant difference b/t the observed and expected frequencies H1 = there is a significant difference b/t the observed and expected frequencies

Create a table of data that includes your expected and observed data.

c) Apply Chi Squared

Example 2: A certain mutation found in fruit flies is hypothesizes to be autosomal recessive. The experimenter crosses two flies that were heterozygous for the trait. The next generation produced 70 wild-type males, 65 wild-type females, 36 males with mutation, and 40 mutant females. Calculate Chi-squared value for the null hypothesis that the mutation is autosomal recessive.

Example 3: In a certain reptile, eyes can be either black (B) or yellow (b). Two black eyed lizards are cross and the result is 72 black eyed lizards, and 28 yellow eyed lizards. State the H0 and H1 Show Chi-Square calculations State df, and p-values in your conclusions

Practice, Practice, Practice…..