Statistics for AP Biology

Understanding Trends in Data Mean: The average or middle of the data Range: The spread of the data Standard deviation: Variation in the data, how far the data lies from the mean. Standard Error: Is one data set actually different from another based on variation and sample size. We will use this to compare experimental groups.

Assumptions for using Standard Deviation and Standard Error The Data has a normal distribution

Calculating Mean Add all data and divide by sample size Data set: 9, 2, 5, 4.

S = Standard Deviation 1. Work out the Mean 2. Then for each number: subtract the Mean and square the result. 3. Add the squared result and divide by n Take the square root of that and you are done!

Calculate Standard Deviation Data Mean Data - mean(Data – mean) (Total) Ʃ Ʃ ÷ n-1 Square root

Calculate Standard Deviation Data Mean Data - mean(Data – mean) (Total) Ʃ26 Ʃ ÷ n Square root2.94

Standard Error of the Mean Divide the standard deviation by the square root of the sample size 2.94 √ 4 = 1.47

Standard Error shows you how accuracy and sample size matter. Compare two Hypothetical sets of Data: S Sample size SE X Set Set 224 1

Chi Squared Statistical hypothesis test: – X 2 value is a “goodness of fit” test. – This is a test to determine the amounts by which the observed values differ from the predicted or expected outcome

What is the predicted or expected outcome of an experiment? In general the expected outcome is called the null hypothesis (H o ) In the null hypothesis you expect that there is no difference between the control group and the experimental group. No relationship between the manipulated and responding variable. The smaller Chi-squared, the closer your data fits the expected outcome based on H o.

Alternative Hypothesis The alternative hypothesis (Ha) is that there is a difference between the control group and the experimental group Or that there is a relationship between the manipulated and responding variable. Chi squared tests how close the observed data is from the expected based on the null hypothesis. You can only accept your H a if Chi-squared test shows that the H o is false.

Example question Are the genes A and B linked? Null hypotheisis H o : the genes are not linked. Alternative hypothesis (H a ): the genes are linked. Perform a test cross and collect data:

When testing whether two genes are linked what is the expected outcome of the null hypothesis? The null hypothesis is that the genes are not linked. What does this mean? It means that the genes will assort independently because they are on different chromosomes. So what will be the expected values of each phenotype? DO A PUNNETT SQUARE!

Predicting the expected outcome for a test cross AaBb x aabb ab aBAB Ab Null hypothesis prediction based on independent assortment!!!!!! What is the expected ratio of offspring phenotypes?

Compare the observed data to expected outcome AaBb Expected number of offspring Observed number of offspring AabbaaBbaabb

Compare the observed data to expected outcome AaBb Expected number of offspring Observed number of offspring AabbaaBbaabb

Perform the Chi squared test on the null hypothesis AaBb Expected number of offspring Observed number of offspring AabbaaBbaabb ( ) 2 ( ) 2 ( ) 2 ( ) 2 245

Perform the Chi squared test on the null hypothesis AaBb Expected number of offspring Observed number of offspring AabbaaBbaabb ( ) 2 ( ) 2 ( ) 2 ( ) X2=X2= X2=X2= X2=X2=1.22

CHI- SQUARE TABLE Degrees of Freedom p Compare chi squared to the critical number based on your degrees of freedom Degrees of freedom: 4-1= 3 Remember: a Chi-squared value greater than the critical value means you reject the null, less than the critical value and you accept the null X 2 =1.22

Use the chi squared test to determine whether the genes G and F are linked? Null hypothesis: Alternative hypothesis: Expected outcome based on the null hypothesis? Observed outcome of crossing GgFf x ggff GgFf Expected number of offspring Observed number of offspring GgffggFfggff

Use the chi squared test to determine whether the genes G and F are linked? Null hypothesis: Alternative hypothesis: Expected outcome based on the null hypothesis? Observed outcome of crossing GgFf x ggff GgFf Expected number of offspring Observed number of offspring GgffggFfggff