In AP Biology - Science skill number 5 is titled statistical tests and data analysis. On test day, have your calculator handy and check your equations and formulas sheet.
In AP Biology - Science skill number 5 is titled statistical tests and data analysis. On test day, have your calculator handy and check your equations and formulas sheet. Always make your math have meaning through analysis, biological application and units. This episode recaps probability (1:41), standard deviation (2:38), error bars (3:09) and Chi-Square hypothesis testing (3:38).
The Question of the Day asks (9:30) A normal mother and colorblind father have a boy and a girl. What is the chance their son is colorblind?
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Hi and welcome to the APsolute Recap: Biology Edition. Today’s episode will recap Statistics
Let’s Zoom out:
Yup - I said statistics. And yes, AP Statistics is an entirely separate course. However, in AP Biology - Science skill number 5 is titled statistical tests and data analysis. Here’s what's expected of you: In the multiple choice section, be prepared to complete equations and perform statistical tests to analyze and interpret data. This could be in individual or set-based questions. FRQs are more specific. FRQ 1 and 2 will require you to perform a calculation whereas FRQ 6 will see if you can use data to evaluate a hypothesis or prediction.
Let’s Zoom in:
Broadly speaking this topic could include, means, rates, ratios, percentages, chi square hypothesis testing, and error bars. These equations are on the formula sheet and have common variables identified. They even remind you what degrees of freedom are! Thanks College Board. This basically all but guarantees that most answers required will be application of numbers, not numbers themselves. Let’s review the biggies.
Starting with the Laws of Probability. This is most relevant to Unit 5 with Genetics. The rules of probability can be applied to follow the passing of single gene traits from parents to offspring. If A and B are mutually exclusive, then add their probabilities together. If A and B are independent, then multiply their probabilities. So what is the probability of flipping one coin and it lands on tails twice in a row? 0.5 x 0.5 = 0.25. What is the probability of two heterozygous parents have two offspring that are both homozygous recessive. 0.25 each, multiplied together is 0.0625 or 6.25%. Punnett squares model the probability of alleles recombining during fertilization.
Standard Deviation is a measurement of how spread out data points are. In standard Error of the mean, the standard deviation value is divided by the square root of the sample size (or n). Larger sample sizes are always better for statistical analysis. For the purposes of the AP Exam, students will not be required to perform calculations using the standard deviation or standard error of the mean equation. However, you must understand the underlying concepts and applications. When graphing error bars in AP Biology, they must indicate +/- 2X the SEM. So if my standard error of the mean is 2, then I need to graph my error bars as 4 above and 4 below the average. If two error bars are overlapping, then there is no statistical difference between the variable groups. Essentially, the data is too spread out from the average to say that the groups are distinct.
And now everyone’s favorite, Chi-Square. This statistical test compares your observed experimental data with an expected calculated outcome, determining if differences are just due to chance or another influencing variable. In statistics a “significant” difference means there is less than 5% chance that the variation in the data is due to random events. Therefore, the variation is most likely due to an environmental factor. A common scenario is to be given observed phenotypic traits and where you must figure out the expected through a punnett square. Observed, expected - sounds like chi square. My advice? Set up a table that breaks the equation down into columns. O, E, O-e, o-e squared, then o -e squared over e. This will make it easier to sum all of your trials in the final column. If we are flipping a coin 50 times and keeping track of heads and tails, this table would have two rows for data collection and our expected value would be 25 since it SHOULD land equal amounts on each side, statistically.
Once your value is calculated, compare your value to the Chi-square table of critical values (again this is on the formula sheet). Your degree of freedom is equal to the number of distinct possible outcomes minus one (so if there is an option of heads or tails in a coin flip, then the degree of freedom is 1). You will find the column of your degree of freedom and the p value row of 0.05, or 95% confidence. Chi square values are often used to reject or fail to reject a null hypothesis. If the calculated Chi-Square value is smaller than the critical value, we fail to reject our null hypothesis because our data is consistent with what we would expect—any slight difference is due to chance. If the calculated Chi Square is larger than the critical value, we reject our null hypothesis because our data is too different from what was expected to explain the differences by chance—there must be some other explanation.
Lastly, Hardy-Weinberg Equilibrium. The Hardy-Weinberg equation is a tool biologists use not only to make predictions about a population but also to show whether or not the population is evolving. There are two equations: p + q = 1 and p2 + 2pq +q2 = 1. Lowercase p represents the frequency of allele 1 in a population whereas lowercase q represents the frequency of allele 2. By convention, p is the dominant allele while q is recessive. This means that p squared is the frequency of homozygous dominant, q squared is the frequency of homozygous recessive, and 2pq is the frequency of heterozygous. These frequencies are fractions of a whole population, represented as decimals, which collectively add to equal 1. If you are given only SOME information in the problem, then start with q2, to solve for q and work from there. If you are given ALL of the information in the prompt, then you can typically count the organisms themselves and won’t have to use the equations at all. Populations are in Hardy-Weinberg Equilibrium when they have large population size, random mating, no mutation, no migration and no natural selection. This is almost never the case in nature.
Time for unit connections. Probability and Chi-square lean towards unit 5: Heredity whereas H-W equilibrium is all about natural selection and Unit 7. Error bars can apply to nearly any unit! But technically, all statistical analysis can.
Alright - what about the exam? Complete practice problems and make sure you look at multiple applied scenarios for multiple choice and FRQ. Need more help? Checkout Bozeman Biology and each of his videos on statistics. Great practical examples.
To recap……
Probability can be expressed as a fraction, decimal or percentage. Standard Deviation is a measurement of how spread out data points are. Overlapping Error Bars indicate no statistical significance and Chi-Square hypothesis testing allows us to reject or fail to reject a null hypothesis. Have your calculator handy and check your equations and formulas sheet. Always make your math have meaning through analysis, biological application and units.
Coming up next on the Apsolute RecAP Biology Edition: Listener’s Choice Episode #3!
Today’s question of the day is about probability.
Question of the day: A normal mother and colorblind father have a boy and a girl. What is the chance their son is colorblind?