13.ARTIFICIAL SELECTION EXPERIMENT RESULTS HW-2

ARTIFICIAL SELECTION EXPERIMENTS HOMEWORK WORKSHEET (Simply fill in the tables and answer questions 1- 10; 30 pts total). YOU SHOULD HAVE COMPLETED THE FOLLOWING:  Descriptive Statistics (drop-down menu showing Sigma): o (means, standard deviation of the samples, coefficients of variation)  Histogram of progeny population  Selection Differential (S), Selection Response (R), using Breeder’s Eqn  Statistical Analysis (data analysis toolpak): o (are the two sample populations significantly different?) FILL OUT THE TABLE BELOW BY INCLUDING THE INFORMATION DETAILED IN QUESTIONS 1-4 (12 pts): 1. Report the means, standard deviations, and coefficients of variation for the original population, the parent population, and progeny population. 2. Calculate S, the strength of selection or selection differential, which is the absolute value of the mean progeny/offspring population sample minus the mean of the original population sample: I T s – T o I 3. Calculate R, the response to selection, which is the absolute value of the mean of the parent population sample minus the mean of the original population sample: I T p – T o I 4. Calculate how heritable the trait we measured was in our samples, h 2 , which is equal to R/S. (Note that you do not square the value for h.) NOTE: YOUR ANSWERS IN TABLE BELOW WILL BE COUNTED WRONG IF YOU INCLUDE TOO MANY SIGNIFICANT DIGITS! You should only include as many significant digits as your data justify. You don’t want to claim that you had higher accuracy than your data allowed. (That’s like saying you counted an average of 4.5678989468 people, when you are only counting whole people, so your average should be not more than 4.7.) SAMPLE SAMPLE MEAN STANDARD DEVIATION (SD) COEFFICIENT OF VARIATION Original Population Selected Parents Progeny/Offspring Population S R h 2 5. What was our response/dependent variable (2 pts)? 6. Copy and paste below your bar chart with custom error bars for your three sample populations (4 pts). 7. Was each sample population equally variable? In other words, did their coefficients of variation (CV) remain about the same, or were some more or less variable? Explain the pattern you observed with respect to variability. Feel free to include your histograms to illustrate if you wish (not required, but do report and explain CVs (2 pts). 8. Did our plants respond to the artificial selection that we introduced? We can use the Breeder’s Equation to determine the degree to which our progeny/offspring sample changed relative to the original sample: R = h 2 S (2 pts). If R was greater than zero, there was a response.

9. Was our trait heritable? (2 pts) h 2 ranges from 0 to 1 because it is simply the ratio of the response to selection divided by the strength of selection. This ratio essentially gives a measure of how much of the phenotypic character we focused on for change (selection) is actually under genetic control. This value is almost always less than 1! (We may have had an issue with “novice data collection” the first time we counted hairs in the original population compared to “expert data collectors” when we assessed the offspring population for the same character (hairiness). 10. Finally, using the data analysis toolpak in Excel, you conducted a t test to determine whether the sample progeny (offspring) differed significantly from the original population. To report the results of your test, you must include the following information (because it is NEVER sufficient to simply report a p value). Basically, you want to know how big your sample sizes were, how much power you had to detect differences, and whether those differences were statistically significant. Recall also that we decided ahead of time that if there was going to be a change in trichome number, we expected the progeny population to be hairier than the original, therefore are using a one-tailed test (the samples are either the same or the progeny are hairier; we don’t expect them to get less hairy) (6 pts). NOTE: YOUR ANSWERS IN TABLE BELOW WILL BE COUNTED WRONG IF YOU INCLUDE TOO MANY SIGNIFICANT DIGITS! SAMPLE SAMPLE SIZE SAMPLE MEAN +/- SD TEST RESULTS Original Population Selected Parents Progeny Population Degrees of Freedom (df) Calculated t value from data Critical t value from t table (ONE TAILED) p Value 11. Now, to interpret your results, look at the p value that resulted from your output. If that value is > 0.05, your data did not support a significant change in trichome number from the original population to the progeny (offspring) population. If that value is <0.05, then your data support that there was a significant difference between the original plants and the progeny that resulted from our selection experiment. You can think of this as a 95% chance that your data were significantly different, assuming normal bell curves:

 How to present : Pie & bar charts Quantitative (numerical) data – Data expressed in terms of numbers.  Continuous – Whole & fractional numbers (ex: time, height, or weight)  Discrete –Only whole numbers possible (ex: counts)  How to present : Histograms, line-graphs, scatterplots, boxplots, bar charts DESCRIPTIVE STATISTICS: DESCRIBING THE DATA Measures of central tendency – How data cluster around some middle value; 2 most common:  Mean (average) – Sum of all values divided by total number of values in the sample/population. This is the most commonly used measure of center under symmetrical data distributions, but is sensitive to outliers (extreme values relative to rest of sample).  Median – The middle value when the data are ordered sequentially (e.g., lowest to highest). Used when data are skewed (not a bell-shaped curve); the median is resistant to outliers. Measures of variability (spread) – Describes how spread out or dispersed the data are. There are two main measures of spread used in biological inquiry, based on the variance:  Standard deviation – Quantifies the variation or dispersion from the average of a dataset. A low standard deviation indicates that the data tends to be very close to the mean; a high standard deviation indicates that the data points are spread out over a large range of values. This calculation is sensitive to outliers.  Standard error – Quantifies the variation in the means from multiple datasets or a sample distribution of your original dataset.  Variance – Measure of how data points are spread around the mean. Used to calculate standard deviation and error as well. Data distributions – Describes the numbers of times each possible outcome occurs in a sample or population. There are two main shapes:  Bimodal – Two distinct “clumps” of data  Unimodal (symmetric, right skewed, left skewed) – One distinct “clump” of data One hump = unimodal (Dromedary Camel) Two humps = bimodal (Bactrian Camel) Normal distribution (symmetric, unimodal) – “bell-shaped”; data are often assumed to be normally distributed (see graph below).

INFERENTIAL STATISTICS: HYPOTHESIS TESTING Scientific hypothesis: Tentative explanation about a phenomenon or a narrow set of phenomena observed in the natural world. This is the backbone of all scientific inquiry! It is important to have a solid biological hypothesis first; it can then be simplified into a statistical hypothesis (as defined below) that becomes the basis for how the data will be collected, analyzed, and interpreted. Statistical hypotheses: After defining a strong biological hypothesis, statistical hypotheses can be created based on what you predict will be the measured outcome(s) in the dependent variable(s). If a study has multiple measured outcomes there can be multiple statistical hypotheses. Each statistical hypothesis will have two components (Null and Alternative).  Null hypothesis (H O ) – This hypothesis states that there is no relationship (no pattern) between the independent and dependent variables. Example: NO difference in amount of corn harvested from organic vs conventional fertilizer.  Alternative hypothesis (H 1 ) – This hypothesis states that there is a relationship (is a pattern) between the independent and dependent variables. Example: there IS a difference in the quantity of corn harvested from organic vs conventional fertilizer. For both biological and statistical hypotheses there should be two types of variables defined:  Independent (explanatory) variable – The phenomenon or phenomena you think will affect the measure you are interested in. Example: type of fertilizer.  Dependent (response) variable – What you measure in the experiment and what is affected during the experiment. The dependent variable responds to (depends on) the independent variable. Example: corn harvest yield. Statistical analysis and conclusion:

 Z-test (1 or 2 sample proportion)  Analysis of Variance aka ANOVA (One- or Two-way, depending on 1 or 2 independent variables)  Linear regression  Chi-square (Goodness of Fit, Homogeneity of Variances, or Independence of Variables)

Most commonly used statistical packages (software to do the math) in undergraduate statistics:  *Excel  Analysis Toolpak in Data tab (free add in)  Google sheets  XL Miner Analysis ToolPak in Add-ons tab (free add in; not as good yet)  SPSS or StatCrunch (usually rented by semester for a class you are taking)  R (free download to your computer but has steep learning curve) Table 2. How do you know which statistical test to use? Research question: Dependent variable type (#): Independent variable type (# (# groups)): Main calculation: Test to use: Is there a difference between groups? Categorical (1) Categorical (0(-)) X 2 Chi-square Numerical (1) Categorical (1(2)) Mean Proportions Z-test Mean values T-test Categorical (1(3+)) Mean values ANOVA What is the degree of relationship between variables? Numerical (1) Numerical (1(1)) Line equation Linear Regression Table 3. What is important to know about each test? Test: Important Calculations: Goal of analysis: Chi-square Expected values (E), Sample size (# of categories), X2 value Determine if there is a difference between Observed and Expected data Prop Z-test Mean Proportion for each group, Standard deviation for each group, Sample size, Z-value Determine if there is a significant difference (>, <, ≠) between the two groups T-test Mean for each group, Standard deviation for each group, Sample size, T-value ANOVA Mean for each group, Standard deviation for each group, Sample size, F-value Determine if one group is significantly different from the other groups Linear Regression Equation of the line (y-intercept and slope), Determine strength of correlation (relationship) between variables