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Science Skills AP Biology Science has principles Science seeks to explain the natural world and its explanations are tested using evidence from the natural world Science assumes we can learn about the natural world by gathering evidence AP Biology Science is a process Scientific ideas are developed through reasoning Scientific claims are examined using collected evidence Scientific claims are subject to peer review and replication AP Biology McClure-Ottmers Science is a process No such thing as “The Scientific Method” involves continuous observations, questions, multiple hypotheses and more observations Science seldom concludes & never proves AP Biology McClure-Ottmers Science is a process--Theories Central to scientific thinking Overarching explanations that make sense of some aspect of nature Based on evidence Allow scientists to make valid predictions Tested in many ways Supported, modified or replaced as new evidence appears Give scientists frameworks within which to work Big ideas within which scientists test specific hypotheses AP Biology McClure-Ottmers Characteristics of Science Conclusions of science are reliable, though tentative Science is not democratic Science is based on evidence, not votes AP Biology McClure-Ottmers Characteristics of science Science is non-dogmatic Not based on faith or belief systems Science cannot make moral or aesthetic decisions AP Biology McClure-Ottmers Developing Hypotheses Proposed explanations Tentatively explains something observed Must be testable and falsifiable Can be supported through evidence, but not proven Proposed as statements, not questions AP Biology McClure-Ottmers Types of Hypotheses Null Hypothesis States that there is no relationship between 2 variables; findings probably occurred due to chance events Alternative hypothesis States that there is a relationship between 2 variables; findings probably did NOT occur due to chance events Scientists often state both types of hypotheses in order to analyze results statistically AP Biology McClure-Ottmers What effect does fertilizer have on the growth of bermuda grass in West Texas? H0—If fertilizer was added to the soil where bermuda grass grows, then no extra growth of the grass would be observed. Ha1—If fertilizer was added to the soils where bermuda grass grows, then the grass would grow at a faster rate than grass without fertilizer. Ha2—If fertilizer was added to the soils where bermuda grass grows, then the grass would grow at a slower rate than grass without fertilizer. AP Biology McClure-Ottmers Experimental Design 1. Determine variables Dependent Variable measured in an experiment Independent Variable changed in an experiment Controlled/constant Variables that are held constant in an experiment AP Biology McClure-Ottmers Experimental Design 2. Designing a procedure Level of treatment Value set for the independent variable Replicates Experiments cannot be valid if conclusions are only based on one or two individuals Procedures usually repeated several times with several individuals Control group Independent variable is either held constant or omitted Different from controlled variables! AP Biology McClure-Ottmers Experimental Design 3. Making Predictions Based on the experiment written in the form of if/then statements Built into a working hypothesis! “If the hypothesis is true, then the results of the experiment will be…” Provides critical analysis of experimental design Used to evaluate results of experiment AP Biology McClure-Ottmers Collecting Data What kind of data is needed to answer question asked? Categories of Questions in Biology: compare phenomena, events or populations Is A different than B look for association between variables How are A and B correlated? AP Biology McClure-Ottmers Collecting Data Decide how data should be collected so that question can be answered—do this BEFORE running experiment! English statistician R.A. Fisher once said, “To consult the statistician after an experiment is finished is often merely to ask him to conduct a post mortem examination. He can perhaps say what the experiment died of.” AP Biology McClure-Ottmers Qualitative Data Not numerical Usually subjective Quantitative Numerical Lends itself to statistical analysis Two types Discrete Finite values Integers or Bucket categories such as “red” or “tall” Continuous Infinite number of values Forms a continuum AP Biology McClure-Ottmers Which graph shows continuous data? Discrete data? Graph A Graph B Adapted from iLoveBiology.net Data Data collected will usually be Parametric—normal distribution Nonparametric Frequencies AP Biology McClure-Ottmers Statistical Tests and Graph Styles AP Biology McClure-Ottmers Comparative statistics --compare phenomena, events, or populations --Is A different from B? Bar Graph Parametric Data (normal data) Box-and-Whisker Plot Nonparametric Data Bar Graph or Pie Chart Frequency Data (counts) Adapted from iLoveBiology.net Association statistics --look for associations between variables --How are A and B correlated? Scatterplot Parametric Data and Nonparametric Data Adapted from iLoveBiology.net Elements of Effective Graphs Informative Title Easily identifiable lines/bars Axes clearly labeled with units X—independent variable Y—dependent Uniform intervals Clarify whether data starts at origin (0,0) Line should not extend to origin if data does not start there Line should not extend past last point Include standard error bars when appropriate AP Biology McClure-Ottmers Bar Graphs Use to Visually compare categorical or count data Visually compare calculated means with error bars for normal data AP Biology McClure-Ottmers Bar Graphs Examples of questions where bar graphs might be produced Are the spines on fish in one lake without predators shorter than the spines on fish in another lake with predators? Are the leaves of ivy grown in the sun different from the leaves of ivy grown in the shade? AP Biology McClure-Ottmers Bar Graphs Standard error bars provide more information about how different two means may be from each other (sample standard error) AP Biology McClure-Ottmers AP Biology McClure-Ottmers Scatterplots Use when comparing one measured variable against another Can calculate linear regression line if relationship is thought to be linear use to help determine statistical correlation between x and y variables infer possibility of causal mechanisms AP Biology McClure-Ottmers AP Biology McClure-Ottmers r = correlation coefficient Range -1 to +1 Increased relationship with values closer to 1 AP Biology McClure-Ottmers AP Biology McClure-Ottmers Box and Whisker Plots Allow graphical comparison of two samples of nonparametric data appropriate descriptive statistics to use with graph are median and quartile values AP Biology Histograms Frequency diagrams Use when an investigation involves measurement data Used to display distribution of data Provides representation of central tendencies and spread of data Use to determine whether data is parametric or nonparametric Must set up Bins Uniform range intervals that cover entire range of data Range of units AP Biology McClure-Ottmers Histograms AP Biology McClure-Ottmers AP Biology McClure-Ottmers Line Graphs Used when data on both axes are continuous Dots indicate measurements that were actually made AP Biology McClure-Ottmers Using Graphs Estimation—Interpolation/Extrapolation Calculating Rate--Use slope m= y y2 – y1 x x 2 – x1 Rise Slope = Run AP Biology McClure-Ottmers Positive Slope Rate Increasing Negative Slope Rate Decreasing Zero Slope Constant Rate Indicates some values were skipped Adapted from iLoveBiology.net Why bother with data analysis? Appropriate techniques allow generation of measures of confidence that lead to greater precision Allows you to make claims with confidence Allows you to decide whether results you observe are due to chance or some real difference AP Biology McClure-Ottmers Descriptive Statistics Used to estimate important parameters of sample data set Allows us to estimate how well sample data represent true population Allows data to be summarized Can show variation, standard error, and confidence that sufficient data have been collected AP Biology McClure-Ottmers Descriptive Statistics Examples Sample standard deviation Describes variability in data Measurements of central tendencies Mean, median, mode, range Sample standard error of sample mean Confidence Intervals Helps determine confidence in sample mean AP Biology McClure-Ottmers Inferential Statistics Includes tools and methods that rely on probability theory and distributions to determine precise estimates of true population parameters from sample data AP Biology McClure-Ottmers Population vs. Sample Often, researchers want to investigate a population (N) may not be feasible to collect data for every member of entire population sample (n) smaller group of members of a population selected to represent population. must be random Adapted from iLoveBiology.net If sample is not collected randomly, it may not closely reflect original population. This is called sampling bias. Adapted from iLoveBiology.net Data Analysis Investigations involving measurement data Construct histogram Determine whether data has normal distribution Could you have a sample distribution that doesn’t “look” parametric but does represent a normally distributed population of measurements? Small sample size Measurement error Sampling error—random or nonrandom? AP Biology McClure-Ottmers Descriptive Statistics Allows data to be summarized/Highlights trends or patterns in data Sample Mean Average of all data entries Measure of central tendency for normally distributed data Population Mean-- µ Average of all data from all members of a population Median Middle value Good measure of central tendency for skewed distributions Mode Most common value Suitable for bimodal distributions and qualitative data Range Difference between smallest and largest value Crude indication of data spread AP Biology McClure-Ottmers Measuring Spread in Data Variance (s2) and standard deviation (s) measure how far a data set is spread out. variance of zero--all values in data set are identical Variance AP Biology Distance from the mean McClure-Ottmers Measuring Spread of Data Differences from mean are squared to calculate variance So…units of variance are not same as units in original data set Standard deviation=square root of variance Expressed in same units as original data set So….more useful than variance! AP Biology McClure-Ottmers Standard Deviation AP Biology McClure-Ottmers Smaller Standard deviation shows values clustered tightly around mean Larger Standard deviation shows values spread out widely from mean AP Biology McClure-Ottmers Standard Deviation Data: 2, 5, 9, 12, 15, 17 1. Calculate mean: 60/6 = 10 2. Find difference between each term and mean x 2 5 9 12 15 17 AP Biology McClure-Ottmers Standard Deviation Data: 2, 5, 9, 12, 15, 17 1. Calculate mean: 60/6 = 10 2. Find difference between each term and mean x 2 (2-10) (2-10)2 64 5 9 12 15 17 AP Biology McClure-Ottmers Standard Deviation Data: 2, 5, 9, 12, 15, 17 1. Calculate mean: 60/6 = 10 2. Find difference between each term and mean x 2 (2-10) (2-10)2 64 5 (5-10) (5-10)2 25 9 (9-10) (9-10)2 1 12 (12-10) (12-10)2 4 15 (15-10) (15-10)2 25 17 (17-10) (17-10)2 49 Total 168 AP Biology McClure-Ottmers Standard Deviation x 2 (2-10) (2-10)2 64 5 (5-10) (5-10)2 25 9 (9-10) (9-10)2 1 12 (12-10) (12-10)2 4 15 (15-10) (15-10)2 25 17 (17-10) (17-10)2 49 Total 168 AP Biology McClure-Ottmers Standard Deviation mean & standard deviation help estimate characteristics of population from a single sample AP Biology McClure-Ottmers Inferential Statistics--SE AP Biology McClure-Ottmers Reliability of the Mean AP Biology McClure-Ottmers Reliability of the Mean AP Biology McClure-Ottmers AP Biology McClure-Ottmers Interpreting & Communicating Results Study data to decide whether hypothesis is supported or falsified Present conclusions in a scientific paper Peer reviewed Published in scientific journal Ideas, procedures, results, analyses and conclusions critically scrutinized by other scientists AP Biology McClure-Ottmers Hypothesis Testing Hypothesis testing does not allow proof or acceptance of the alternative to the null hypothesis! Testing allows us to find support for the alternative hypothesis by rejecting the null hypothesis. AP Biology McClure-Ottmers Hypothesis Testing Formal process to determine whether to reject null hypothesis 1. state hypotheses—null and alternative should be mutually exclusive 2. Determine which test statistic to use 3. Analyze sample data and find value of test statistic 4. Interpret results—if value is unlikely based on null hypothesis then reject AP Biology McClure-Ottmers AP Biology McClure-Ottmers Example—English Ivy Leaves Do shady English ivy leaves have a larger surface area than sunny English ivy leaves? Propose Hypotheses H0 = The true population mean width of ivy leaves grown in the shade is the same as the true population mean width of ivy leaves grown in the sun. H1 = The true population mean width of ivy leaves grown in the shade is larger than the true population mean width of ivy leaves grown in the sun. AP Biology McClure-Ottmers Example—English Ivy Leaves Sampling Choose smaller samples instead of entire population Why? How? Random and unbiased Collected and measured max width in cm of 30 leaves from each habitat AP Biology McClure-Ottmers Example Just looking at this data in this form does not answer question AP Biology McClure-Ottmers Example Data Analysis determine confidence in data collected Is difference between two groups real or due to some chance event? Data measurements Units are cm continuous measurement data not counts or categories What is first step? Construct histogram to check for normal distribution! AP Biology McClure-Ottmers Normally distributed? Close enough! AP Biology McClure-Ottmers Example Since Data are Parametric Calculate Descriptive Statistics Mean Standard deviation Calculate Inferential Statistic Standard Error AP Biology McClure-Ottmers Example AP Biology McClure-Ottmers Example Produce bar graph to compare means including error bars of ±1 SE Do SE bars overlap? Would SE bars overlap if ±2 SE were graphed? What does SE suggest about two populations? Use SE statistic as inference to describe confidence that means of samples represent true population means AP Biology McClure-Ottmers Example SE Bars indicate there is a statistically significant difference between two populations More rigorous statistical test will need to be performed to confirm that two populations are different from one another AP Biology McClure-Ottmers Example Most biological studies establish a critical value of the probability of whether results occur by chance alone When observations deviate from the predictions, how much variation should be tolerated before rejecting null hypothesis? In biological investigations, a 5% critical value is often used as a decision point for rejecting null hypothesis. Could set more stringent critical value (1% or 0.1%) In life-and-death issues often associated with medical studies AP Biology McClure-Ottmers AP Biology McClure-Ottmers Example For two leaf populations p=0.016% less than 5% critical value reject null hypothesis that there is no difference between means of two populations provides support for alternative hypothesis leaves in shady areas are larger than leaves found in the sun in English ivy plants Only provides support for alternative hypothesis— doesn’t cause you to accept it! Additional studies chlorophyll amounts, leaf area, stomata densities, or light response curves. AP Biology McClure-Ottmers More Hypothesis Testing —Chi Square Test Use with frequency counts Test to see if data supports null hypothesis No difference between observed and expected values Any difference is due to chance Compare observed and expected values Is variance from expected values due to random chance? Is there another factor influencing data? X AP Biology Ʃ 2 = (o – e)2 e McClure-Ottmers AP Biology McClure-Ottmers Chi-Square Example An ecologist is studying habitat preferences of periwinkles on the rocky coast line of the New England Coast. She hypothesizes that more periwinkles will be found closer to the tide line. To test her hypothesis, she collects data by counting the number of periwinkles within a .5m2 quadrat sample that she observes on a rocky coast line location at low tide. Determine if the difference in number of periwinkles observed in each location is statistically significant. AP Biology McClure-Ottmers Distance from low tide # of periwinkles observed At low tide line 35 2 m above low tide 24 2 m above low tide 10 3 m above low tide 3 4 m above low tide 2 Total 75 Null Hypothesis: There is no difference in the number of Periwinkles observed at each of the water levels. If Null Hypothesis is accepted then there is no difference in the distribution of periwinkles on the shoreline AP Biology McClure-Ottmers AP Biology Category o Low tide 35 1m above 34 2 m above 10 3 m above 3 4 m above 2 e o-e (o-e)2 (o-e)2/e McClure-Ottmers AP Biology Category o e Low tide 35 21 1m above 34 21 2 m above 10 21 3 m above 3 21 4 m above 2 21 o-e (o-e)2 (o-e)2/e McClure-Ottmers AP Biology Category o e o-e Low tide 35 21 14 1m above 34 21 13 2 m above 10 21 -11 3 m above 3 21 -18 4 m above 2 21 -19 (o-e)2 (o-e)2/e McClure-Ottmers Category o e o-e (o-e)2 Low tide 35 21 14 210 1m above 34 21 13 169 2 m above 10 21 -11 121 3 m above 3 21 -18 324 4 m above 2 21 -19 361 (o-e)2/e 2 AP Biology McClure-Ottmers Category o e o-e (o-e)2 (o-e)2/e Low tide 35 21 14 210 10.00 1m above 34 21 13 169 8.05 2 m above 10 21 -11 121 5.76 3 m above 3 21 -18 324 15.43 4 m above 2 21 -19 361 17.19 2 56.43 AP Biology McClure-Ottmers p-value is predetermined choice of how certain we are. Smaller p-values--more confidence we can claim. p = 0.05 means that we can claim 95% confidence. AP Biology McClure-Ottmers Compare chi-square value to table of values according to the number of degrees of freedom df = number of categories – 1 df = 5-1=4 AP Biology McClure-Ottmers If X 2 value is less than critical value, accept null hypothesis. difference is not statistically significant If X 2 value is greater than or equal to critical value, reject null hypothesis. difference is statistically significant AP Biology McClure-Ottmers Reject the null hypothesis. There is a statistically significant distribution of periwinkles. Variance between observed and expected results would occur from random chance alone only about 5% of the time 95% of the time variance would be due to something other than chance AP Biology McClure-Ottmers