1. AP Biology Science Skills

2. 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

3. AP BiologyMcClure-Ottmers 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

4. AP BiologyMcClure-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

5. AP BiologyMcClure-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

6. AP BiologyMcClure-Ottmers Characteristics of Science  Conclusions of science are reliable, though tentative  Science is not democratic Science is based on evidence, not votes

7. AP BiologyMcClure-Ottmers Characteristics of science   Science is non-dogmatic Not based on faith or belief systems   Science cannot make moral or aesthetic decisions

8. AP BiologyMcClure-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

9. AP BiologyMcClure-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

10. AP BiologyMcClure-Ottmers What effect does fertilizer have on the growth of bermuda grass in West Texas?   H 0 —If fertilizer was added to the soil where bermuda grass grows, then no extra growth of the grass would be observed.   H a1 —If fertilizer was added to the soils where bermuda grass grows, then the grass would grow at a faster rate than grass without fertilizer.   H a2 —If fertilizer was added to the soils where bermuda grass grows, then the grass would grow at a slower rate than grass without fertilizer.

11. AP BiologyMcClure-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

12. AP BiologyMcClure-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!

13. AP BiologyMcClure-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

14. 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 BiologyMcClure-Ottmers

15. 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 BiologyMcClure-Ottmers

16. Data   Qualitative 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 BiologyMcClure-Ottmers

17. Which graph shows continuous data? Discrete data? Graph A Graph B Adapted from iLoveBiology.net

18. Data   Data collected will usually be Parametric—normal distribution Nonparametric Frequencies AP BiologyMcClure-Ottmers

19. AP BiologyMcClure-Ottmers Statistical Tests and Graph Styles

20. Comparative statistics --compare phenomena, events, or populations --Is A different from B? Parametric Data (normal data) Nonparametric Data Frequency Data (counts) Bar Graph Box-and-Whisker Plot Bar Graph or Pie Chart Adapted from iLoveBiology.net

21. Association statistics --look for associations between variables --How are A and B correlated? Parametric Data and Nonparametric Data Scatterplot Adapted from iLoveBiology.net

22. 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 BiologyMcClure-Ottmers

23. Bar Graphs   Use to Visually compare categorical or count data Visually compare calculated means with error bars for normal data AP BiologyMcClure-Ottmers

24. 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 BiologyMcClure-Ottmers

25. Bar Graphs   Standard error bars provide more information about how different two means may be from each other (sample standard error) AP BiologyMcClure-Ottmers

26. AP BiologyMcClure-Ottmers

27. 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 BiologyMcClure-Ottmers

28. AP BiologyMcClure-Ottmers

29. AP BiologyMcClure-Ottmers r = correlation coefficient Range -1 to +1 Increased relationship with values closer to 1

30. AP BiologyMcClure-Ottmers

31. 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

32. 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 BiologyMcClure-Ottmers

33. Histograms AP BiologyMcClure-Ottmers

34. AP BiologyMcClure-Ottmers

35. Line Graphs   Used when data on both axes are continuous   Dots indicate measurements that were actually made AP BiologyMcClure-Ottmers

36. Using Graphs   Estimation—Interpolation/Extrapolation   Calculating Rate--Use slope AP BiologyMcClure-Ottmers m =  y y 2 – y 1  x x 2 – x 1 Slope = Rise Run

37. Positive Slope Negative Slope Zero Slope Rate Increasing Rate Decreasing Constant Rate Indicates some values were skipped Adapted from iLoveBiology.net

38. 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 BiologyMcClure-Ottmers

39. 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 BiologyMcClure-Ottmers

40. 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 BiologyMcClure-Ottmers

41. 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 BiologyMcClure-Ottmers

42.   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   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 Population vs. Sample Adapted from iLoveBiology.net

43. If sample is not collected randomly, it may not closely reflect original population. This is called sampling bias. Adapted from iLoveBiology.net

44. 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 BiologyMcClure-Ottmers

46. 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 BiologyMcClure-Ottmers

47. Measuring Spread in Data   Variance (s 2 ) and standard deviation (s) measure how far a data set is spread out.   variance of zero--all values in data set are identical AP BiologyMcClure-Ottmers Variance Distance from the mean

48. 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 BiologyMcClure-Ottmers

49. Standard Deviation   AP BiologyMcClure-Ottmers

50. AP BiologyMcClure-Ottmers Smaller Standard deviation shows values clustered tightly around mean Larger Standard deviation shows values spread out widely from mean

51. 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 BiologyMcClure-Ottmers

52. 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 BiologyMcClure-Ottmers

53. 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 Total168 AP BiologyMcClure-Ottmers

54. 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 Total168 AP BiologyMcClure-Ottmers

55. Standard Deviation   mean & standard deviation help estimate characteristics of population from a single sample AP BiologyMcClure-Ottmers

56. Inferential Statistics--SE   AP BiologyMcClure-Ottmers

57. Reliability of the Mean   AP BiologyMcClure-Ottmers

58. Reliability of the Mean   AP BiologyMcClure-Ottmers

59. AP BiologyMcClure-Ottmers

60. AP BiologyMcClure-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

61. 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 BiologyMcClure-Ottmers

62. 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 BiologyMcClure-Ottmers

63. AP BiologyMcClure-Ottmers

64. Example—English Ivy Leaves   Do shady English ivy leaves have a larger surface area than sunny English ivy leaves?   Propose Hypotheses   H 0 = 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.   H 1 = 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 BiologyMcClure-Ottmers

65. 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 BiologyMcClure-Ottmers

66. Example   Just looking at this data in this form does not answer question AP BiologyMcClure-Ottmers

67. 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 BiologyMcClure-Ottmers

68. AP BiologyMcClure-Ottmers Normally distributed? Close enough!

69. Example   Since Data are Parametric Calculate Descriptive Statistics Mean Standard deviation Calculate Inferential Statistic Standard Error AP BiologyMcClure-Ottmers

70. Example AP BiologyMcClure-Ottmers

71. Example   Produce bar graph to compare means including error bars of ±1 SE AP BiologyMcClure-Ottmers 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

72. 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 BiologyMcClure-Ottmers

73. 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 BiologyMcClure-Ottmers

74. AP BiologyMcClure-Ottmers

75. 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 BiologyMcClure-Ottmers

76. 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? AP BiologyMcClure-Ottmers X 2 = (o – e) 2 Ʃ e

77. AP BiologyMcClure-Ottmers

78. 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.5m 2 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 BiologyMcClure-Ottmers

79. Distance from low tide # of periwinkles observed At low tide line35 2 m above low tide24 2 m above low tide10 3 m above low tide3 4 m above low tide2 Total75 AP BiologyMcClure-Ottmers 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

80. Categoryoeo-e(o-e) 2 (o-e) 2 /e Low tide35 1m above34 2 m above10 3 m above3 4 m above2 AP BiologyMcClure-Ottmers

81. Categoryoeo-e(o-e) 2 (o-e) 2 /e Low tide35 21 1m above34 21 2 m above10 21 3 m above3 21 4 m above2 21 AP BiologyMcClure-Ottmers

82. Categoryoeo-e(o-e) 2 (o-e) 2 /e Low tide35 2114 1m above34 2113 2 m above10 21-11 3 m above3 21-18 4 m above2 21-19 AP BiologyMcClure-Ottmers

83. Categoryoeo-e(o-e) 2 (o-e) 2 /e Low tide35 2114210 1m above34 2113169 2 m above10 21-11121 3 m above3 21-18324 4 m above2 21-19361 22 AP BiologyMcClure-Ottmers

84. Categoryoeo-e(o-e) 2 (o-e) 2 /e Low tide35 211421010.00 1m above34 21131698.05 2 m above10 21-111215.76 3 m above3 21-1832415.43 4 m above2 21-1936117.19 22 56.43 AP BiologyMcClure-Ottmers

85.   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 BiologyMcClure-Ottmers

86.   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 BiologyMcClure-Ottmers

87.   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 BiologyMcClure-Ottmers

88.   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 BiologyMcClure-Ottmers