ap biology science skills. ap biology science has principles science seeks to explain the natural...
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AP Biology
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
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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
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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
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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
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Characteristics of Science Conclusions of science are reliable,
though tentative Science is not democratic
Science is based on evidence, not votes
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Characteristics of science Science is non-dogmatic
Not based on faith or belief systems
Science cannot make moral or aesthetic decisions
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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
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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
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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.
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Experimental Design
1. Determine variablesDependent
Variable measured in an experiment
IndependentVariable changed in an experiment
Controlled/constantVariables that are held constant in an experiment
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Experimental Design
2. Designing a procedureLevel of treatment
Value set for the independent variable
ReplicatesExperiments cannot be valid if conclusions are only based on one or two individualsProcedures usually repeated several times with several individuals
Control groupIndependent variable is either held constant or omitted Different from controlled variables!
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Experimental Design
3. Making PredictionsBased 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
Collecting Data What kind of data is needed to answer
question asked? Categories of Questions in Biology:
compare phenomena, events or populationsIs A different than B
look for association between variablesHow are A and B correlated?
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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.”
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Data Qualitative
Not numerical
Usually subjective
QuantitativeNumerical
Lends itself to statistical analysis
Two typesDiscrete
Finite values
Integers or Bucket categories such as “red” or “tall”
ContinuousInfinite number of values
Forms a continuum
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Which graph shows continuous data? Discrete data?
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
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AP Biology McClure-Ottmers
Statistical Tests and Graph StylesStatistical Tests and Graph Styles
Comparative statistics --compare phenomena, events, or
populations --Is A different from B?
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 Graphor
Pie Chart
Adapted from iLoveBiology.net
Association statistics --look for associations between
variables --How are A and B correlated?
Association statistics --look for associations between
variables --How are A and B correlated?
Parametric Dataand
Nonparametric Data
Scatterplot
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
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Bar Graphs Use to
Visually compare categorical or count data
Visually compare calculated means with error bars for normal data
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Bar Graphs Examples of questions where bar graphs
might be producedAre 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?
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Bar Graphs Standard error bars provide more information
about how different two means may be from each other (sample standard error)
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AP Biology McClure-Ottmers
Scatterplots Use when comparing one measured
variable against another Can calculate linear regression line if
relationship is thought to be linearuse to help determine statistical correlation between x and y variables
infer possibility of causal mechanisms
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r = correlation coefficientRange -1 to +1Increased relationship with values closer to 1
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Box and Whisker Plots Allow graphical comparison of two
samples of nonparametric dataappropriate descriptive statistics to use with graph are median and quartile values
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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
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Histograms
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AP Biology McClure-Ottmers
Line Graphs Used when data
on both axes are continuous
Dots indicate measurements that were actually made
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Using Graphs Estimation—Interpolation/Extrapolation Calculating Rate--Use slope
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m =y y2 – y1
x x2 – x1
Slope = RiseRun
Positive Slope
Positive Slope
Negative Slope
Negative Slope Zero SlopeZero Slope
Rate Increasing
Rate Decreasing
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
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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
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Descriptive Statistics Examples
Sample standard deviationDescribes variability in data
Measurements of central tendenciesMean, median, mode, range
Sample standard error of sample mean
Confidence IntervalsHelps determine confidence in sample mean
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Inferential Statistics Includes tools and methods that rely on
probability theory and distributions to determine precise estimates of true population parameters from sample data
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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. SamplePopulation vs. Sample
Adapted from iLoveBiology.net
If sample is not collected randomly, it may not closely reflect original population.
This is called sampling bias.
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 dataConstruct histogram
Determine whether data has normal distributionCould 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?
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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
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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
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Variance Distance from the mean
Measuring Spread of Data Differences from mean are squared to
calculate varianceSo…units of variance are not same as units in original data set
Standard deviation=square root of varianceExpressed in same units as original data set
So….more useful than variance!
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Standard Deviation
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AP Biology McClure-Ottmers
Smaller Standard deviation shows values clustered tightly around mean
Larger Standard deviation shows values spread out widely from mean
Standard Deviation
Data: 2, 5, 9, 12, 15, 17
1. Calculate mean: 60/6 = 10
2.Find difference between each term and mean
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Standard Deviation
Data: 2, 5, 9, 12, 15, 17
1. Calculate mean: 60/6 = 10
2.Find difference between each term and 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
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Standard Deviation
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Standard Deviation mean & standard deviation help estimate
characteristics of population from a single sample
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Inferential Statistics--SE
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Reliability of the Mean
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Reliability of the Mean
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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
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.
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Hypothesis Testing Formal process to determine whether to
reject null hypothesis1. 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.
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Example—English Ivy LeavesSampling
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
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Example
Just looking at this data in this form does not answer question
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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!
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AP Biology McClure-Ottmers
Normally distributed?
Close enough!
Example Since Data are Parametric
Calculate Descriptive StatisticsMean
Standard deviation
Calculate Inferential StatisticStandard Error
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Example
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Example Produce bar graph to compare means including
error bars of ±1 SE
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Do SE bars overlap?
Would SE bars overlapif ±2 SE were graphed?
What does SE suggestabout two populations?
Use SE statistic as inference to describe confidence that means of samples represent true population means
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
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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
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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.
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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 valuesIs variance from expected values due to random chance?
Is there another factor influencing data?
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X 2 = (o – e)2Ʃ e
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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.
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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
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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
Category o e o-e (o-e)2 (o-e)2/e
Low tide 35
1m above 34
2 m above 10
3 m above 3
4 m above 2
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Category o e o-e (o-e)2 (o-e)2/e
Low tide 35 21
1m above 34 21
2 m above 10 21
3 m above 3 21
4 m above 2 21
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Category o e o-e (o-e)2 (o-e)2/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
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Category o e o-e (o-e)2 (o-e)2/e
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
2
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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
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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.
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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
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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
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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
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