AP Biology Science Skills. AP Biology Science has principles Science seeks to explain the natural...

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

AP Biology McClure-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


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


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


Characteristics of Science Conclusions of science are reliable,

though tentative Science is not democratic

Science is based on evidence, not votes


Characteristics of science Science is non-dogmatic

Not based on faith or belief systems

Science cannot make moral or aesthetic decisions


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


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


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.


Experimental Design

1. Determine variablesDependent

Variable measured in an experiment

IndependentVariable changed in an experiment

Controlled/constantVariables that are held constant in an experiment


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!


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?


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.”


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


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



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


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


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


Bar Graphs Use to

Visually compare categorical or count data

Visually compare calculated means with error bars for normal data


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?


Bar Graphs Standard error bars provide more information

about how different two means may be from each other (sample standard error)


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



r = correlation coefficientRange -1 to +1Increased relationship with values closer to 1

Box and Whisker Plots Allow graphical comparison of two

samples of nonparametric dataappropriate 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


Histograms


Line Graphs Used when data

on both axes are continuous

Dots indicate measurements that were actually made


Using Graphs Estimation—Interpolation/Extrapolation Calculating Rate--Use slope


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


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


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


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


Inferential Statistics Includes tools and methods that rely on

probability theory and distributions to determine precise estimates of true population parameters from sample data


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


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.


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?


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


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 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!


Standard Deviation



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


Standard Deviation


Standard Deviation mean & standard deviation help estimate

characteristics of population from a single sample


Inferential Statistics--SE


Reliability of the Mean



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.


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


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.


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


Example

Just looking at this data in this form does not answer question


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!



Normally distributed?

Close enough!

Example Since Data are Parametric

Calculate Descriptive StatisticsMean

Standard deviation

Calculate Inferential StatisticStandard Error


Example


Example Produce bar graph to compare means including

error bars of ±1 SE


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


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


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.


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?


X 2 = (o – e)2Ʃ e

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.


Distance from low tide

# of periwinkles observed

At low tide line 35

2 m above low tide 24




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

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



Low tide 35 21

1m above 34 21

2 m above 10 21

3 m above 3 21

4 m above 2 21



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



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



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


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.


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


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


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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