Download 0-Sci Method Data Statistics

Experimental Design,
Describing Data and
Statistical Analysis
AP Biology
Part 1: Experimental Design
 The goal of scientific investigation is to
obtain and interpret reliable scientific
data.
 In biology, we engage in the scientific
method in order to answer questions
about the natural world.
Scientific Method
 Make observations – Identify an event you’d like to
understand more about.
 Formulate a question – What testable, data-driven
question can you ask about the event?
 Form a hypothesis – Write a statement that could answer
the question. The statement should be both testable and
falsifiable.
 Test the hypothesis – Collect data and observations that
helps you determine whether your hypothesis is accurate.
 Data Analysis – Graphs, computations, and/or statistical
tests that allow the scientist to determine patterns.
 Draw conclusions – Interpret your data and observations,
attempted to support or refute your hypothesis.
In science, nothing can be proven, only supported!
Variables
 Variables – Things that change in an experiment.
 Changes can be a part of the experimental design OR
something you’re measuring in order to answer your
question.
 Independent variables are controlled or chosen by the
scientist. On a graph, placed on the x-axis.
 Dependent variables are measured or observed by
the scientist. On a graph, placed on the y-axis.
 Use the sentence: “The _______ depends on the
______.” to help you figure out which is which.
Practice identifying variables
 Let’s start by considering some biological questions
(pay attention to the IV and DV here):
 How do solutes dissolved in water affect water’s
properties of adhesion and cohesion?
 What temperature is ideal for an enzyme-mediated rate
of reaction?
 How do toxins impact the rate of mitosis in onions?
 Are mealworms more attracted to grains or meats?
 How do environmental conditions impact the rate of
transpiration?
Constants
 A constant is something that should be kept
the same for the entire experiment,
especially between different trials.
 E.g., temperature, humidity, light levels, etc.
 Might also be called a “controlled variable”
 Something that, if not maintained at a consistent
level throughout the experiment could reasonably
impact your data.
Controls
 A control is something used as a standard of
comparison in an experiment.
 It is often the same conditions as your experimental
conditions, just without the independent variable.
 A basis for comparison that allows you to claim that
changes in your dependent variable are likely due to
your independent variable.
 Any time you are interpreting data, you should
intentionally and explicitly look at the control and
state, “… as compared to the control” or use numbers
to do this explicitly. Ex: “The number of drops of
acetone that could be held on a penny was 6 less
than the control.”
Positive & Negative Controls
 There are two types of controls: positive and
negative. Some labs have one or the other,
some have both; this just depends on your
experimental design.
 A positive control is designed where a “known”
response is expected. For example, we expect
bacteria to grow on nutrient agar.
 A negative control is designed where no response
is expected. This shows that your experimental
setup is working properly. For example, we expect
that antibiotics to kill bacteria grown on nutrient
agar that has been supplemented with antibiotics.
Types of Data & Observations
 Scientific observations can take two forms:
Qualitative or Quantitative.
 Qualitative data refers to the qualities of
something (e.g., color, shape, texture,
odor).
 Ex: The liquid turned orange after we added the
iron.
 Quantitative data refers to the quantity of
something (e.g., amount or value)
 Ex: The mass increased 4 grams.
Collecting Data
 We need to have a sufficiently large sample size. 40
is ideal, but it’s pretty unrealistic for our class. The
data need to be normally distributed.
 In some applications, repetition (multiple trials) is
more realistic than collecting many individuals.
 Trials occur when you do the EXACT same thing
repeatedly. No variations at all.
 Why are large, unbiased samples so important?
 The goal is that your sample is indicative of the entire
population. So the 10 plants you find the transpiration of
are indicative of every plant of that species, in those
conditions, on the planet. Crazy.
 The goal: the sample mean and spread (called Standard
Deviation) is the same as the population mean and
spread.
This is where a bell curve comes from:
A large, unbiased sample allows us to
make inferences of the population.
The individuals in the sample are a
reasonable approximation of the
population. Of course there will be
variation, but as long as we have a large,
unbiased sample, results should be
legitimate and variation should produce a
bell curve around the mean.
Part 2: Describing Data
 Visual Descriptions of Data are Graphs
 Use whatever graph best allows for the visualization of
relationships
 Bar
 Line
 And all of their many variations
 Descriptive Statistics –
 Complete calculations to understand the intricacies of the
data. Your calculator will help!
 Mean
 Median
 Standard Error of the Mean
 Interquartile Range (IQR)
 We will often graph a dataset’s descriptive statistics rather
than the raw data in order to show relationships more
clearly.
Graphing Requirements
 A good title (Y vs. X of _____)
 Label your axes with units, and use evenly spaced and
scaled numbers to spread out the data.
 Clearly mark data points.
 When making a line graph, draw a line of best fit
 Any extrapolation beyond the last data point should be
shown with a dashed line.
What kind of graph do I make?
Bar Graphs…
 Behold: the return of the BAR
GRAPH! The only rule to
graphing is that you make the
one that represents your data
the best.
 Bar graph: Used for categorical
independent variables.
 Since we always do multiple
trials, the top of the bar
represents the MEAN of the trials
of that data.
 Might have error bars, which
show the variation in the data.
Box & Whisker
Plot
 Box & Whisker plots are modified bar graphs that show
how the data is spread out using quartiles.
 Your calculator will find your quartiles for you. 
Line Graphs
 Line graph: Used for continuous
independent variables.
 Might have two y-axes for multiple
scales
 Might plot the means, and have error
bars to show variation in data.
 Might have a log scale
Constructing a Data Table
 The rules are much the same as
graphing: have a good title, have
labels and units clearly indicated,
and of course, USE A RULER.
 Depending on your data, your
independent variable may go on
the left or across the top. Either is
appropriate.
I have the data. Now what?
Descriptive statistics describe your
data.
 Calculate descriptive statistics for each
group – control and experimental:
 Mean (or average)
 Standard Deviation – How spread out your
data is from the mean you just calculated.
 Standard Error of the Mean – How confident
you are that your sample mean includes
the population mean.
Using your TI-84 to lighten the load:
 Consider this: I’ve taken my temperature every
morning for the last two weeks. Here are my findings:
97.8
98.1
98.7
98.4
98.3
97.9
97.4
97.7
98.2
98.3
97.6
98.9
98.6
98.5
 . Calculate by hand the standard deviation
 Remember the equation is
Using your TI-84 to lighten the load:
 Consider this: I’ve taken my temperature every
morning for the last two weeks. Here are my findings:
97.8
98.1
98.7
98.4
98.3
97.9
97.4
97.7
98.2
98.3
97.6
98.9
98.6
98.5
 Enter the dataset in a list by pressing “Stat” then “Edit”
 When you are finished, it will look like this.
Using your TI-84 to lighten the load:
 To have your calculator compute descriptive
statistics for this list of data:
 Press “Stat”
 Press over to highlight “Calc” along the top.
 The top option is “1-var Stats” – select that.
 Your screen will read like this:
 Ensure the correct List is specified; leave FreqList
blank
 Press down twice to highlight “Calculate” and hit
enter.
Using your TI-84 to lighten the load:
 The output is shown at the right, and
matches the defined terms on your
formula sheet:
 I highlighted the mean (x) and
standard deviation (Sx). I also
highlighted n, the sample size.
 Your calculator does not automatically
calculate 𝑆𝐸𝑥 for you – you must do
that on your own. But it’s just plug in
values from your calculator!
 When graphing, you will typically
graph 𝑥 ± 2𝑆𝐸𝑥 , so be prepared to do
a bit more arithmetic.
Showing descriptive statistics
graphically: box and whisker plot
 This same output also generates the values necessary
to produce a boxplot. Simply scroll down to see it all.
Showing descriptive statistics
graphically: mean±2SEM
 How different is
different enough?
 The larger the error bar, the less confident we
are that the calculated mean is representative
of the entire population.
Part 3: Statistical Analysis
 Answering the question: How different is different
enough?
 “My control data has a mean of 12 cm/year and
experimental data has a mean of 15 cm/year.”
 Is there a biological relationship here?
 “I flipped this coin 20 times and got 14 heads and 6
tails; that’s pretty different from the 10 heads and 10
tails I was expecting.
 Is this coin most likely fair? Or “loaded”?
How do we go about answering
biological questions?
 Collect data: large, unbiased sample.
 Describe the data with descriptive statistics (mean,
SEM)
 Write statistical (null and alternative) hypotheses
 Determine appropriate statistical test
 Calculate the test statistic, critical value, and
determine degrees of freedom. (Calculator!)
 Interpret statistical test with respect to statistical
hypotheses.
 Draw a scientific conclusion, using support from the
statistical test.
Now, to statistical tests…
 All statistical tests work on fancy, calculusbased areas under curves that indicate
probabilities… Don’t worry about it. Just be
able to interpret it.
 We’re trying to distinguish between natural
variation in a dataset and variation that is the
result of the independent variable.
 “What is the probability that my two data sets
are different?”
 Are boys taller than girls? Some boys are shorter
than some girls. How do we answer that
question?
Taking your data to court:
 In a court of law, a defendant is found to be either
guilty or not guilty. A defendant is never found to be
innocent. Why not?
 Remember, in statistics, we are trying to determine if
two datasets are different enough to claim a
biological relationship exists with the independent
variable.
 In statistical analysis, you write a null hypothesis (the
defendant – that there is not a relationship with the
independent variable), and it is find to reject it or fail
to reject it. What’s the difference?
 How different do two datasets need to be in order to
be different enough to claim they are different
enough and a biological relationship exists?
Taking your data to court:
 Think of yourself like a prosecutor, trying to provide
sufficient data to support rejecting the null
hypothesis.
 So, we write statistical hypotheses, two of them for
every statistical test. Don’t let the language upset
you.
 Null hypothesis, or H0, just says “There is no significant
difference between X and Y.”
 Means that the distributions of your two datasets
(experimental and control) overlap too much for you
to claim that the data comes from two different
populations.
 Alternate hypothesis, or HA, just says “There is a
significant difference between X and Y”
 Means that the distributions of your two datasets are
sufficiently different for you to claim that the data
comes from two different populations.
 It’s your goal to attack the null hypothesis,
showing you have significant evidence
against it. In doing so, you lend support to
(BUT DO NOT PROVE!) the alternate
hypothesis.
 Ultimately, you obtain a probability, or pvalue: the probability of getting this data by
chance alone; that your two datasets are
from the same population, or your data are
within reason for an expected outcome.
 Biologists are typically willing to allow 5%
error. So, we look for a p-value of 0.05 or less
in order to reject the null hypothesis and
accept the alternate hypothesis.
Two non-biological questions:
 Do vehicles get better highway MPG
when using cruise control compared with
when not using cruise control?
Null: There is not a significant difference in
the gas mileage using cruise control vs.
not.
Alternate: There is a significant different in
gas mileage using cruise control vs. not.
 Is this weird looking coin I just found in the
hallway a fair coin? Or is it “loaded”?
Null: There is not a significant difference in
the number of heads vs. tails flipped on this
coin compared to a fair coin.
Alternate: There is a significant…..
So, now we test the
hypotheses we wrote:
 There are loads of different statistical tests.
You need to calculate two this year:
 One when you are comparing two datasets to one
another (like the gas mileage question)  two
sample t-test.
 One when you are comparing a single dataset to
expected values (like the fair coin question: Heads
vs. Tails)  Chi-Square test.
 You will need to be able to interpret p-values
of all tests, but these are the only two I’ll ask
you to calculate.
Practice! From earlier:
 Do vehicles get better highway MPG when
using cruise control compared with when
not using cruise control?
 Null: There is not a significant difference in
the gas mileage using cruise control vs. not.
 Alternate: There is a significant different in
gas mileage using cruise control vs. not.
 Enter your data into two lists (Stat; 1:Edit) in
your calculator – one list for each
treatment.
MPG with cruise
control
MPG without cruise
control
26
27
22
19
25
26
23
24
28
24
22
21
24
26
24
22
28
27
21
23
Two Sample T-test:
 Now, perform the t-test:
 Stat, over to TESTS
 4:2-SampTTest…
 Data
 List 1: L1
 List 2: L2
 Freq1: 1
 Freq2: 1
 µ1:≠ µ2
 Pooled: No
 Calculate, hit enter.
T-test:
 There are two pieces of information you need
from this list:
 T= is the t-statistic
 P= is the p-value (BE CAREFUL with Scientific
Notation: 1.1E-5)
 P-value will always be between 0 and 1
(remember, it’s a probability)
 In general, the larger the t-statistic, the smaller
the p-value.
 If the p-value is less than 0.05 we reject the null
hypothesis and accept the alternate
hypothesis.
 If the p-value is greater than 0.05 we fail to
reject the null hypothesis.
 This is usually not what we “want” because it
means there is no significance between our
control and experimental conditions.
More on a t-test
 So, what is our statistical conclusion?
 What is our scientific conclusion?
Shift gears to the other test: Chisquare Goodness of Fit (GOF)
 Use this test for data when you are comparing
one (observed) data set to predicted
(expected) values.
 The coin flip example.
 1:2:1 ratios of progeny – think Punnett squares!
 Evaluating whether organisms are attracted or
repelled by something in their environment.
 Does this population meet the predictions of
the Hardy-Weinberg equilibrium?
 Statistical hypotheses are generally the same!
 Null: There is no difference between the expected
and observed data.
 Alternate: There is a difference between the
expected and observed data.
Calculating Chi-square
 Is this weird looking coin I just found in
the hallway a fair coin? Or is it
“loaded”?
Null: There is not a significant difference
in the number of heads vs. tails flipped
on this coin compared to a fair coin.
Alternate: There is a significant…..
 Enter the data and do the test:
Flip
Observed
Expected
Heads
12
15
Tails
18
15
How to enter data for
X2GOF…
 Enter your data into two lists:
 Observed data in List 1
 Expected data in List 2
 Then:
 STAT, over to TESTS
 Down to D:X2GOF-Test
 Observed: L1
 Expected: L2
 df:? (enter the number of options -1)
 Calculate and hit enter.
More on Chi-square
 So, what is our statistical conclusion?
 What is our scientific conclusion?
 Consider sample size: add a zero to
everything and rerun the test:
 The proportions have NOT changed.
 What happened to the results?
 What does this indicate about the
importance sample size? When could
patterns in data be overlooked?
Flip
Observed
Expected
Heads
120
150
Tails
180
150
Doing Chi-square by hand:
 Looks scary, just algebra. And you don’t have to be
very precise.
 Use the table if you want!
Categories
(outcome)
Expected
(e)
Observed
(o)
Heads
15
12
Tails
15
18
o-e
(o-e)2
Sum:
 So, now what?
 How many degrees of freedom?
 What’s the critical value? Assume p=0.05
(𝒐 − 𝒆)𝟐
𝒆
But what does it all
mean?!?!
If the Chi-square value is greater than the
critical value, p is less than 0.05 and the H0
may be rejected. The expected and
observed values are sufficiently different
to reject the null hypothesis.
If the Chi-square value is less than the
critical value, p is greater than 0.05 and
the H0 may not be rejected: the expected
and observed values are too similar to
reject the null hypothesis.
Why? Such torture…
 Remember, the goal is to answer questions
about the natural world.
 Quantitative evidence helps us come to
justifiable answers to our questions.
 Just claiming two experimental conditions yield
“different” results is insufficient. How different?
Different enough? Statistics allows us to
defensibly answer questions.