Graphing Skills
Scatterplot vs Line GraphData points independent of each other.o The next value does not
depend on the previous
Labeling Axes
1. The independent (manipulated) variable is the X axis
2. The dependent (responding variable) is written along the vertical axis
3. Units on any variables should be included in () following the axis title
Scaling Axes• Step 1: Find the range for the
variables (biggest – smallest)
• Step 2: divide the range by the # of intervals you want
• You don’t want your data smooshed –spread it out!
• Step 3: Use the rounded number to mark off intervals along the axis
Which one would get credit?
Plotting Points
• Step 1: Select the first pair of values from the data (X and Y – they are not always zero!!)
• Step 2: Draw a light dashed line from the number on the X axis and over from the number on the Y axis
• Step 3: where these dotted lines cross, put a dark point. Repeat for all points.
Best Line Fit or Curve
• Look for a pattern or trend• If so – draw a STRAIGHT LINE (do
not connect the dots) that represents that trend
• All points should lie near or on the line
• For points not on the line –about ½ should fall above and ½ below
• Your line should NOT extend beyond your range of data (extrapolation)
Correlation does not imply causation
Correlation does not imply causation
The Scientific Method in
Action
SCIENCE
• If you don’t make mistakes, you’re doing it wrong
• If you don’t correct those mistakes,
you’re doing it really wrong
• If you can’t admit that you’re
mistaken – then you’re not
doing it at all!
What is Science?
(verb) it is an activity carried out by scientists, with
certain raw materials, purpose and methodology in
order to gain knowledge
(noun) it is the result of this activity: a well-
established and well-tested body of facts, laws and
models that describe the natural world.
Science involves the critical evaluation of ideas and
information
Scientists maintain a “healthy skepticism” about
information and ideas
– the best way to evaluate ideas is the scientific method
– Only field where ideas are tested
Acceptance of “truth” From inherited customs, traditions
Authority figure
Trial and error
Deductive reasoning Assumptions from existing knowledge
Uses logical arguments (If… then)
Where do we get knowledge?
Scientific Method
Scientific knowledge begins with an observation and a
proposed explanation.
Explanation called a hypothesis
A hypothesis is testable and falsifiable
In science hypotheses are tested by using them to
make predictions about the outcome of an
experiment
Scientific Method Scientific method
– More reliable for obtaining information
You can test what you believe to be true
Others can repeat your experiment
Opportunity to prove false
– Follows general set of systematic procedures
– Steps are followed in order to answer a research
question
Ethics
The Scientific Method
1. Observe an event.
2. Develop a Hypothesis which makes a prediction.
3. Test the prediction.
4. Observe the result.
5. Revise the hypothesis.
6. Repeat as needed.
7. A successful hypothesis becomes a Scientific
Theory.
hypothesis
test
Scientific Method Everyday Science
Observation Spaghetti sauce is red.
Hypothesis (prediction) Use tomatoes.
Test Heat pot of tomato sauce.
Observe result Taste the sauce - bland.
Revise hypothesis? Use tomato sauce and garlic!
New test? Add garlic, taste - not so bland.
Scientific Theory Grandma’s Recipe.
Scientific Method Medical Science
Observation Patient has high cholesterol
Hypothesis (prediction) Certain chemicals may dissolve cholesterol
deposits.
Test Give 100 patients these chemicals, give 100
patients placebo.
Observe result Same number lower their cholesterol as
placebo patients.
Revise hypothesis? Try different combo of chemicals.
New test? Re-run medical test. Observe results.
Scientific Theory Lipitor reduces cholesterol.
Problem/Question
John watches his grandmother
bake bread. He ask his
grandmother what makes the
bread rise.
She explains that yeast
releases a gas as it feeds on
sugar.
Caution!
Be careful how you use effect and affect.
Effect is usually a noun and affect, a verb.
Example: “The effect of sugar amounts on the rising of bread.”
Example: “How does sugar affect the rising of bread?”
Observation/Research John researches the
areas of baking and
fermentation and tries to
come up with a way to
test his question.
He keeps all of his
information on this topic
in a journal.
Formulate a Hypothesis
After conducting further
research, he comes
up with a hypothesis.
“If more sugar is added,
then the bread will rise
higher.”
Ockams Razor
It states that among competing hypotheses, the one with the fewest
assumptions should be selected. Other, more complicated solutions
may ultimately prove correct, but—in the absence of certainty—the
fewer assumptions that are made, the better.
Hypothesis
The hypothesis is an educated guess about
the relationship between the independent
and dependent variables.
Note: These variables will be defined
in the next few slides.
"If I give a plant an unlimited
amount of sunlight, then the
plant will grow to its largest
possible size."
Hypothesis is written as an If…then…statement
Problem/Question
John wonders if the amount of sugar
used in the recipe will affect the size
of the bread loaf?
Variables in an Experiment
Independent Variable
The independent, or
manipulated variable, is a
factor that’s intentionally varied
by the experimenter.
John is going to use 25g, 50g,
100g, 250g, and 500g of sugar
in his experiment.
Dependent Variable
The dependent, or responding variable, is the factor that may change as a result of changes made in the independent variable.
In this case, it would be the size of the loaf of bread.
Control Group• In a scientific experiment, the
control is the group that serves as
the standard of comparison.
• The control group may be a “no
treatment" or an “experimenter
selected” group.
• The control group is exposed to
the same conditions as the
experimental group, except for the
variable being tested.
• All experiments should have a
control group
• Because his grandmother always
used 50 grams of sugar in her
recipe, John is going to use that
amount in his control group.
Independent variable: condition or event under study (only 1
can reliably be tested at one time)
Dependent variable: condition that could change under the
influence of the independent variable (what you measure)
Controlled variables: conditions which could effect the
outcome of the experiment so they must be held constant
between groups
– This is especially important as your results have little significance
without a controlled experiment. Remember, “correlation does
not equal causation”
– Used for comparison
Causation vs Correlation
Constants• John’s teacher reminds him to
keep all other factors the same so
that any observed changes in the
bread can be attributed to the
variation in the amount of sugar.
• The constants in an experiment
are all the factors that the
experimenter attempts to keep the
same.
• They might include:– Other ingredients to the bread recipe,
oven used, rise time, brand of ingredients, cooking time, type of pan used, air temperature and humidity where the bread was rising, oven temperature, age of the yeast…
Trials
Trials refer to replicate
groups that are
exposed to the same
conditions in an
experiment.
John is going to test
each sugar variable 3
times.
Theories and Natural Laws
Theory: a description of the world that covers a relatively large number of phenomena and has met many observational and experimental tests
Law of Nature: theory (or group of theories) that has been tested extensively and seems to apply everywhere in the universe
One test is worth a thousand expert opinions.
– Bill Nye
Collect and Analyze Results
John comes up with a table he can use to record his data.
John gets all his materials together and carries out his experiment.
Size of Baked Bread (L x W x H) cm3
Amt. of
Sugar (g.)1 2 3 Average
Size (cm3)
25 768 744 761 758
50 1296 1188 1296 1260
100 1188 1080 1080 1116
250 672 576 588 612
500 432 504 360 432
Size of Bread Loaf (cm3) Trials
Control group
Collect and Analyze Results
John examines his data and notices that
his control worked the best in this
experiment, but not significantly better
than 100g. of sugar.
John rejects his hypothesis, but decides
to re-test using sugar amounts
between 50g. and 100g.
Can you tell which group did the best?
Size of Baked Bread (L x W x H) cm3
Amt. of
Sugar (g.)1 2 3 Average
Size (cm3)
50 1296 1440 1296 1344
60 1404 1296 1440 1380
70 1638 1638 1560 1612
80 1404 1296 1296 1332
90 1080 1200 972 1084
Size of Bread Loaf (cm3)
Trials
Control group
Conclusion
John finds that 70
grams of sugar
produces the
largest loaf.
His hypothesis is
accepted*
Graphs
Graphs help us visualize
numerical data.
There are several different
types of graphs:
–Bar graphs
–Pie graphs
–Line graphs
Candidates should be able to recognize trends in data presented in the
forms of tables or in graphical form. For example, they should be able to
recognize whether or not there is a relationship between two variables
and to comment on this in the context of a stated hypothesis.
Developing your Hypothesis
IF….THEN…Statements
If = independent variable What is being manipulated (basis of your hypothesis)
Control group: your experiment WITHOUT this group
X axis
Then = dependent variable What you’re measuring
Y Axis
Qualitative vs Quantitative
Just as it’s necessary to observe, it’s also
important to quantify observations in some way
– For example: define “tall”
Bar Graphs
Bar graphs are
used to show a
comparison of
multiple
objects. 0
10
20
30
40
50
60
1 2 3 4 5 6 7 8 9
Nu
mb
er
of
Fle
as
Dog Identity
Pre-collar
Collar
Pie Graphs
Pie graphs are
used to
compare the
parts of a
whole.
Ingredients
glue
baby powder
sulfur
secretingredient
Line graphs
Line graphs are
used to show
the relationship
between
variables.
0
10
20
30
40
50
60
Week 1 Week 2 Week 3 Week 4 Week 5 Week 6
Nu
mb
er
of
Fle
as
Collar
No Collar
Right from Wrong
The theory of gravity, theory of electricity, the germ theory
of disease, and the theory of evolution are tested, accepted
explanations for events that occur in nature.
Theories can really never be completely proven, only
disproven. When new evidence comes along, we must
modify our theory or at times even get rid of it and start over
again
The Need for Statistics
How do you tell a really odd but correct result from a WRONG result?
The simple answer is: you can never tell for certain that a given result is “wrong”. All we can do is determine whether a given result is likely or unlikely.
There are 2 ways of getting a weird statistical measurement: an unusual result from the correct theory, or a result from the wrong theory. These are indistinguishable; because of this fact, statistics is never able to discriminate between true and false with 100% certainty.
Reasonability
What is a “reasonable” result is subjective and arbitrary.
For most work (and for the purposes of this class), a result is said to not differ significantly from expectations if it could happen at least 1 time in 20. That is, if the difference between the observed results and the expected results is small enough that it would be seen at least 1 time in 20 over thousands of experiments, we “fail to reject” the null hypothesis.
For technical reasons, we use “fail to reject” instead of “accept”.
“1 time in 20” can be written as a probability value p = 0.05, because 1/20 = 0.05.
Another way of putting this. If your experimental results are worse than 95% of all similar results, what you measured was very unlikely.
Critically Thinking
Identify and evaluate premises and conclusions in an argument
Analyze conclusions based on evidence versus those based on value judgments
Assign weight to opposing viewpoints based on chains of reasoning, sources of information (reliability)
Adjust weighting depending on relevance to central issue, lack of specific evidence or contradictions