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