Accuracy vs. Precision and the Scientific Method

1
Accuracy vs. Precisionand the Scientific Method
2
(No Transcript)
3
(No Transcript)
4
(No Transcript)
5
(No Transcript)
6
A. Review

• What does the pattern of averages represent in
  slide two?
• Pattern of averages many repetitions
• What is the purpose of repetition in science?
• To over come human error or randomness
• Eg. Large sample populations, same experiment
  many times over with the same results.
• Will repetition eliminate systematic errors?
• NO! A scientist has to allow for margin of error
  or adjust, like aiming higher to compensate or
  mechanically adjust the scope.

7
4. Target Analogy to Sci. Method

1. Target is the expected outcome
2. The holes represent actual outcome
3. Precision and accuracy represent analysis of
   results
4. In science we analyze expected vs. actual
   outcomes and come to conclusions

8
B. Review of Scientific Method

• Observations and Research
• Inferences
• Hypothesis
• Experiment
• Variables
• Results
• Conclusion and Discussion

9
7. Part 1- Observations/Research

• What are we interested in???? Come on think!
• RHS example-jet propulsion
• Make observations and research the topic
• Observations are measurable

10

• Research can come from a few areas or many. You
  cannot make an educated guess with out knowing
  something about the topic.
• You can get information through
• Reading assignments in the text book.
• Using the internet.
• Remembering personal experience.
• Notes form lectures.
• Books from library or personal.

11
2. Inferences

• Not measurable
• What is an inference?????
• a logical interpretation of an observation based
  on facts
• I have my license now, therefore, I am eligible
  to drive

12
3. Implications

• Now that I have my license I will drive everyday
  to school like my brother.
• You may or may not drive to school everyday like
  your brother. You may not drive at all!
• Implications are possible outcomes, but not
  necessarily actual results. These are
  assumptions or possibilities. Good luck with that!

13
e. Deductive/Inductive reasoning

1. Adham I've noticed previously that every time I
   kick a ball up, it comes back down, so I guess
   this next time when I kick it up, it will come
   back down, too.
2. Rizik That's Newton's Law. Everything that goes
   up must come down. And so, if you kick the ball
   up, it must come down.

14

• Adham is using inductive reasoning, arguing from
  observation,
• Inductive Todays science going from
  individual facts to large theories. while Rizik
  is using
• deductive reasoning, arguing from the law of
  gravity.
• Deductive Early science (philosophy)
• Start with the general idea and reduce it to
• its smaller facts.

15
NEXT
16
3. HYPOTHESIS

• We call this the educated guess based on
  academic research.
• How would you explain this????
• Okayits an educated (from facts) guess that
  will be answered (hopefully) with

17
4. Design and experiment/test
18
AKA. Materials and Methods

1. Otherwise known as the test procedure
2. Why is it important to be accurate and precise???
   Why is it important to be clear and concise?
3. So it can be repeatedlike excuses for being
   tardy to class. You and your friends stay late
   for lunch resulting in lateness, thus you devise
   an excuse and see if that works
4. because we all know youll try it again if it
   does work, it not move something else

19

• You must document everything done in an
  experiment so others can reproduce the experiment
  to confirm (or disprove) your results.
• Measurements must be recorded and exact!

20
a. What are variables?????

1. Manipulated/Independent Variable
2. What you change? MV (IV)
3. Responding/Dependant variable
4. What responds to the ? RV (DV)
5. Control (s) the unchanged variable to compare to
   the Manipulated ? C
6. Identifying variables assignment (front)

21

• What variable was your control, what was your
  dependent variable, your independent variable?
• This makes graphing easier
• your independent variable is on the X-axis and
• your dependent variable is on the Y-axis.
• Graphs are analytical tools to aide in
  interpreting your data. (Note graphs are used
  only in quantitative data.)

22

• 5 Analysis/Results (Quantitative and
  Qualitative)
• What does the data from your results tell you?
• Hard numbers are stated here. No discussion or
  interpretation of results is given. Graphs and
  data tables are referenced so reader can see
  mathematical results visually. Percent margin of
  error is also part of results both systematic and
  random. (Quantitative)
• When subject A consumed 2000 grams of black
  licorice containing caffeine, systolic and
  diastolic blood pressure increased by 10 points,
  3000 grams and so on. You describe what actually
  happened. (Qualitative) What would your control
  and variables be in this experiment????

23
Time to play!!!!!

• Graph your height experiment Lab
• Measure Up Lab

24

• In the graph your height experiment identify
  controls and variables
• C- same meter stick for all students
• MV-inches (X axis)
• RV-centimeters (Y axis)
• Results? expected outcome 2.54 cm per in and
  actual was______ with a margin of error.
• What type of error did we have?
• random because sticks were off slightly (human)
• How did we adjust for error? Many samples

25

• 6-Conclusion
• Was your hypothesis right or wrong? You accept or
  reject your hypothesis and discuss
• A discussion of what you discovered by doing
  this experiment. Any formulas you proved, or
  derived by doing this experiment should be
  discussed. Did you accomplish your purpose? In
  other words What did you learn. What tool was
  most significant in explaining your findings?
  (Inferences)
• If your hypothesis was wrong you should think
  things over or trouble-shoot, write a new
  hypothesis, and retest. (implications)

26
C. Significant Digits and Scientific Notation

• Sig. Fig. rules
• Digits from 1-9 are always significant (non
  zero).
• Zeros between two other significant digits are
  always significant
• Final zeros to the right of the decimal point are
  significant digits.
• Zeros used solely for spacing the decimal point
  (placeholders) are not significant.

27
Step 1 Add all the numbers together 13.501
6.101 7.4 0.68 12.0
28

• 1.) Determine the least-significant place of each
  term in the addition.
• The least-significant place of 6.101 is the
  thousandths place.
• The least-significant place of 7.4 is the tenths
  place.

29

• 2.) The result of addition should be rounded to
  the same least- significant place as the term
  with the largest least-significant place.
• The result should be rounded to the tenths place.
  

30

• 3) Round the result to the proper
  least-significant place.
• The arithmetic result of 13.501 rounded to the
  tenths place is 13.5.

31
Examples

• 2804
• 4 sig. fig
• 2.84
• 3 sig. fig
• 0.0029
• 2 sig. fig
• .003068
• 4 sig. fig
• .100
• 3 sig. fig. because final zero is trailing and
  therefore sig.

32

• 34, 780, 0.507,1.200, and 2
• Add these together and what is the final answer
  using the rules of sig. figs.?
• Did you get the number 817.707?
• What is your final answer?
• You can only have an answer that is as precise as
  the number containing the least amount of sig.
  figs.
• 800

33
Scientific Notation

1. Rule for Addition and Subtraction - when adding
   or subtracting in scientific notation, you must
   express the numbers in the same power of 10. 
   This will often involve changing the decimal
   place of the coefficient. (use lowest number of
   exponent)
2. Rule for Multiplication - When you multiply
   numbers with scientific notation, multiply the
   coefficients together and add the exponents.  The
   base will remain 10.
3. Rule for Division - When dividing with scientific
   notation, divide the coefficients and subtract
   the exponents.  The base will remain 10.
4. Complete worksheets

34
Examples

• Express in Scientific Notation
• 5800
• 5.8 x 103
• 450,000
• 4.5 x 105
• 302,000,000
• 3.02 x 108
• 86,000,000,000
• 8.6 x1010

35
Examples

• 6.0 x 10-3 mg 2 x 10-4 mg
• Change 2 to .2 to make 10-3
• Exponents now the same so add
• Make exponents the same
• 6.0 .2 6.2 x 10-3
• 6 x 10-8 4 x 10-8
• 2 x 10-8

36
Examples

• (2 x 104m) (4 x 108m)
• 2 x 4 8 x 1012 m2
• Add the exponents
• 6 x 108 kg/2 x 104 m3
• 6/2 3 x 104 kg/m3
• Subtract exponents

37
Direct Relationship
Direct Relationship ymxb
38
Inverse Relationship y a/x
39
Quadratic relationship yax2 bx c parabola
40

• In physics we measure
• Distance in meters (m)
• Mass in kilograms (Kg)
• Time in seconds (s)

41
Assignments

• Chapter 2 practice problems 1-3,6-8b,9a-9c,12a-12b
  ,13-17b (starts on page 20)
• Chapter 2 review problems 30-43 and 46-47 (starts
  on page 39)
• Chapter 2 study guide handout