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Title: Accuracy vs. Precision and the Scientific Method


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Accuracy vs. Precisionand the Scientific Method
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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.

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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

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B. Review of Scientific Method
  • Observations and Research
  • Inferences
  • Hypothesis
  • Experiment
  • Variables
  • Results
  • Conclusion and Discussion

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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

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  • 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.

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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

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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!

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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.

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  • 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.

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NEXT
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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

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4. Design and experiment/test
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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

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  • 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!

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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)

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  • 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.)

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  • 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????

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Time to play!!!!!
  • Graph your height experiment Lab
  • Measure Up Lab

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  • 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

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  • 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)

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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.

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Step 1 Add all the numbers together 13.501
6.101 7.4 0.68 12.0
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  • 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.

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  • 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.

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

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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.

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  • 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

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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

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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

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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

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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

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Direct Relationship
Direct Relationship ymxb
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Inverse Relationship y a/x
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Quadratic relationship yax2 bx c parabola
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  • In physics we measure
  • Distance in meters (m)
  • Mass in kilograms (Kg)
  • Time in seconds (s)

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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
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