Transcript Document

» In order to create a valid experiment, the experimenter can only change
ONE variable at a time
» The variable that is being changed by the experimenter is called the
INDEPENDANT
______________________
variable.
» The variable that changes as a result of the independent variable is called
DEPENDENT
the ________________
variable.
» In physics there is no CONTROL variable, instead there are
» CONTROLLED variables. These are kept the same throughout the
experiment because they also affect the dependent variables being
tested, thus affecting the outcome of the experiment
Your knowledge and grade in physics is related to the
amount of quality time you spend studying..
independent variable: ?
dependent variable: ?
The graph shown here is ok. Why only ok?
The graph »shows
overallthe
trend
(average
value).
In science
If youus
arethe
measuring
amount
of bacteria
over time,
what iswe
thecare
about BOTH the
averageand
value
and some
measure of the variation in the
independent
dependent
variable?
data.
Dependent Variable
on the y-axis!
Independent Variable on the x-axis!
Data nearly always has variation. Variation is when you do the
same exact experiment / measurement but get a slightly different
result.
There are many causes of variation in data, including:
instrument uncertainty
No measuring instrument is fully precise. Instrument uncertainty is how
much competent users of an instrument (e.g. a ruler) are likely to differ in
their measurement. For example, people using a ruler may disagree by
about + 0.4 mm.
uncontrolled variables
Its nearly impossible to fully control all variables. Un- or poorly- controlled
variables will cause variation in your results. For example, changes in wind
speed and direction would effect the results of a projectile launching
experiment.
Sampling from a population
Sometimes you are measuring a small number of individuals from a larger
population who differ in some trait. This is very common in biology but is
NOT usually relevant to physics.
» In ANY science, we care about the variation in the data nearly
as much as the overall outcome / trend.
Why?
» Because the variation gives us some (NOT perfect) idea of
how close our measurement is to the TRUE value.
» Variation also limits our ability to make a conclusion about an
overall trend or difference in our data.
This is real
data, btw!
Different sciences report the variation in their data in different
ways. For example, biologists often use standard deviation.
Physicists report measurement uncertainty.
Measurement = (mean value ± uncertainty) unit of measurement
The uncertainty shows the area
around the average value where
the true value of the
measurement is likely to be
found.
uncertainty uncertainty
mean
value
Measurement
values
For example, the result (20.1 ± 0.1) cm basically communicates
that the person making the measurement believes the value to
be closest to 20.1 cm but it could have been anywhere between
20.0 cm and 20.2 cm.
Calculating measurement uncertainty is easy!
I’m starting to understand measurement uncertainty,
what is that???
Inbut
an experiment,
this means that for
every level of your independent (x)
𝑟𝑎𝑛𝑔𝑒 𝑜𝑓
𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑚𝑒𝑛𝑡𝑠
It’s
the
instrument
uncertainty
of
the
launch
projector.
variable,
you would calculate the
Uncertainty =
2
uncertainty in your measurement (y
value)
Example: Distance of horizontal travel of a projectile launched at different angles.
Angle of
launch
(+ 5o)
Average
distance
travelled (m)
Uncertainty
in distance
travelled (m)
Trial 1
Trial 2 Trial 3
Trial 4 Trial 5
20
6.2
6.6
6.7
6.2
6.4
6.4
0.3
40
9.9
9.6
9.5
10.1
9.8
9.8
0.3
60
8.7
9.1
8.6
8.3
8.6
8.7
0.4
80
3.1
3.5
3.7
3.2
3.3
3.4
0.3
Horizontal Distance travelled (m)
Calculate the other uncertainties.
How would you write a measurement in your lab report?
(8.7 + 0.4) m
Remember:
Instrument uncertainty is the amount by which competent users might disagree
on a measurement.
» Instrument uncertainty might be given by the instrument or estimated by the
user
˃ For example, for digital instruments (like a digital scale) the instrument
uncertainty is usually + the smallest increment. So, if you measure 1.02 g,
the uncertainty is + 0.01 g.
˃ On analog instruments, the uncertainty is usually + half the smallest
increment. So, if you measure 25.35 cm with a ruler, then the uncertainty
is + 0.05 cm.
˃ Sometimes, humans can’t possibly be as precise as the instrument they
use. For example, a stopwatch might be exact to 0.01s, but there is no
way a human can react that quickly! The uncertainty of a normal person
using a stopwatch might be + 0.3 s.
» We report instrument uncertainty whenever we take a single measurement of
something … in experiments, this usually means our independent variable (x)!
A major part of any lab is evaluating the strength of your data, identifying the
possible sources of error, and suggesting improvements or further lines of inquiry
for the future.
DO NOT ANSWER: “I think my data are good because I worked hard and didn’t
mess up. I could do better if I had more time and better equipment.”
Instead,
» use your uncertainties to comment meaningfully on whether or not you can
really make a conclusion or find a trend.
» Think carefully about sources of error (often, these are poorly controlled
variables that are affecting your results, but sometimes your whole approach
may be flawed).
» If your uncertainties are really large you should explain why and suggest how
to reduce them in the future.
» If you obtained the expected results then think of a follow up question you
could study. If the results were surprising, think of a way to figure out why
you got those results.
LABS ARE NOT MEANT TO BE FUN, OR
EASY, OR TO BOOST YOUR GRADES.
(though, I do hope you enjoy it, and I always always hope you earn a good grade!)

We do labs so that you learn how to investigate a
problem and how to analyze data. By 11th grade, you
should know how to investigate a problem fairly well.
One of our big focuses this year, then, is how to analyze
data in a rigorous fashion.
(so, use this ppt as a reference AND DO YOUR BEST
WORK on the upcoming lab!!)
4. DRAWING A GRAPH
In many cases, the best way to present and analyze data is to make a graph. A graph is a visual
representation of 2 things and shows nicely how they are related. A graph is the visual display of
quantitative information and allows us to recognize trends in data. Graphs also let you display
uncertainties nicely.
When making graphs:
1. The independent variable is on the x-axis and the dependent variable is on the y-axis.
2. Every graph should have a title that this concise but descriptive,
in the form ‘Graph of (dependent variable) vs. (independent variable)’.
3. The scales of the axes should suit the data ranges.
4. The axes should be labeled with the variable, units, and instrument uncertainties.
5. The data points should be clear.
7. Error bars should be shown correctly (using a straight-edge).
Error bars represent the uncertainty range
8. Data points (average value ONLY!) should not be connected dot-to-dot fashion.
A line of best fit should be drawn instead. The best fit line is not necessarily
the straight line and should pass through all of the crosses created by the
error bars. Approximately the same number of data points should be
above your line as below it.
9. Think about whether the origin should be included in your graph (what
is the physical significance of that point?) Do not assume that the line
should pass through the origin.