2. » 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 ______________________ variable. » The variable that changes as a result of the independent variable is called 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 INDEPENDANT DEPENDENT Your knowledge and grade in physics is related to the amount of quality time you spend studying.. independent variable: ? dependent variable: ?

3. » If you are measuring the amount of bacteria over time, what is the independent and dependent variable? Independent Variable on the x-axis! Dependent Variable on the y-axis! The graph shown here is ok. Why only ok? The graph shows us the overall trend (average value). In science we care about BOTH the average value and some measure of the variation in the data.

4. 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: 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. 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. 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. instrument uncertainty uncontrolled variables Sampling from a population

5. » 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!

6. Measurement = (mean value ± uncertainty) unit of measurement uncertainty meanvalueuncertaintyMeasurement values The uncertainty shows the area around the average value where the true value of the measurement is likely to be found. Different sciences report the variation in their data in different ways. For example, biologists often use standard deviation. Physicists report measurement uncertainty. 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.

7. Calculating measurement uncertainty is easy! In an experiment, this means that for every level of your independent (x) variable, you would calculate the uncertainty in your measurement (y value) Angle of launch (+ 5 o ) Horizontal Distance travelled (m) Average distance travelled (m) Uncertainty in distance travelled (m) Trial 1Trial 2Trial 3Trial 4Trial 5 206.26.66.76.26.4 0.3 409.99.69.510.19.8 0.3 608.79.18.68.38.68.70.4 803.13.53.73.23.33.40.3 Example: Distance of horizontal travel of a projectile launched at different angles. Calculate the other uncertainties. How would you write a measurement in your lab report? (8.7 + 0.4) m I’m starting to understand measurement uncertainty, but what is that??? It’s the instrument uncertainty of the launch projector.

8. 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)!

9. 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.

10. 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 11 th 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!!)

11. In groups of 2-3, examine a graph. Can you understand exactly what data is shown? Is there a clearer way to convey the same data? Try to find as many flaws with it as possible. Also identify the good aspects of the graph.

16. 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. 6. Error bars should be shown correctly (using a straight-edge). Error bars represent the uncertainty range 7. 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. 8. 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. 9. The graph should have a legend stating what the error points represent (e.g. Error bars show measurement uncertainty.)

17. Descriptive title Descriptive headings AND units Should give both RAW data and PROCESSED data (averages,uncertainty) Data should be recorded using appropriate sig figs (use trailing zeros, if necessary!). Look back at the table in calculating measurement uncertainty for an exemplar

18. I will assign you to groups. Read the rubberband lab instructions, then do the prelab for your exit ticket.