Hints for finding error in your experiment

You should be able to answer the following questions about ALL the data you collect in each of the labs you do this semester:

• Is my data any good?
• Can I throw out this point?
• Is this value close enough to this other value to be able to say they are equivalent?
• Which of the measurements that I have made are most likely to cause the biggest source of error in my answer?
•  Is a graph of the data going to show me something useful or significant?

Is my data any good?

• Precision tells you how much spread there is in your data and indicates how carefully you did the experiment. Precision is reported as a confidence limit which is determined from the standard deviation.
• Accuracy (reported in your lab write up as relative error) measures how far the mean of a set of data points is from the accepted or true value.
• So if you make very careful measurements with a bent meter stick, your measurements will be precise (a small confidence limit) but not accurate (large relative error).

Can I throw this data point out?

• Use a Q-test to see if you can throw out a point. You only apply a Q-test once to a set of data. Do not use a Q-test on data you are going to graph.

Is this value close enough to this other value to be able to say they are equal?

Suppose you have a value of 10.3 meters with a confidence limit of ±0.2 meters. So the measured value is between 10.1m and 10.5m. Now suppose you get a second set of data by another method for the same measurement (you think they are suppose to be equal). This second set gives you a reported value of 10.4m ± 0.2m. Have you proved that the values are the same? Well, the range on the second set goes from 10.2m to 10.6m so it overlaps the range of the first set. So yes you can conclude that the two measurements give the same result (at least to the precision of your results).

Which of the measurements that I have made are most likely to cause the biggest error in my answer and how do I know?

In several early experiments this semester you calculate the angle of an incline by measuring the height of one end and the length and use trigonometry. For example suppose you measure a height of 3cm and an lenght of 99cm. Using inverse sine you get an angle of 1.736^o. Now suppose you missed the 99cm by 1cm so that the true value is 100cm. In that case the angle is 1.719^o. You have a relative error of 1% between these answers. Now suppose the height is off by 1cm so that the true value is 4cm. This gives an answer of 2.316^o with a relative error of 28%. Obviously you will want to measure the height much more carefully than the length in order to avoid error in the angle. This is true in many experiments: The acuracy of some measurements affect your outcome more than others. You should always try to determine if this is true in every lab and if so, report which measurements are more critical and why (give a sample calculation like the one above).

Should I make a graph of my data?

A graph is used when the data is expected to change for each measurement. Suppose you measure the height of the same tree every year in a biology experiment. You do not expect to get the same answer each year, so it would not make any sense to find the average of the numbers you collected nor does it make sense to find a confidence limit or do a Q test because each value is suppose to be different. (Notice that the formulas in part I above are useful only  when the data is expected to be very close to a constant value. Do not use those formulas for data on a graph!)

 All graphs should be done with a computer program for graphing or graphing calculator. No hand drawn graphs will be accepted for any lab.

Most of the graphs for this lab will be straight line graphs. In the micro computing labs on campus there are copies of the program called Graphical Analysis which is available for both Apple and Windows computers. You may use other graphing programs as long as they will do a linear regression (least square) fit (no pie charts please!). You may also use your TI-82/85/86 to do the regression line and print the screen in PS100.