Tutorial 3: Data Analysis.

In an experiment to find the value of a resistor, the voltage across the resistor was varied and the consequent current was measured as in the table below. Using the relation V=IR, find the value of the resistor. (The instruments were carefully calibrated before use to eliminate offset errors)

This problem is representative of how Osiris might be used in the laboratory. In such a situation, data points can be entered as collected in order to provide a constantly updated graph - allowing the user to spot points which do not agree with the trend. Since such points often imply that something of interest is happening, these can then be duly investigated.

Before starting, we must consider exactly what to plot. Traditionally, the variable which is altered (in this case the voltage) is plotted on the x axis and the variable measured (in this case current) is plotted on the y-axis. We can rearrange the equation V=IR to become . From this we deduce that if the current is plotted wrt the voltage, the gradient should be the quantity - compare it with the equation of a straight line, y=mx+c.

• Create a new file, "Example5", in Osiris using the System screen or the "New file" option in the "File" menu (PSION-N).

Before entering the data, it is also a good idea to set the Ranges and Grid to sensible values.

• Select the "Range" option from the "Axes" menu or press PSION-R.

• Fill in the dialog as follows:

  Show axes	Yes
  X minimum value	-1
  X maximum value	16
  Y minimum value	-0.01
  Y maximum value	0.15

• Press Enter to Complete the Dialog.
• Press PSION-G or press Menu and select "Grid" from the "Axes" menu.

• Fill in the dialog as follows:

  Grid	Manual
  Grid colour	Grey
  X interval	1
  Y interval	0.01

• Press Enter to Complete the Dialog.

We shall now enter the data. Our data points have negligible error in V and an error of +/- 0.001 A in I. We can use this to give the points error bars.

• Select "Plot" from the "Graph" menu or press PSION-P.
• Use the arrow keys to select "Data point" from the list of options presented and press Enter.

• Fill in the dialog as follows:

  Plot Colour	Black
  X value	2
  X error	0
  Y value	0.022
  Y error	0.001

• Press Enter to Complete the Dialog.
• Enter the other points in the same way - It is quite useful to do this in list view as you can see what you have already entered.

To find R, we must plot the line of best fit for this data. This is done by a "utility" - a small program which extends the functionality of Osiris. Utilities could, for example, provide either a macro for a commonly used graph or a mathematical function not related to graphing. If you have a little knowledge of OPL, you can write your own utilities.

• Select "Utility" from the "Tools" menu or press PSION and the "-" key.

A description of all the utilities which are currently installed is displayed. Two linear best fit utilities are provided: "Least-squares best fit line" and "Origin-forced best fit line". The former uses a least-squares method to fit a line to the data, the latter does the same except that the line is forced through the origin. It is important to consider which to use very carefully - just because the line theoretically goes through the origin does not always mean that it should be so plotted due to the possibility of a zero offset error in the readings. In our case, as the instruments were calibrated, we can safely use the "Origin-forced best fit line" utility.

• Use the arrow keys to select "Origin-forced best fit line" and press Enter.

The dialog displays the gradient of the line which is 0.01001188. The resistor's value is the inverse of this value, ie about 100 Ohms.

• Press Enter to plot the best fit line. If you are in the list view, change back to the graph view with the diamond key.

Now that you've completed this tutorial, you should understand how to enter data points with errors and display a line of best fit for your data. You should also understand how to launch utilities from Osiris.

As usual, a list of suggestions for further experimentation are provided. Do make sure you have saved your work before you try them - use "Save" from the "File" menu or press PSION-S.

• Try some of the other utilities provided with Osiris. More will be added as Osiris develops so the list below is not exhaustive.
  • Quadratic equation solver - Finds the value of x for a quadratic equation by formula. This utility is used as an example in Tutorial 6 which shows you how to write your own.
  • Vector product calculator - Calculates the vector or "cross" product of two three dimensional vectors.
  • Scalar product calculator - Calculates the scalar or "dot" product of two three dimensional vectors.
• Delete one of the data points and replace it with a value which is out - 0.017 A, 1.0 V for example. Notice that the best fit line automatically changes with the new value.
• Try choosing "Constants" from the "Tools" menu and then "Edit constant". A number of new constants have appeared! These are updated every time the graph is redrawn by the data analysis plugin. You should be careful not to use these names for your own constants.

  xsum	The sum of all the x values.
  ysum	The sum of all the y values.
  xysum	the sum of the products of the paired x and y values.
  xxsum	The sum of the squares of the x values.
  n	The number of data points.
  xavg	The mean x value.
  yavg	the mean y value.

• Look at "Example5" in list view again. You will see that the line of best fit has been added as a Cartesian equation in terms of the above constants.
• Check that these constants are changed every time the graph is redrawn: delete them all and then redraw the graph with "Redraw" from the "Graph menu" (Psion and the "+" key together). Once the graph is redrawn, check to see if they're still there.