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Plotting and Analyzing Data with Origin 7.5

To learn how to make a graph such as the one shown above, follow the discussion below the graph. Click on a feature of the graph, or the text links beneath it, to jump to the instructions for that feature.

Introduction

Origin is a convenient data analysis and graphics program that runs in Windows on PCs. You can use Origin to plot data, transform raw data to more meaningful quantities through column-based calculations, compare data to a theoretical model using linear and nonlinear least-squares fitting, and determine the quantitative agreement between the data and model.

Entering Data

You may type data directly into a data sheet or import data from the clipboard, from a text file, from an Excel data sheet, or from a large variety of other file formats. The action starts in the File|Import menu item, and you can learn about various file formats in the online help. Instructions for importing common kinds of data follow here.

Bear in mind this important point: the basic unit of data is the column. In Origin, a column may be designated to represent X values, Y values, Z values, X error bars, Y error bars, or labels. By default, the first column is called A(X), the second is B(Y), and additional columns may be added using Column|Add New Columns... You can set the function of a column using the column box obtained by double-clicking on the column head, or with the pop-up menu obtained by right-clicking on the column head.

Keyboard Entry

• Enter advances the cursor down the column
• Tab advances the cursor to the right
• Shift tab move one cell to the left
• Double click on the column name to edit column headings, and to set display formats and options

Import from the Clipboard

If the data exist in some other program, copy them to the clipboard, switch to Origin, select the upper left corner of the region of a data sheet into which you wish to place the data, and paste. If the data are not tab-delimited (e.g., comma separated values), this method does not work. Save the data in a text file and proceed with the following, instead.

Text Import from a File

For simple files, you can use the File|Open command to access the text file. Select the kind of file from the popup menu, then pick the file. If Origin's default options for parsing the text file don't work, try the File|Import command and provide more information about the structure of your data file.

Data Import from an Excel File

Origin 7.5 can work with data from Excel without having to import it into an Origin worksheet. Just open the Excel file with File|Open Excel.... On the other hand, performance may be better if you import the data. Just use copy and paste.

Calculations

You can enter values into a column using a formula based on another column.

1. Select the column into which you want to enter the results by clicking on the column name.
2. Choose Data|Set Column Values
3. Enter the formula you want to use in the text box. Useful functions include:
   • col(x): returns the value in column x. Note: x is the name of the column.
   • log(x): common log of x.
   • x^y: x raised to the y power.
   • sin(x), cos(x), tan(x): your everyday trig functions.
   • asin(x), acos(x), atan(x):inverse trig functions.
   • NOTE: all trig functions work in radians by default.
4. Set the rows for which you want this formula to apply (upper right-hand corner).
5. Click on Do It.

Plotting Functions

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Computing and Plotting Residuals

Residuals are the difference between the actual data points and the fitted line or curve. To compute residuals, you must first perform the fit. In version 3.5 or higher, you then select the same fit function from the fitting menu to bring up the fit dialog, which will now contain a popup View menu of options. Select Paste Residuals to Data Window... A column is appended to the data sheet linked to the graph, and given the title Residuals. (A new column is always generated, even if you already have a column called Residuals.)

To produce a panel of residuals on the graph, you must use the Double Y style. If you already have the graph made using another style, bring it to the front, go back to the Gallery menu and select Double Y and put the column of residuals on the Y2 axis. Then click to Replot the graph. Unfortunately, you have to fix up all the error bars again.

Plotting Data

A data set is placed in a single column. Each Y column is associated with the nearest X column to its left. These associations are indicated by affixing a number after the Y in the column heading. For example, a column marked Y2 is associated with the X2 column. In each layer, you can have multiple X columns and multiple Y columns. Unless you specify otherwise, a Y column will be automatically graphed against its associated X column. In addition, you can have a x and y error columns for each X or Y data set. Note that version 5 allows you to plotted data from more than one data sheet on a plot.

Once you have entered your data, do the following to create a graph:

Plotting Adjacent Data sets

1. Select the column holding the x data.
2. Choose Column|Set as X, or right-click on the column heading and use the Set As... menu.
3. In place of the previous two steps, you can double click on the column heading and select X from the Set Column As pop up menu.
4. If you have a (several) column(s) of errors:
   • Select the column(s).
   • Choose the command Column|Set as Error Bars (or choose Err Bars after double clicking on the column heading.)
   • For x error column, you will need to also choose Column|Error Bar Options and click on X error bar.
5. Select the x, y, and errors columns.
6. Choose the command Plot|Scatter.
7. It may be useful at this point to expand the window by clicking the up arrow at the right of the title bar.

Plotting Non-Adjacent Data sets

The procedure outlined above only works if all your columns are contiguous. If they are not, the following alternate procedure is necessary. Please note that all data sets that form a single data plot must be on the same worksheet.

1. Without any columns selected, choose Plot|Scatter.
2. Single click on the name of the column you want to hold the xdata.
3. Click on the X button.
4. Repeat this process for Y, yEr, and xEr.
5. Click on the Add button.
6. Repeat steps 2-5 for each y column. The x columns need not be the same.
7. If you want to remove a dataplot from the list of dataplots to be made, single click on it and then click on the Remove button.
8. Click on OK.

Resizing and Moving the Plot Layer

If you want to change the size of the layer, do it before adding any labels, so that you can pick a font size that fits the graph. There are two ways to adjust the size the layer or move it around on the page. The first is:

1. Double click on the gray plot-layer button in the upper left-hand corner.
2. Click on Layer Properties.
3. Enter new values of the height, width, left, and top.
4. Click on OK, then click on the new OK.

The other is:

1. Single click on a corner of the axes. They should change color,and eight control points should appear (one at each corner and the bisections of the sides).
2. To move the layer, click anywhere inside the axes and drag it to its new location.
3. To resize the layer, click on one of the control points and drag to a new size. The control points in the corner can be used to adjust the size both horizontally and vertically, while the control points at the bisections can only change the size in the direction perpendicular to the side.
4. When finished, single click anywhere outside the layer but still on the page. The old plot will now disappear, and a new one will materialize within the box.

Adjusting the Axes

Adding a Box Around the Plot Area

By default, Origin will put a frame around the plot area only if you plot the scatter type. If you made some other type of graph, you will need to add one. Here's how:

1. Bring up the x axis dialog box by either double-clicking on the axis or choosing Format|Axes|X Axis
2. Select the Title and Format tab
3. Click on the icon for the Top axis and check the box Show Axis and Ticks.
4. Format the ticks to go inward on all axes.
5. Click on OK

Adjusting the Scale

By default, Origin adjusts the range of each axis automatically. You can override its choice as follows:

1. Double click on the x or y axis, or choose Format|Axes|X Axis or Format|Axes|Y Axis
2. Enter a new value for the lower bound.
3. Press Tab and enter a new value for the upper bound.
4. You may want to adjust Increment, the distanc between two consecutive tick marks or enter the number of tick marks directly.
5. If desired, click on Goto X or GotoY and repeat this procedure.
6. Click on OK when finished

Fixing the Plot Symbols

Data points should be plotted as individual points with a symbol size that makes sense for the number of data points in the plot and the plot size. There should not be a line connecting successive points. Points should be shown with error bars, if available.

Turning off lines and/or modifying plot symbols

• By default, there should be no connecting lines.
• A dialog box for modifying the line and plot symbol can be brought up by double clicking on a data point in the plot area or by double clicking on the plot symbol in the legend.
• If you have several data series on the same graph, you will need to perform the following:
  1. Double click on one of the data series to open the dialog box.
  2. Click on the Ungroup.
  3. Click on OK.
• If you have a theoretical curve, it should be a function graph and not a normal data plot. However, its display (and other) properties can still be modified by double clicking on it.

Error Bars

The easiest way to put error bars on a plot is to "bless" the appropriate column(s) of errors before creating the plot. You can bless the column by right-clicking in the column head and using the Set As... command. Alternatively, you can add one or more error bar columns to a data set after the graph is made using the Plot | Add Error Bars... command.

Asymmetric Error Bars

If the positive-going error bar differs from the negative-going one, you need to have two error bar columns in your data sheet. Bless both of them as y error bars, as described in the previous section. Then make the plot. (Or add one or more error bar columns to an existing graph.) You will see two overlapping sets of error bars on your data series.

Now double-click on the error bar for a data point on the graph. A dialog opens that shows the name of the error bar column and has (among other items) check boxes positive and negative. Uncheck one or the other. Then repeat this for the second error bar on a data point.

Function graphs are exactly what their name implies: graphs of functions you specify. They are most useful for adding a theoretical curve to a plot of experimental data. The only restriction on the types of graphs is that y must be an explicit function ofx which can be represented using Origin's built-in functions. They can be added as follows:

1. Select Plot|Add Function Graph
2. Enter the function in the edit area.
3. Select other options as desired and click on OK

Annotating the Graph

You may add additional text labels using the text tool ("T" inthe Toolbox) and add lines, with or without arrows, with the line tool. Labels you don't want can be deleted by selecting them and pressing Del. In any text editing box, there are several buttons which can be used to embellish your text:

• B   bold.
• I   italic.
• +   superscript.
• -   subscript.
• U   underline.
• G   Greek

These may be used in one of two ways. One is to select text already written and then click on the button. The other is to click the button, type your text, and then end the effect by either clicking on Normal or pressing Right-Arrow.

These are some of the most important Greek letters:

Fitting Data

Fitting to a Line

The method described below makes use of Origin's built in linear regression tool. This has the advantages of being quick and easy, but has the disadvantage of ignoring the uncertainties (errors) in your data. It does not calculate a meaningful χ², so you cannot readily determine how confident you can be of the fit. In general, you should define an appropriate fitting function, as described in Fitting to an Arbitrary Curve.

1. If the linear regression tool bar isn't visible, selectTools|Linear Fit.
2. Make sure the data set you want to analyze is the active data set. You can do so by selecting the Data. There will be anX next to the active data set. If the data set is inactive, then click on it or press the underlined number to its left.
3. Click on the Settings tab.
4. Make sure that the Span X Axis box is checked.
5. If desired, check the Residual Data box. This will create a residuals column in the worksheet, which will make it easier to calculate χ².
6. Click on the Operation tab.
7. Check the the Error as Weight box.
8. If desired, check the Through Zero box. This forces the line to pass through the origin.
9. Click on Fit

The result will appear in the Script Window. You will need to enlarge the window and scroll up several lines in order to see it. To enlarge a window in Windows, click on the lower right-hand corner and drag it to the new size. You can cut and paste the results from there into a text label on the plot as follows:

1. Make sure there is already a text label for the text to go to, or click on T in the Toolbox to create a new one.
2. Select the text with in the script window, and chooseEdit|Copy or press Control-C.
3. Double click on the text label to open it.
4. Single click within the text edit area to de-select the text. This prevents that text from being destroyed when you paste.
5. Position the cursor where you want to insert the text.
6. Select Edit|Paste orpress Control-V.

Fitting to an Arbitrary Curve

The arbitrary curve fitter (called NLSF for Nonlinear Least-Squares Fitter) in Origin is both powerful and complex. Consult the Origin manual for a complete description of its capabilities. The following section will simply provide a tutorial for basic operation.

Warning: unless you set the options correctly, Origin 5 will NOT use your uncertainties, even though they appear on the graph, and will give incorrect values for χ² and the uncertainties in the fit parameters. Follow the instructions below carefully to be sure Origin does your fit correctly.

The example will be a linear fit function of the form y = mx+ b. This function has two free parameters, namely m andb.

1. Choose Analysis|Non-linear Curve Fit.
2. Choose Function|New or click on the button with a white piece of paper with just f(x) on it. (When you quit Origin, it will ask you if you want to save your new function. Choose Discard All.)
3. Enter a name for your function in the Name box.
4. Check the User-defined Names box.
5. Click in the Parameter Names box (alternatively, press Tab) and typem,b.
6. Click in the large equation box at the bottom and type the equation m*x+b. In general, you may use any of the functions listed above in defining your fit function.
7. Choose Action|Data set or click on the button with a matrix on it.
8. In the Datasets box, single-click on the dataset you want to be the y data and click on Assign.
9. Choose Options|Control or click on the button with a marionette on it. From Weighting Method, select Instrumental. This means it will take into account your y-error column when doing the fit.
10. Choose Action|Fit or click on the button with a green light on it.
11. At this point, you will need to set initial values for the parameters. Click in each box and enter the value you expect the parameter to be.
12. Make sure that the Use Chi-Squared formula for errors box is unchecked.
13. Click on 10 Iter.. If the fit goes less than a full ten rounds (the display will tell you how many rounds it completes) then you're done. Otherwise, click on it again. If you receive an error message or if the parameters never stop changing, see Numerical Note below.
14. Click on Done!. The curve will be plotted, and the results will appear in a text box on the plot.
15. Double click on the text box, and choose Black Line fromthe Show Background drop-down menu.
16. NOTE: the value of χ² is really χ² per degree of freedom.

Numerical Note

Nonlinear curve fitting is a tricky business. Most often its success rides on choosing initial guesses for the parameters that are close to the best-fit values. If they are too far away, the process may get stuck in a local minimum, unable to find the best fit.

There are four main possibilities that arise when Origin gives you an error message while during LM.

1. The function was entered incorrectly. For example, "mx" insteadof "m*x." Choose Function|Edit to correct the mistake.
2. The original parameters given were so far from the target the LM iterations headed in the wrong direction, eventually causing numeric overflow. Try entering different starting values.
3. The function being fit is discontinuous. This mainly occurs with trigonometric functions. LM only works with differentiable functions. You will need to change your data in such away as to make the function continuous.
4. The fitting involves either very large or very small numbers. The LM method is overly gross in the changes it makes, and the function heads of in the wrong direction. This can be corrected by constraining the variables to certain ranges. Choose Options|Constraints.

If Origin never settles on stable values of the parameters, then you probably have too many. Try either eliminating some of them or prevent them from being varied by clicking on the Vary? check box in the Fit window.

Printing Graphs

For use in a lab notebook, it is very convenient to print a version of your graph that is small enough to permit you to annotate the graph and explain its significance on the same notebook page. A graph with a plot area of about 4 inches by 3 inches is quite good for this.

Left to its own devices, Origin will fill the entire page. This is usually bigger than you want. To shrink it down, click on the lower right corner of the plot area until you get a square drag handle. Resize the plot area until it is the size you want. Even better, you can double-click the gray square at the top left corner of the plot window and enter the size you wish directly.

Written by Itai Seggev and Peter N. Saeta.

Copyright © Harvey Mudd College Physics Department 241 Platt Blvd., Claremont, CA 91711 909-621-8024 http://www.physics.hmc.edu/ WebMaster (at) physics.hmc.edu Last modified: 05 January 2010