The Biology 331 How To Manual by Dr. Donna Giberson

Transcription

1 An excerpt taken from: The Biology 331 How To Manual by Dr. Donna Giberson Donna J. Giberson, Dept. of Biology, UPEI

2 15 Part 3 Graphing basics (Using Microsoft Excel 2007 and Minitab 16)

3 16 A. Getting started: The basic Line Graph One of the most common types of graphs is a line graph or x-y graph where you just plot one set of numbers against another. We ll start with that to get you started in graphing with Excel and Minitab. The first part of this section will run through graphing basics in both programs, including how to set up the data and how to customize the graph to make it suitable for scientific data reporting. Then we ll go through each graph type individually to see how to set them up. Note: Excel is a business related spreadsheet program, and though it allows you to make graphs, the graphs are clunky and difficult to customize for scientific reporting. This section of the manual will show you how to do this customizing, but graphing programs are much easier to use for most purposes. 1. Basic graphs in Excel 2007 Scatter plots (also known as X-Y graphs) For this example, we will return to the Pulses dataset, and graph height vs weight of our student participants. Remember that the independent variable (the one that is set by the researcher, or which doesn t change) goes on the x-axis, and the dependent variable (the response variable, or the one we expect to change based on x ) goes on the y-axis. In this example, height is fixed, so it is the independent variable, and weight is the dependent variable. To plot in Excel, data to be plotted must be in adjoining columns. Method: a. Setting up the data: Highlight the data you want to plot - Click on the Insert tab on the upper property bar, then choose scatter plot. For this example, choose the option with no connecting lines. Excel will generate an automatic graph that is far from the sort of graph you need to show your patterns. The problems include: a) no axis titles b) a meaningless title c) gridlines, and no idea of units d) the points are crowed at one end of the graph remove redundant objects remove gridlines add axis titles and units

4 b) Customizing the graph: i) range of axis numbers (to fix the crowding at the right side of the graph: - click on your graph to make the Chart Tools layout appear at the top of your page if it isn t visible 17 - click on axes to get into the axis menu on the Chart Tools Layout tab. In this case, we want to alter the x-axis, so click on the primary horizontal axis, then click on more primary horizontal axis options This will open the Format Axis window, which will allow you to set your axis options. - change the checkmarks from Auto to Fixed in the axis options, then type in the values you want. For example, you may want to set your minimum value at 55 rather than zero, and then your major units should go up by 5 rather than 20.

5 18 You should see a definite improvement immediately, but there are still many things that need to be done to make this an effective graph. ii) turn off grid lines - return to the Chart tools layout tab, and click on gridlines - pick the primary horizontal gridlines, then choose None. iii) remove titles or other objects that don t add to the graph information (e.g. Series in the graph above, or any title that might appear at the top of the graph) - simply highlight it and press delete iv) adding axis titles add the axis titles by going into the Axis Titles menu, and choosing the axis. This will place an axis place holder on your graph, and you can simply type what you want (remember to add units). If you need to change the font size, right click on the title and choose font from the menu.

6 19 Now you have a passable graph, but one that can still be fixed. Some suggestions include removing the outer box, changing the point symbols to something that look nicer, and perhaps spreading the points out a bit more to make them look better. v. removing outer box - right click on the outer part of your chart to get the chart menu window: - click on format Chart Area to get the chart format window: - Pick the tab for border color and choose no line vi. Changing the point symbols - click on the points on the graph to highlight them, then right-click to open the data series menu. Choose format data series

7 20 - in the format data series window, choose the tab for Marker Options - Check the box beside Built-in then choose the shape and size from the drop-down menus. I recommend simple dots and a point size of about 2 (if you have different data sets on the graph, you can choose dots and squares, for example). - to change the colour of the points, choose Marker Fill and Marker Line Color and choose the colour you want (usually black, unless you have different data sets shown with different colours). Note: the points in Excel are made up of two colours; one for an outline ( marker line color ) and the actual point ( marker fill). You will have to change the colour for both of these to get your points to be the new colour. Our new graph is now ready to use and just needs a Figure legend (see the section on making table and figure legends in the Part 3, Tables): (see p. 10) Figure 1. Relationship between height and weight in a group of university students taking part in a running study.

8 21 vi. Trend line: Finally, if you would like to add in the trend line (the regression line showing the best relationship between the two variables, just click on Trendline in the Chart tools layout menu. c. Specialized line graphs: i. Plotting two datasets on the same graph Example: Can we plot height against weight for our student participants, but separate out the male and female students and see them as separately coloured dots? To do this in excel, we need to go back to our dataset, and do some sorting and moving of data.

9 Note: the data set-up is critical for this section: 22 The data should be set up so that you have one column for the independent (x-axis) variable, and then a column for each of your dependent variable groups. However, you have to have these data in order from smallest to largest first, so will have to sort the data. - copy and paste the columns with sex, height, and weight into another part of your spreadsheet. - sort the data by your independent variable (in this example, height) - now leave the data for one sex in one column, and move the data for the other sex into the next column - highlight the three columns of data (just the numbers) - click on Insert from the upper property bar, and choose scatterplot as for the first example. As with the first example, you see a graph that has all the points crowded over to the right, and many problems in formatting. Follow the instructions from the start of this section to customize your graph. Go through the steps to customize your graph, to get a professional graph that looks like the one on the right. Note: it is a lot of work to get a nice graph in Excel, but it is possible. You ll likely find Minitab to be much easier.

10 23 ii. Graphs with two Y-axes, and 2 sets of data It is fairly easy to plot multiple graphs on one page, but not so easy to plot data so that they have two different y-axes. We ll use a sample set of data from Bio 326 to illustrate this. Consider a set of data like the one below. You would like them plotted on the same graph with a single x-axis but the y-axis ranges are so different you would like to be able to set up two y- axes, with different scales on them. First you must set them up to have a single x-axis, by copying and pasting the data: -put the x-axis in one column, and the two y- axis numbers as shown 1. Highlight your data, and click on the Insert tab, then scatterplot. You can pick the scatterplot with no lines, scatterplot with a smoothed line, or scatterplot with straight lines The graph you get won t be quite what you want yet; be prepared for a bit of customizing.

11 24 2. Double click on your chart to highlight it. Then look for the format tab in the top property bar. 3. Click on the arrow beside chart area in the upper left corner, then choose the series you want to put on the other y-axis from the drop down menu. In this case it is the partition coefficient. Then click on Format selection to get the window to format the data series. Under the series options, check the box for secondary axis and press close

12 25 You ll now have a chart that shows both axes, and the data will be better spread out on the x-axis. This doesn t help you to spread things out over the x-axis, but it does help with the y. note that it may be possible to put a break in the x-axis if there is a large range between the sets of data, but with these, there is overlap, so that may not work. Next, you re going to want to add axis labels, get rid of grid lines and the like. The bio 331 lab manual covers these things (e.g. axis labels are on p. 77 and other tips are on p ) After going through that, you should have a graph that looks like the one below, or at least customized to the point that you like it. Don t forget a complete and descriptive figure legend!

13 26 2. Basic Graphs in Minitab version 16 a) Setting up the data - depending on the type of graph being made, data will need to be in adjoining columns, a single column, or a single column with a grouping variable in another column. We ll start with the simple scatterplot, with data in adjoining columns. The example to the right is the Pulses dataset from our discussion of spreadsheet basics. Notice that the minitab window is broken into a session window and a worksheet window. To graph the scatterplot (x-y graph), click on graph from the upper property bar, and select scatterplot from the drop-down menu. Notice that a large number of graph types are shown in the list; we ll cover some of the other types in a later section. 1. select the scatterplot at the top of the list., then select the simple scatterplot from the list of scatterplot types. -click OK

14 27 2. Choose the data to be plotted. - place your cursor in the cell just below Y variables, then choose your y-axis variable by highlighting it in the list at the left. Once it is highlighted, click on Select - place your cursor in the cell just below X variables, then choose your x-axis variable by highlighting it in the list at the left. Once it is highlighted, click on Select Remember that the independent variable should be on the x-axis, and the dependent variable should be on the y-axis. Choose your variables and place them in the appropriate boxes (In this case, we re trying to predict weight from a person s height, so we ll put height as our x- axis and weight as our y-axis) Your starting graph will look like this: This graph starts out in much better shape than the Excel graph did, but we still need to do some things to make it look more professional to include in reports. The things that are wrong with this graph are: - missing units for the axis labels - font size for axis labels and numbers should be larger - the outer box around the graph should be removed, and the inner box should have the top and right line removed - the title should be removed - the shading outside of the graph area should be removed. double- Note: Most manipulations of Minitab graphs can be done by clicking on the part to be changed

15 28 a) Basic Customization of the Minitab graph: i) adding units and changing fonts of the axis titles: - double click on an axis label to get this window: - change the font size and add in units to the text window. In this case height is given in inches. - change the weight as well, to give weight in pounds - Capitalize the axis titles. ii) changing font size of the axis numbers to make them easier to read: - double click on the numbers of the y axis to get the y- axis edit scale window - click on the Font tab to change the font size - repeat for the x-axis iii) Removing the right and upper axis lines: - click on the Show tab of this edit scale window. Remove the checkmark for the high box in the axis line. Repeat for the other axis. iv) Remove title from top of graph (Note: do not include a graph title if you have a figure legend) - highlight the title, and delete

16 29 v) Remove the outer box and shading around the graph: - double-click anywhere on the shaded part of the graph to open the edit graph and figure regions window. - click on the tab for Figure Attributes - For Fill Pattern, check Custom, then choose N for none in the Type box - For borders and fill lines, check Custom then chose none in the Type box - click on the tab for Graph attributes - under borders and fill lines, check custom, and choose None. vi) change colour and shape of points being graphed - double click on your points to enter the Edit Symbols menu. - click on the small arrow beside Automatic to see the colour chart, and choose your colour. Now you have a professional quality graph that you can add a figure legend to and submit to your instructor.

17 30 vii) adding the trendline to your graph: - you need to specify that you would like the trendline from the start of the graphing process in Minitab, so choose Graph from the property bar, and select Scatterplot, but this time, choose the option with the regression line. Work through the steps of selecting your data, and customizing the graph as shown in the previous pages to create a graph that looks like the one below: Remember to add a Figure number and legend to your graph... see p. 10 for how to construct a figure legend.

18 31 c. Specialized line graphs i) two sets of data on the same graph (e.g. data where you can separate out groups, such as males and females) - choose graph from the property bar, then choose scatter plot from the drop down menu. - now choose the with groups option. If you choose the with Regression and Groups, it will also plot the trend lines for both groups for you. In this example, we will plot the height and weight data, separated out by the sex of the participants. This time, our dialogue to select the data also allows you to specify grouping variables. You don t need to manipulate the data as you did in Excel, but just need to specify what your groups will be: - Select your dependent and independent variables, as you did for a simple graph (by placing your cursor in the cell for the y or x variable), then highlighting the variable from the variable list, and clicking on select. - Now place your cursor in the Categorical variables box, and then highlight your grouping variable (in this case, sex), and click on select. -click OK

19 32 Your base graph will look like the one at right Customizing hints (details of these operations can be found in the previous section): - remove title by highlighting and deleting - double click on each axis label to change the font, add units, and capitalize the labels. - double click on the shaded area of the graph to change the graph and figure attributes so there is no outer box, upper and right hand axis line, or shading. - double click on the axis numbers if you want to increase their font size - Key: - click on the Key and drag it to another place on the graph if you wish to - double click on the numbers (1 and 2) for the key for sex, and type out the entire name for male and female to make it easier for the reader to follow - double click the full legend to change the font of the words in the key (you may need to resize the text box with the key to make everything fit. Your final graph should look like the one at right:

20 33 ii. Graphs with 2 different y-axes (This is example is from Bio 326, General Physiology, where the x-axis is hemolysis time, and the y-axes are molecular weight and partition coefficients (x100) - set up data so that the y data are in different columns - click on graph in the upper property bar, then choose scatterplot from the drop down menu. Now choose with connect and groups for your graph type. [note: a "regression" line is the best straight line for the data. the "connect" line joins the dots with a line] - now choose your variables. Hemolysis time is the x-axis variable for both, and the other two are the y-axis variables. - now click on Multiple Graphs and make sure the overlaid on the same graph box is checked. - click OK, to get the first draft of your graph (which will need to be customized, as in the previous section).

21 34 You can remove the outer boxes and shading, alter the font of axis labels and numbers, and modify the axis labels as explained in the previous section. To see the second (right hand) y-axis, first double click on the y-axis numbers on the left side of the graph. 1. Double click on y-axis numbers to get the edit scale dialogue 2. Click on the tab for secondary in the top row of tabs 3. Choose which axis you d like to have on the left (primary) and right (secondary). Click on the arrows to the right of the scale boxes to make your choice. 4. Customize the graph to produce the range of axis numbers and other attributes that you want, to achieve a graph looking something like the one at left.

22 35 b) Bar charts to show differences among groups Types of Bar Charts: - Bar charts - Bar charts with error bars - Box and Whisker plots Note: Frequency Histograms are a different type of bar chart which will be covered in the next section. (p. 63). Spreadsheet packages vs graphing/stats packages for graphing data: A big difference between professional graphing packages and spreadsheets is that spreadsheets won t do graphs that require analysis before plotting them (in other words, if you want to plot the average values for a column, you have to do the averaging first in Excel then the plot average values, whereas a graphing package will do the averaging and plotting in one step). You may find it easier to work with graphing/stats packages for most of your graphing than try to struggle with the spreadsheets. Purpose of a bar chart or Box & Whisker plot - these plots allow us compare average (mean or median) values for groups of data, and if error bars are included on the plots, we can also gain important information about the overall spread of the data. For example if we were comparing the numbers of chipmunks captured in three locations on PEI, based on sampling a number of areas within each site, our data might look like this: sample area Site 1 Site 2 Site mean Standard Dev. (or Std. Error) In Excel, we would have to calculate the average and standard deviation, then plot those values. In Minitab, the computer will do these calculations for us.

23 1. Plain bar chart and bar chart with error bars in Excel 2007 Method: - Enter data (or open data set) for manipulation. Use the arithmetic functions in Excel to calculate the mean and standard deviations (or Standard Error, or 95% confidence Limit, whichever error bars you are using). Then set up two columns of data as shown for your means and standard deviations (or other error values). 36 If you need the standard error, calculate it using the equation: SE = SD n set this up so that the groups you wish to compare are in different rows. a) Simple bar graph - Highlight the data you would like to plot, including your column with the text labels. (For this example, do not highlight the SD column, since we are not plotting the error bars) - click on the Insert tab on the upper property bar, then choose column in the graph menu (Note: Excel calls the simple bar chart a column graph). - choose the simple 2-D column Note: Never use 3-D graphs unless you have data with 3 variables, where you plot 3 axes on your grapy.

24 37 You ll see the simple bar graph, allowing you to compare the numbers of chipmunks found in the three sites. -We will return to how to customize the graph to make it more professional looking when we ve learned how to add error bars to the graph. (p.39). b) bar graph with error bars: Excel has a function for plotting error bars on graphs, but the basic function just plots the same error bar on each graph. Follow the instructions below to get differential errors plotted. - Highlight the mean values as in the first example - Double click on one of the bars to open the Chart Tools tab on the property bar - Click on the Layout tab - Select Error Bars, then select More Error Bar Options

25 38 - In the Format Error Bars window, decide if you want to have error bars that just go above your bar, or if you want them to go in both directions. - click Custom, and then specify value. - in the Custom Error Bars dialogue, click on the small red arrow at the right. That lets you go back to your spreadsheet to highlight the data values you want. Highlight the three values below SD, and click on the red arrow again, and click OK (Note: if you need Standard Error, Calculate it from the equation on p. 36, and made an SE column) - now click Close In other words: 1. Click arrow, return to spreadsheet and highlight values 2. Click arrow in smaller window to return to larger window 3. Click OK

26 39 c. Clean up the graph What needs to be done? - remove gridlines - remove Series 1" (key not needed unless there is more than one dataset) - add Y-axis label with information on Std. Dev. and units (does it need a further x-axis label?) - remove outer box on graph - make the bars look more professional (change to colour black, change spacing between the bars) To start, double click on any bar to open the Chart Tools menu. Click on the Layout tab: a) horizontal gridlines: click on Gridlines on the Chart Tools layout, select Primary Horizontal Gridlines, and choose NONE. b) add axis title to y-axis: - Choose Axis titles from the Layout tab, then Primary Vertical Axis, then Rotated Title. This will automatically place a title into your graph. Highlight it and type your title, including units. Change font size if necessary from the font menu under the Home tab. c) remove objects (such as series by clicking and deleting

27 40 Your Graph so far: - still need to remove outer box and tidy up the bars d) remove border: - Right click on the outside border of the graph, and click on Format Chart Area. - Change the Border Colour to no line from automatic. e) format bars Bar colour: Choose the bar colour from the Design tab under Chart Tools, or right-click on any bar, and click on Format Data Series (see next page), and click on Fill and Border colour.

28 Bar Spacing: Bars representing separate groups should be separated from each other should only touch when they represent a graded series of numbers (such as we find in a frequency histogram). To set up how close bars are to each other, right-click on one of the bars, and choose format Data Series from the menu. 41 In the Format Data Point dialogue, you can change this spacing. - Series overlap refers to cases where you have groups of data (e.g. if you were looking at male and female chipmunks in each of your three sites, you might want to group the males and females a bit closer together than the sites). A good value for this (if you have groups within your groups) is -20% - Gap width lets you change the distance between each series (i.e. each site). A good value here is usually 50% of the actual bar width for a single series and 70% to separate out groups. Your final graph is a professional looking product that you can submit with your assignment.

29 d) Bar graphs with groups For this example, lets look again at our chipmunk example, but assume that we have data for both males and females. 42 sample area Site 1 Site 2 Site 3 males females males females males females mean Standard Dev. Standard Error Construct your bar graph as in the previous example. - Highlight the values (and their group labels) to make a group graph. - Choose Insert on the property bar, then Column from the graph menu. - Choose the simple 2-D graph

30 43 Your graph will show your data grouped by your grouping variable (in this example, it is the sex of the chipmunks) Add the error bars using the same method as for the ungrouped data (p. 38) - double-click on any bar in the first series (e.g. the bars for the males) to open the Chart Tools menu, and choose the Layout Tab, then Error Bars, and finally More Error Bar Options (exactly as in the previous example). In the Format Error Bars dialogue: - Choose the error bar display (e.g. bars extending above the bar) - Choose the values by clicking Custom then clicking on the small red arrow to re-enter the spreadsheet to highlight the SD column (or other error values, e.g. SE) for the series you re working on (in this case the males) (see p. 38 for full example). Click OK - Repeat for the other series (females).

31 Customize your graph as before (p ) to obtain a professional quality graph. The base graph to this point is shown at right: You still need to: - turn off gridlines - add y-axis label - adjust font size as necessary - adjust range of y-axis numbers - choose colours that are more professional looking 44 After customizing your graph, it should like this one: Remember to add a legend to your graph: see p. 10, in the Table Basics Section.

32 2. Plain bar chart and bar chart with error bars in Minitab a) getting started: data entry in Minitab (see the data entry section on p for more details) Different formats of data entry (different ones are needed for different types of analysis) 1. Data in adjoining columns (see columns C1-C6 above) 2. Data in one column (C11), grouping variables in other columns (C7 and C10) 3. Combination: two groups of data in adjoining columns (male data vs female data) but site in one column For most analyses in Minitab, we set it up as in scenario #2, with data in one column, and grouping variables in other columns.

33 46 All Graphs in minitab: - Select Graph from the property bar, then select your graph type from the drop-down menu. For a simple Bar graph with no error bars, choose Bar chart (For a Bar graph with error bars, you will need to choose Interval Plot - we ll return to these when we ve covered the simple bar chart.) Example 1: Simple bargraph, male data only (e.g. splitting the dataset) -This is an example of when you only want to use part of your dataset. - there are two ways to do this: A. Leave data in one format, and let Minitab split the data for you B. Physically split your dataset so the part you want is in one column (e.g. males) a) Let Minitab split the dataset for you: 1. Select Data from the upper property bar 2. Select Split worksheet from the drop-down menu 3. select the variable by which you d like to split the worksheet (in this case, we want the males, so we ll split it by sex)

34 47 This will split your worksheet into 2, one for the males and one for the females. This is the preferred way to handle your data, since you don t have to be doing as much copying and pasting. If you choose this option, follow the instructions below, but use the Male worksheet, and choose column C11, abundance b) alternatively, you can manually organize data so that the male abundance data are separated from the female data (i.e. you would set up and use column C8 in the example above). Once you have the data ready to graph: 1. Enter the Bar Chart dialogue by selecting Graph from the property bar, then Bar Chart. - Choose a function of a variable from the drop down menu - choose simple for the bars. - click OK

35 48 2. Select your variables (note: if the variable box on the left is blank, click your mouse in the graph variables white box. - make sure that Mean is selected in the Function box - select the column of data you want to plot (It would be the male abundance column if you manually split the data, or the abundance column if you let Minitab split the data for you) - click select - select the grouping variable (in this case, we are plotting by site, so select site - click OK 3. Here is the base graph to begin customizing i. Remove title ii. Increase font size for axis labels, and give y-axis a better title iii. Make the bars look more professional iv. Remove shading and boxes Most changes in Minitab are made by double clicking on the part of the graph you want to fix i. Remove title by clicking on it, and deleting ii. Fix axis labels: - Y-axis: double click on label to enter the Edit Axis Label dialogue - change font as desired - type in new text for label - check box for apply same font - X-axis: double click on label as above

36 49 (Axis labels, continued) - double click on the left hand Y-axis to enter the Edit Scale dialogue - to change the range of numbers, click on the scale tab - to change font, click on Font tab - to remove extra (right hand) y-axis line, click on show tab, and uncheck the box under high - double click on the x-axis to enter the scale dialogue for the x-axis - to remove upper x-axis line, click on show tab, and uncheck the box under high iii. Make the bars look more professional: - to change the colour of the bars, double click on any bar and change borders or fill from the attributes tab. - to change spacing between the bars, double click on the x-axis to enter the Edit Scale dialogue - Select the Scale tab - uncheck the box beside Gap between clusters and type in a different value. (0.5 means that the space between bars will be 50% of the width of the bar) iv. Remove shading and outer boxes - Double click anywhere in the shaded region - Set the Graph attributes and Figure attributes to custom and then set the type so that borders and fill lines are set to None and fill patterns are set to N - click OK

37 50 Your graph is now ready to submit: 4. One final thing you could do to customize this graph is if you know the names of your sites, you could type the actual names in, rather than just leave it as numbers you ll have to explain: - To change your x-axis labels: - double click on your x-axis to open Edit scale dialogue - click on Labels tab - check the box beside Specified - type in the values you want (e.g. Bonshaw Cavendish Cornwall Bonshaw Cavendish Cornwall Figure 1. A comparison of average male chipmunk abundance from three locations on PEI, Summer 2011.

38 Example 2: Simple bar graph, both males and females on the same graph 51 See p for setting up the data to graph 1. Select Graph from the property bar, and choose Bar graph from the dropdown menu 2. In the Bar Chart dialogue, Select the A function of a variable option from the drop down menu, then choose Cluster for your graph type. - click OK 3. In the Bar Chart function dialogue, make sure the Mean function is selected, then choose your variables: - your graph variable should be the one with the data numbers in it; for this example, it is abund - your grouping variables will be the ones you want to see for your groups: - the first one should be the major grouping (in this case, site) - the second one will be the sub-grouping (in this case, we want to see sex grouped within the site groups, so choose sex 4. Customize your graph: - remove title - remove outer box & shading - type in appropriate Y-axis and x-axis labels - make sure axis fonts are large enough - make sure bars in subgroupings are not touching -see pp for details on customizing.

39 Example 3: ungrouped bar graph with error bars (see p. 45 for how to set up data) note: Minitab will plot bars with the 95% confidence limits or with the Standard error of the mean (not with the standard deviation). Therefore, if you must plot the standard deviation, you should use another graphing program, such as Excel. 52 Error bars on a graph give information about how variable the data are, so we can assess whether our averages are really different from each other. 1. Standard Deviation (SD or s): Fig. 1. Comparison of mean abundance of male chipmunks from - this tells us how much variation there is plots (n=8) in three PEI localities, summer, in a single dataset. If data are normally distributed, 66% of the data points should fall within one standard deviation of the mean. 2. Standard Error of the Mean: - this tells us how reliable we think the mean is, based on the variation in the data set (SD) and the sample size in our data (n). SE = SD n - this value indicates that the mean has a 66% chance of falling within the bounds of the SE 3. 95% confidence limit: - this is related to standard error (SE) in that it assesses how reliable or accurate the mean is, but indicates that the mean has a 95% chance of falling in the bounds shown. Method: 1. Set up data so that columns to compare are in adjoining columns (see p. 45 for example). 2. Select Graph from the upper property bar, and choose Interval plot from the drop down menu 3. In the Interval Plots dialogue, choose multiple Ys, simple (since you have multiple data sets & no groups) 4. Select your data: Select the columns with the data you want to compare (you can highlight them all in one step by holding the [control] key down as you click on the variables) 5. Click on the [Data View] button

40 6. In the Interval Plot - Data View dialogue, check the boxes beside interval bar and bar - click OK to return to the previous dialogue, and click OK again. 53 This gives you your base graph, ready to customize: 1. Remove title: click on title and delete 2. Remove shading and outer box: double click on shaded area, and set all the figure attributes and graph attributes to Custom, then set the fill and border options to None or [ N ] 3. Type in an appropriate Y-axis label: double click on the label (Data), to enter the Edit Axis Label dialogue for that axis, and make the changes. Repeat for X-axis 4. Increase Y-axis font size: Double click on Y-axis and change the font size using the Font tab 5. X-axis Labels: Double click on the labels to enter the edit scale dialogue; click on labels tab to change the label (as shown at right), and click on the font tab to change the font size.

41 54 6. Specifying the error bars: Minitab provides the 95% confidence limit by default, so you need to change this to the Standard Error. - double click on any error bar To change the colour: - in the attributes tab, click custom, then click on the arrow beside the Colour box. Choose Black To change the type of error bar and its direction: - in the Options tab, Check the box beside Standard Error, and choose upper one-sided from the drop down menu. - click OK

42 55 Example #4: Groups with Error Bars (See p. 45 for how to set up the data for graphing; data should be set up with the data in one column and the grouping variables in other columns) 1. Select Graph from the property bar, then choose Interval Plot Fig. 1. Comparison of average abundances for male and female chipmunks in three locations in PEI, Summer, Choose Multiple Ys with groups and select variables as shown. - graph variable should be the column with all the data numbers in it - categorical variables should be the groups: the first one is the main group, and the second is the subgroup. 3. Click on Data View and check the boxes beside Interval plot and bars. Uncheck any other boxes. Click OK to get the base graph for customizing.

43 56 1. Remove title: click and delete 2. Remove shading and outer box: double click on shaded area, and set all the figure attributes and graph attributes to Custom, then set the fill and border options to None or [ N ] 3. Type in an appropriate Y-axis label: double click on the label (Data), to enter the Edit Axis Label dialogue for that axis, and make the changes. Repeat for X-axis 4. Increase Y-axis font size: Double click on Y-axis and change the font size using the Font tab 5. X-axis Labels: Double click on the labels to enter the edit scale dialogue; click on labels tab to change the label (as shown at right), and click on the font tab to change the font size. 6. Specify error bar type and colour - double click on any error bar To change the colour: - in the attributes tab, click custom, then click on the arrow beside the Colour box. Choose Black To change the type of error bar and its direction: - in the Options tab, Check the box beside Standard Error, and choose upper one-sided from the drop down menu.

44 57 Now we have a graph that looks like this... what s left to fix? 1. Change colours in bars to help distinguish subgroups more easily 2. Fix x-axis to look more professional 1. Bar colours - double click on any bar to open the edit bars dialogue - click on the tab for groups You can assign attributes by group, so you can have bars from one group in one colour, and the bars from the other group in another colour. In this case, we d like the bars for females to be a different colour than the ones for males, so select sex, and click OK This gives a very colourful graph, with a Key included - this means that if you wish to remove the male and female from the x-axis labels, you can, and have the bars specified using the key. - alternatively, you can keep the labels in the x- axis, and delete the key.

45 58 Publication (or course-submission) graphs should be done in shades of grey, rather than colour, since they may be duplicated or printed in Black and White. - click on one of the bars (you may have to click a second time to highlight all the bars in that group, then double click. That will let you enter the Edit bars dialogue just for that grouping. - check the box for Custom, then choose your bar colour. For this first one, pick Black - click OK - now repeat for the bars in the second group. That will give you bars in two shades of grey (black and grey). 2. Fix x-axis - Double-click on the axis labels (the words) to enter the edit scale dialogue. Click on the font tab to increase the font size, then click on the labels tab to type in better labels. -uncheck the boxes under Auto a) to remove the male and female and replace them with nothing, type in two sets of quotation marks with a space between them (i.e. ) b) to change site numbers to site names, delete the numbers and type in the names, with a space between c) to remove the axis labels, just delete them. Click OK

46 59 This graph is in good shape now, but if you want to use the key ( legend ) it should have larger font. - move the key to where-ever you would like by clicking and dragging it Double click on the key to enter the edit legend dialogue. - change border to None to remove the box - click on Header Font to increase the font for the header (in this case sex ) - click on Body Font to increase the font for the text in the key itself (i.e. male, female) - click OK (You may have to resize the legend by clicking and dragging to get the larger font to show) Double click on each word if you want to modify the text.... and you have a finished graph, ready for you to construct a figure legend.

47 3. Comparing groups with non-normal data: Box and Whisker Plots 60 If data are non-normal, you need to use a graph style that shows the median rather than the mean, and shows the range of the data on either side of the median. The type of graph to use in this case is called a Box and Whisker Plot. - Select Graph from the property bar, and choose Boxplot from the dropdown menu. Note: For simple boxplots, the data must be set up so that each group is in an adjoining column As with the bar charts, you can choose a simple plot, or one where the different y columns can be grouped together. In these examples, we ll look at our chipmunk data and run through a simple and a grouped example. Example 1: simple boxplot with multiple y-columns Select Multiple Ys, Simple and click OK

48 61 Select all the columns you want to graph (the data must be in adjoining columns) Options for the Data View are shown at right. most of the time, we just want the interquartile range box, and the outlier symbols Click OK (Note: the outlier symbols plot as stars at the ends of the distribution to let us know if we have outlier values. They will only be present if we have unusually high or low values in our data set) Your box plot before and after customization:

49 62 Example 2: grouped boxplot with multiple y-columns NOTE: Data need to be in a single column, with grouping variables in separate columns to do grouped boxplots. Select Multiple Ys, with groups and click OK Select your variables: - the variable with your data is abundance, so that should go in the graph variable - you are grouping by site first, then you want to see subgroups of sex, so put the grouping variables in that order. Your box plot before and after customization: Notice how you can see the full range of the data with the box and whisker plot.

50 63 Frequency Distributions Frequency distributions are used to determine the relative numbers of things (animals, plants, students...) that fall in certain categories. For example, a mark frequency distribution is used to determine how many students fall into various mark categories after an exam or course, such as 50-60%, 60-70% and so on. Frequency distributions not only give important biological data (such as how many fish fall into certain size or age classes), but are also used to help test assumptions about the mathematical fit of certain data. You have probably heard of the normal or bell curve distribution, for example... that is one type of a frequency distribution. When frequency distributions are used to assess the shape (distribution) of the data, it is not usually necessary to worry about how axes are set up, since we just want to see the shape of the data. If they are being used to show actual data, however (like student mark distributions or sizes of fish or plants for life history analysis), we need to know how to modify the axes. A) Frequency Histograms in Excel 2007 Frequency distributions are usually easy to do in statistical or graphing software packages, but can be much more difficult to do in spreadsheets such as Microsoft Excel. First you have to determine your intervals and type them in manually, then you have to use the computer to calculate the frequency distribution, and only then can you graph it. - Determining intervals Method: open the pulses dataset in Excel 1. Determine your maximum and minimum values in your Excel dataset, so you can set your intervals. For example, in the pulses 1 column of the pulses dataset, the minimum value is 54 and the maximum value is 96. (sort the data to determine this) Rule of thumb for number of intervals ( bins ) for a dataset: - need enough to see a pattern (e.g. minimum of 10, preferably around 20) but not too many so that gaps may appear in the data. - be prepared to try out more than one option - For this dataset, I would choose intervals that go from 50-55, 55-60, 60-65, and so on. Important: we don t want to count numbers twice, so what this really means is intervals that go from 50 to 54.9, 55 to 59.9, , and so on. 2. Insert a couple of columns to the right of your Pulses 1 column. Now type your interval numbers into a blank column in your spreadsheet as shown at right (see example on next page). Note: Just type the numbers from the left column of this example, since the right column is just an explanation of the left column numbers... i.e. what Excel is understanding from what you have typed # explanation 54 number that is number that is 100

51 64 Your Excel spreadsheet should look something like this: 3. Now click on the blank space beside the first interval on your spreadsheet, and type in =frequency( FREQUENCY(data_array, bin_array) should appear as a small window below your cell this means you must specify your data array first, and the bin array second to carry out the analysis data array = the column with your data in it bin array = the column where you define your bins (intervals) 3. Specifying the data array first use your mouse to highlight the values in the pulse 1 dataset (your data array), then type in a comma now use your mouse to highlight your bin values (the intervals), and type a closed bracket ) press the down arrow. on your keyboard. A single number will appear. In this example, that should be a 2 count the number of intervals you have in your bin (intervals) column; in this case it is starting at the cell with the single number, highlight the number of cells +1 (i.e. in this case, highlight 11 cells).

52 65 4. Carrying out the frequency analysis: press [F2], to make the formula appear again. then press [control] [shift] [enter]. The frequency values should appear in the cells you highlighted. Explanation: what this means is that there are 2 values between 50 and 54, 3 between 55 and 59, and so on. (e.g ) Note: if you have numbers extending beyond the decimal point, be sure to set your bins to one decimal place beyond those given in your data Interesting note: these values are entered as formulae, so if you would like to copy and paste them into another program, you first need to convert them to number values (see p. 7). highlight the values, and copy them paste them in the column beside the bin intervals use the paste options to convert to values

53 66 Graphing the frequency distribution: 1. Highlight the data you want to graph. 2. Choose the insert tab from the property menu, then pick the graph type you want. In this case we want a column chart, which is what Excel calls any graph that has vertical columns. Pick the simplest 2-D column graph type, and click on it. Excel gives you the graph shown at right and opens up the Chart tools so you can modify your graph.

54 67 Important: if all you need at this point is the frequency distribution so you can check its shape, this is as far as you need to go. If you are plotting a frequency distribution to include in a report, however, you need to do the modifications to make this report-ready. 3. make sure the source data is correct: we highlighted our source data before beginning, so it should be okay. If you had not done this, or if you notice an error, you can click on Select Data on the Design property bar, or right-click on the x-axis, and choose Select Data You ll see the window shown at right. You can either type in the correct values, or click on the small red arrow beside the Chart data range window, to return to the spreadsheet to select your data (by highlighting). Highlight the appropriate data, if necessary, then click on the small red & blue box again, and that puts you back into the select data window. If all is now correct, click OK 4. Adding axis labels: click on the layout tab of the Chart tools, and click on axis titles - choose the axis you want to add a label (title) to, and indicate where you want it by clicking on it. Do this for both the horizontal and the vertical axis. -This action will place an axis title by each axis, and you ll need to edit them to say what you want. Right click on the axis title, and choose Edit Text from the drop-down menu. Then just type in what you want. To change the font (e.g. to make it larger or to change the font type), click on font. Do this for both axes.

55 68 This graph is still not suitable for presentation, however, since there is too much distance between the bars, the x-axis numbering is incorrect, and the borders and gridlines are not appropriate to a scientific graph. To customize, we need to: 1. Turn off the title & outer box 2. Alter the x-axis so that our categories are indicated correctly 3. Decide whether the bars should be touching or not, and if so, change them so they are 4. Remove gridlines and outside border 1. Turn off extraneous information The title and bar legend (key) are redundant, so add nothing to our graph. Click on them and delete. remember that if the data are in different groups, your bars should not touch each other, but if they run continuously from one category to the next, the bars should touch 2. change the width and colour of the bars a) Right-click on any bar to access the Format Data Series dialogue. Click on it to open. - Change the Gap Width from 150% to 0% Now the default colour in Excel makes it hard to read, so that must be fixed.

56 69 What colours should you choose for bars and lines? The rule of thumb is to choose colours that will photocopy well and still let you see the patterns, since your report will usually be printed or copied in black and white. b) Change the bar colour - Still in the Format Data Series Dialogue, click on the Fill tab to change the colour to Grey by checking the Solid Fill and choosing a new colour from the drop down menu.. c) Add a dark border to make the bars easer to see: - click on border color and to give the bars a black border. - if necessary, make the border thicker in border styles The graph is coming along, but still needs more work:

57 70 X-Axis labels for a frequency histogram You x-axis must clearly indicate that you are looking at a range of numbers. - if you have a single tick mark below a bar, and one number below that tickmark, then you are telling your reader that every record making up that bar is equal to that number. - in the example at right, you are telling the reader that there were two numbers with the value of 1', three with the value of 2' and so on. This is not correct, so we have to re-do the x-axis to make it reflect our actual data. We can fix this x-axis labels in two ways: 1. Type the full range of numbers for each bar (e.g , 55-60, and so on) 2. Place tick marks at the edges of the bars, and label the tickmarks. This is the preferred option since it is easiest to read. (you must use the Text tool for this whichever option you choose) 3. Make sure tick marks are at edges of bars Open the Format Axis window by right-clicking on the axis numbers on your graph, or by going into the Axes section under the Layout Tab, clicking on the axis you want to modify (e.g. horizontal for the x- axis), and choosing more primary horizontal axis options a) be sure that axis labels is set to None to turn off the category numbers b) be sure that Position axis is set to Between tick marks

58 71 c) Type in new axis labels that match your data (use the text box tool on the "insert" tab) - click anywhere on the graph to highlight it, then use the mouse to resize the graph so you have room to type your numbers below and to insert a Y-axis label at the left. - Insert a text box from the Insert tab on the property bar - Type in your new labels, based on the bins specified in your original spreadsheet. 4. Turn off gridlines: - Select Gridlines from the Layout tab of the Chart Tools menu, then Primary Horizontal Gridlines - click on None 5. Insert Y-Axis label - Select Axis Titles from the Layout Tab of the Chart Tools menu. - Choose Rotated title from the drop down menu for the Primary Vertical Axis An axis title will appear to the left of your graph; highlight it and type in the text you want. Change the font as necessary from the Home tab on the property bar.