This is the first week of a two-week lab studying cell motion. This week we will learn how to use

Excel to analyze the 1-D motion of an amoeba from stop-motion images. Next week we will be

analyzing videos of cell motion: 1) wound closure, 2) neutrophil motion, and 3) bacteria

motionâ€”to determine whether or not a patient should be prescribed antibiotics. Clearly, the

relative speeds of the wound closure, neutrophils, and bacteria will affect your decision. Thus it

becomes important that we learn how to quantify the motion of cells.

On the next page, you will see a graph of the movement of Dictyostelium discoideum, shown as a

sequence of outlines of the amoeba cell at 3.0-minute intervals. Your task is to record and analyze

the motion of the amoebaâ€”specifically, the position, instantaneous and average speed, and

instantaneous and average acceleration. Rather than do all of the mathematical calculations by

hand, Excel can help you do the calculations much more quickly and efficiently. This week you

will practice and master the skills necessary to bend Excel to your will and make it do the grunt

work. Next week, you will be expected to be experts at these skills so take turns and help each

other learn.

Deliverables:

Either individually or with a partner, you will submit a set of graphs (y vs. t, v vs. t) with your

data tables and the typed responses to these questions:

1) What do these graphs say about the motion of this organism?

2) Look at the top speed for the organism. If the organism were moving at the top speed for an

entire day (24 hours) how far would it travel. Compare this to the length of the human

body.

3) What did you learn from this first online lab? What do you think the instructors are hoping

you start to learn and practice from this?

You will upload the graphs, tables, and typed responses in one PDF to the assignment page in

canvas. It is incredibly hard to grade if there are several pages of uploads.

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apted from K. Moore, J. Giannini, B. Geller & W. Losert (Univ. of Maryland, College Park)

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Table 1: Your position vs. time graph â€“ Using the figure above, find the position for the amoeba

for each time given in the graph. Remember, each snapshot of the amoeba is taken in three second

intervals (hence the intervals given in the graph). For consistency it is best to pick the same part of

the amoeba every time (say the top point). When you are done create a graph of your position vs.

time. Usually we use a scatter plot for data like this but this time we will use a line graph. Be

careful to show units! You may use either google spreadsheet or excel. There is an excel review on

the next page.

t y

0

3

6

9

12

15

18

21

24

27

30

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Table 2: Your velocity vs. time graph â€“ Remember, your velocity is Î”y/Î”t , so if you can

calculate the average velocity ( y2

â€“ y1

)/ (t2 âˆ’ t2

) during each time interval in the table above. As an

approximation, we can say that this average velocity occurs in the middle of the time interval so

1.5s for the first velocity, 4.5s for the second velocity, etc, as can be seen in the table below. Once

you complete the table, make a graph for velocity vs. time.

t v

1.5

4.5

7.5

10.5

13.5

16.5

19.5

22.5

25.5

28.5

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Excel Tutorial Reference

Intro to Scientific Data Analysis with Excel

Excel (or any spreadsheet program) can help you do calculations quickly and efficiently. But Excel

is only a software programâ€”it can only be as smart as the instructions that you give to it. Today

you will practice and master the skills necessary to bend Excel to your will and make it do the

grunt work. After today, you will ALL be expected to be experts at these skills so take turns and

help each other learn. Take notes for the future if you are worried that you will forget. Each

version of Excel (as with the other Microsoft Office programs) varies slightly, but familiarity with

one version should help you intuitively guess/explore the other versions. Some of you may feel

that you are already familiar with Excel; please READ the Technical document anyway! It

contains specific scientific norms that you need to learn.

Entering Data

To enter information in a cell, click on the cell (e.g., cell A1â€”column A, row 1) and type the

information. When you are finished, press â€˜Enter.â€™ You will see the information in the cell. To edit

the information, click on the cell and type (erases previous entry) or click on the cell and then click

on the formula bar to edit (the formula bar is above all the cells but below all the icons for text

manipulation (bold, italicize, center in cell, etc.).

Title each column with the quantityâ€™s name and units. In the cells beneath each column title, enter

the data that you have collected by typing the numbers into the cells. When you have finished

entering your data, save the file by pressing â€˜Ctrlâ€™ + â€˜Câ€™ (name the file and note the saved location

for future use) or by selecting the â€˜Fileâ€™ tab, then the â€˜Save asâ€™ icon. Save regularly to avoid losing

work. Every time you save the file, it overwrites the previous version.

The number of decimal places displayed in the cell can be controlled by icons in the â€˜Numberâ€™

menu on the â€˜Homeâ€™ tab. Use these icons to give your data uniform appearance.

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Generating Columns of Data Calculated from a Formula

To generate information from a formula (i.e., to mathematically manipulate cells), click on a cell

and begin with =. All Excel entries for which you expect a numerical result/output MUST begin

with an equals sign, =. The mathematical manipulators are what you would expect: * to multiply, /

to divide, + to add, and â€“ to subtract. To exponentiate, type ^ and the power (e.g., 62 is 6^2). Let us

say you wished to multiply the entry in cell A1 by 60. To do this you would click on the cell where

you wish the output to go and then type â€˜=60*A1.â€™ You can type the input cell, A1, on the

keyboard, or you can use the mouse to click on cell A1 while typing the formula. For more

complex mathematical operations, parentheses often become necessary. Excel will color-code the

parenthesis to help you see where each set opens and closes. Be VERY careful with your

parentheses! (Again, Excel is only as smart as the instructions that you give to it!)

If you wish the same mathematical formula to be applied to every cell in a column (e.g., column F

is column A times 60), type the formula into the output cell for the first row. Then click on the

output cell and move your mouse over the bottom, right corner of the cell. Your pointer will

change shape and become a plus. Press down the left mouse button, drag down to the last cell you

wish to effect, then release the mouse button. The cells will automatically fill in. By clicking on

any of these cells, you can see in the formula bar that the formula has been adjusted to reference

the correct input cell (i.e., for the row you are currently in). The same process can be used to copy

a formula across a row into multiple columns. If, in a formula, you wish to reference a specific

column or cell (that will NOT change when the formula is dragged over a column or row), use the

$ symbol: e.g., $A1 will always be column A, but the row number can change; and $A$1 will

always be column A and row 1â€”neither can change.

Generating Graphs

When creating a graph/plot, Excel will usually plot the first column on the independent/horizontal

axis and the second column on the dependent/vertical axis. You should always check that the

correct data has appeared on the correct axis. If the data has been entered with the columns in

reverse order, this can be fixed after the plot is created. To generate a graph/plot, use the mouse to

highlight the data that you wish to graph (if the data is adjacent, just highlight the entire chunk; if

the columns are not adjacent, highlight each column separately while holding the â€˜Ctrlâ€™ key). Once

the data is highlighted, click on the â€˜Insertâ€™ tab and then the â€˜Scatterâ€™ icon (on the â€˜Chartsâ€™

menuâ€”other types of charts may be appropriate for different data types, but the Scatter plot is the

most commonly used).

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From the sub-types of scatter plot available, choose the one that hasdata points but no lines. A

graph will appearâ€”but you are NOT finished yet! The design of the graph can be adjusted using

the â€˜Chart Layoutâ€™ menuâ€”you will want to be able to label the individual axes with the quantity

graphed and its units and you will want to be able to title the graph. When the graph has been titled

(for the â€˜vs.â€™ format, it is always â€˜Dependentâ€™ vs. â€˜Independentâ€™) and the axes have been properly

labeled, you can choose to keep or delete the Legend (not needed if only one data set is plotted,

absolutely necessary for multiple data sets). The location of the chart can be changed by:

left-clicking on the chart (the upper right corner works well), then right clicking and choosing

â€˜Move Chartâ€™ from the menu. It is often best to make the chart a â€˜New Sheetâ€™ (so that it doesnâ€™t

block your view of the data)â€”give it an appropriate title and click â€˜Okay.â€™ You chart will become

its own sheetâ€”and your data will disappear! But the data is not goneâ€”to find it, use the tabs on

the bottom of the Excel window (â€˜Sheet 1â€™ is usually the data; now might be a good time to rename

it â€˜Dataâ€™: right click, select â€˜Renameâ€™ and name it).

Before you finish, check that the correct data has been plotted on the correct axis and that the axis

labels match the quantities plotted. If the original columns were in reverse order, this can be

adjusted by left-clicking on a data point (to select the data), and then right-clicking and choosing

â€˜Select Dataâ€™. Click on the Legend Entry you wish to adjust, and then click â€˜Edit.â€™ Highlight the

appropriate Series X and Series Y data and then click â€˜Okay.â€™

Adding a Best Fit (â€œTrendlineâ€) to a Graph:

To add a line of fit (called a â€œTrendlineâ€ in Excel) to a graph, left-click on a data point to select the

data, then right-click and choose â€˜Add Trendline.â€™ Choose the appropriate Trend/Regression type,

and tick the boxes for â€˜Display Equation on chartâ€™ and â€˜Display R-squared value on chartâ€™. As a

general rule, do not â€˜Set Interceptâ€™ to a specific number (i.e., do not force the origin to be part of

the trendline). Do you know what the R-squared value really means? If not, you should look it up!!

Look at the equation for the trendline and think about it. What does the slope mean? What does the

y-intercept mean? What does this R-squared value mean?

Adding Error Bars to the Data Points on a Graph

Error bars represent the uncertainty of the measurement of the data. Do you have uncertainty? Do

you have uncertainty in both quantities (horizontal and vertical)? Is the uncertainty the same for all

data points, or does it change with the value of the quantity plotted? Wherever you have

uncertainty, you must have error bars! Once you have determined the amount of uncertainty, you

can add error bars by clicking on the â€˜Layoutâ€™ tab (inside the â€˜Chart Toolsâ€™ tab) and clicking on the

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â€˜Error Barsâ€™ icon. To get both horizontal and vertical error bars, a good choice is the â€˜Error Bars

with Standard Error,â€™ and then click on the vertical and horizontal bars (individually) and right

click to â€˜Format Error Bars.â€™ Apply the error bars according to the decisions that you have made

about your uncertainty. To remove either vertical or horizontal error bars, left-click on the bars,

then right- click and choose â€˜Delete.â€™ (Future Lab Skill Goal: How do we propagate uncertainty

into calculated quantities?)

Other Cool Tools

As a spreadsheet program, Excel can do a lot of useful statistical analysis and mathematical

manipulation. Some functions you will find useful include: Sum, Average, and Standard

Deviation.

To Sum elements, click on the cell in which you wish the result to appear, then enter â€˜=sum.â€™

Immediately, Excel will list possible formula options that begin with â€˜sumâ€™. For a simple

summation of elements, you would choose the SUM function, which you have already typed, but

you should note the other options available. Open parentheses following your sum, so that you

have now types â€˜=sum(â€˜ and then highlight the cells to be summed. Close your parentheses and

press â€˜Enter.â€™ (It would look like this â€˜=sum(A1:A5)â€™ for a sum of the cells in rows 1 through 5 of

column A.)

To Average elements, click on the cell in which you wish the result to appear, and then enter

â€˜=average(.â€™ Highlight the cells you wish to average and then close your parentheses and press

â€˜Enter.â€™ Note that Excel will offer you a list of average functionsâ€”the most commonly used option

is the AVERAGE function. (It would look like this â€˜=average(A1:A5)â€™ for the average of the cells

in rows 1 through 5 of column A.)

To perform a Standard Deviation on a set of elements, click on the cell in which you wish the

result to appear, and then enter â€˜=stdev(.â€™ Highlight the cells you wish to perform a standard

deviation upon and then close your parentheses and press â€˜Enter.â€™ Note that Excel will offer you a

list of standard deviation functionsâ€”the most commonly used option is the STDEV function.

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