#simple-statistics

1.) Using your Group’s data, expand the Table you made for arrows 5 & 6 of Lab 1 with the following columns:

 Standard Deviation (SD); calculate for each Treatment

 Average + SD, and Average –SD; calculate both for each Treatment

For question one, please turn in a table featuring your group’s data with one row for each of the treatments (Binocular, Monocular non-dominant, Monocular dominant) and columns for each of the trials (3). At the end of each row, include two new columns. One column should have the mean for that treatment, and one columns should have the sample standard deviation.

Here’s an example using sample binocular data:

Treatment Trial 1 Trial 2 Trial 3 SD Average +SD Average –SD Binocular 28 27 31 2 30 26

Note that there are only significant figures out to the ones column for the SD and mean because we can only have whole paperclips!

2.) Using the information just calculated, answer the following questions (1.5pts):

Were the SDs similar between Treatments?

What factors could have contributed to those differences/similarities?

Describe the benefits of using the SD versus the Average to compare Treatments.

Now compare the standard deviations you just computed for each Treatment group. Which has the largest SD? The smallest? Was binocular close to Monocular ND or Monocular D? Did they all look very similar?

These kinds of questions tell us about how different our treatment groups might be from each other. Try to think about what having a bigger or smaller SD might mean for the data in each treatment group.

Next, let’s think about what could cause the trends you see in how spread apart your data are for each treatment. Why do you think you see differences between the standard deviations of these different treatments? If all the standard deviations are very similar, why do you think that is?

Finally, let’s consider why we might want to talk about our SD instead of our mean. What kind of information does our SD convey? What kind of information does the mean tell us? How could using both the SD and the mean give us more information than just considering one of them?

Think about how talking about the spread of our data might inform our understanding of our treatments instead of considering where the majority of our data lie. Does it tell us something about how separate the groups might be?

3.) Make a graph of your Group’s data (You may find Appendix B, Line Graphs in your lab manual to be helpful for this exercise.) (2pts)

Axis labels: the X-axis should be the Trials, the Y-axis should be the number of paper clips put in the flask.

There should be three data points for each Trial (one for each Treatment within each Trial).

Each data point should have error bars representing the Standard Deviation you calculated for that Treatment (using the numbers you calculated in 1.b above).

Include a legend identifying which data points belong to which Treatment.

Now we want to present our data so other scientists can view it! How can we present it so that they know how different each of our treatments was for each trial?

Well, we can present each trial for each treatment as a point on a graph. We want our independent variable on the X-axis and our dependent variable on the Y-axis. Since we are worried about number of paperclips put in the flask for each trial, we will use Trial # on our X-axis because we got to change that on purpose. We will use # of paperclips put in the flask on our Y-axis because we want to know how that varied by trial. Because we also want to be able to see the differences between treatments for each trial, we’ll also color all the points for each treatment different colors. For example, Binocular can be blue, Monocular Dominant can be orange, and Monocular Non-dominant can be black. Make sure to include a key for your reader to tell them what each color means! If you are still lost, take a look at the graph that Dr. Oswald included in the spreadsheet. Your graph should look something like that.

Now how do we show the spread of our data for each treatment?

Hello, error bars, my old friends! It’s nice to see you in my graph again. Error bars tell your reader how likely it is that you might get a different value if you were to perform your experiment again by telling them about how different your trials were for this experiment. Here, your error bars are your SD. These will appear on your graph as little I’s that surround your data points. The length of the | is determined by how big your SD is. In our Binocular example above, each of my binocular points would be surrounded by a line of length 2 units. If you are having trouble doing this in excel, here is a tutorial. You may also draw these in for this assignment (ONLY), but you will have to make them very neat and use a straight edge!

4.) Using full sentences, compare your Group’s graph to the graph of your Section’s data that was included in the Excel Spreadsheet provided after lab:

Did other Groups have similar SDs to your group’s SDs? If not, describe the differences. (1pt)

Describe 3 possible explanations for your answer to (a). (1.5pts)”

If you haven’t already, take a look at the graph Dr. Oswald made of section 5’s data (Wed 14:30-17:30). Now look at the graph you just made using your group’s data. Does your group’s data look like our section’s data? If it doesn’t, how is it different? Maybe your group was very consistent and put the same number of paper clips in the flask each time, but our whole section was not very consistent, and every group put in a different number of paperclips for each treatment and trial. Is the spread of your data greater than or less than the whole section’s? Maybe your group’s SD is exactly the same as the whole section’s.

Now that you have noticed the differences between the spread of your group’s data and our section’s data, think about why you might see these differences. How might having more data points (a bigger sample size) alter the SD of our data? What factors do you think affected the variability of our data? For example, the fact that each group had a different experimenter might affect the differences between groups, while using the same experimenter between trials might affect an individual group’s SD. Try to think of three reasons your data and our section’s are more or less spread out in comparison to each other.

Notes:

Computing the sample mean for each Treatment group:

1.) Add all the samples in your Treatment group together (Σ).

2.) Divide by the total number of samples you gathered (N).

Here is an example for binocular data:

Treatment Trial 1 Trial 2 Trial 3 Σ N Mean Binocular 28 27 31 86 3 28

You will notice that 86 does not divide evenly into 3! Because we have only whole numbers in our sample, our precision is to the ones digit, so we have to exclude that extra 2/3 we get when we divide our sum by our N. Make sure to keep track of sig figs.

Computing the sample standard deviation:

1.) We’ll need the mean we computed before and all our data. First, we take all our data and we subtract the mean from each data point (the deviation for the mean).

2.) Now we take each of those deviations from the mean and we square them.

3.) Now take the mean of all those squared deviations from the mean.Here, we take the mean with a twist: instead of dividing by N, the number of samples, we divide by N-1. This is the sample variance!

4.) Take the square root of the variance to get the SD.

Here is an example for binocular data:

Trial # # Paperclips Mean Deviation (Deviation)2 Σ(Deviation)2 N-1 Variance SD 1 28 28 0 0 -- 2 -- -- 2 27 28 1 1 -- 2 -- -- 3 31 28 3 9 -- 2 -- -- Total -- -- -- -- 10 2 5 2

Watch out for those sig figs again!