Research Experience- Part 5. Analyzing Your Data

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1 Research Experience- Part 5 Analyzing Your Data The goal for this week is to analyze your data. Scientists don t collect data just to keep it to themselves. After they ve collected their data, they need to analyze it to see whether or not their hypothesis is supported or rejected based on the results of their experimentation. They then write up and prepare their results for peer review, either as a journal article similar to the one you read in the jigsaw activity, or as an oral presentation at a scientific conference. In either case, the research is presented to other scientists that are experts in the field that can look at the research and decide whether they agree with the conclusions that the authors make. If they agree, the research gets published or discussed and presented again elsewhere, so that others can build on the research and scientific knowledge is advanced. If the experts disagree with the conclusions, it goes back to the researcher to address any issues the reviewers might have, which could mean simple changes (yay!) or even more experiments (ugh). As scientists in this course, you will need to go through some of the same steps that a scientist in a research lab would do in terms of analyzing your data, determining whether your results support or reject your hypothesis, and then presenting these results for peer review (your fellow lab mates). You will not have to perform any elaborate statistical analyses on your data, but you will need to perform basic analysis of your data and prepare it for presentation in terms of creating tables and graphs as needed. Instructions You have performed your experiment and collected your data! Now you are ready to start analyzing your data. It is a good idea at this point to stop and think through what you are going to do. Review your hypothesis, read through Section A below on "Introduction to Data Analysis" and determine which analysis would be appropriate in order to determine if your data supports or refutes your hypothesis. Once you choose which analyses are appropriate (there will probably be more than one), you should conduct your analyses and examine your results. Think about your results in terms of supporting or failing to support (rejecting) your hypothesis. Ask your TA for help or guidance as needed. Often times, a picture is worth a thousand words! Think about creating simple graphs of your data to show relationships between two measurements. Read Section B below to get a little more information on creating simple graphs. Getting help with your data analysis If you need help with understanding any of these basic statistics, you can ask your group members, other classmates, your TA or you can search for help on the Internet - there are many free tutorials at Internet sites like: YouTube and Khan Academy ( If you plan on using Excel to analyze your data, there are two available handouts available to you - one on learning how to use Excel and another on how to do basic data analyses in Excel. There are also lots of Excel learning tutorials on the Internet that you can find on your Biol 1010 Data Analysis Handout 1

2 own. If you have questions about Excel that are not in the handouts, you can also find those answers on the Internet. If you're unsure on how to proceed, ask your TA for help. Section A. Introduction to Data Analysis Scientific research can be divided into two categories theoretical and empirical. Theoretical research uses mathematics and logic to prove beyond any uncertainty that certain propositions are true. Empirical research is about drawing conclusions from observations. The group experiment that you did in this class was empirical research. To examine the data that you've collected you should start with examining summary statistics of your data. Statistics is a sub-discipline of math that is concerned with (a) collecting data (i.e., observing the phenomenon of interest), (b) organizing and summarizing this data, (c) analyzing the data and (d) drawing conclusions from it. You will use very basic summary statistics to analyze your data so that you draw conclusions from your data based on your stated hypothesis. Summary statistics provide a way of succinctly characterizing your data. Common summary statistics are the mean, median, mode, range, variance and standard deviation. 1. Mean The mean, also known as the average, is calculated by summing (adding up) all of the measurements in a list and dividing that total by the number of measurements in the list. Example: You measure the weight of 9 of your classmates and get the following values (in pounds): 125, 172, 188, 155, 138, 158, 170, 164, 172 mean weight (lbs) = = 1442 / 9 = lbs The mean gives an estimate of the average value of all of your data. 2. Median The median measurement is the middle measurement value when the measurements are arranged in ascending or descending order. The median is of high value when describing large datasets. The median will be the point where half the measurements fall below that number, and half of the measurements will be above that number. Example: In the above example where classmates are weighed, the measurements are put into order and the middle measurement is the median value: 125, 138, 155, 158, 164, 170, 172, 172, 188 <--- The median weight = 164 lbs Biol 1010 Data Analysis Handout 2

3 If there is an even number of measurements, the median value is the average of the middle two measurements. 3. Mode The mode is the measurement value that occurs most frequently in the list of measurement values. Example: In measurements of classmate weights, the measurements are put into order and the middle measurement is the median value: 125, 138, 155, 158, 164, 170, 172, 172, 188 <--- The mode = 172 lbs The mode is useful for telling you which value occurs most frequently. 4. Range The range of measurement values is equal to the largest measurement value minus the smallest measurement value. Example: In measurements of classmate weights: 125, 138, 155, 158, 164, 170, 172, 172, 188 <--- The range = = 63 lbs The range is useful for telling you about the spread of your data (large value=large spread in values). 5. Variance Variance is the average squared distance from the mean. Like range, variance tells us if our measurement values are spread way out (large variance), or, if the measurement values are fairly close in value (small variance). The mathematical formula for variance is complicated and you will not be expected to understand it. Any spreadsheet that you use to analyze your data will have this mathematical formula already programmed into the software (e.g., Excel). If you decided to use variance in your data analyses, just use the software's built-in function for variance. Variance is useful for giving you a measure of the spread of your data. Beware that because the data values are squared, the units are also squared. This issue of having squared units is resolved with the use of the standard deviation. 6. Standard Deviation The standard deviation is calculated by taking the square root of the variance. This is another statistical analysis that you can perform using any software's built-in function. Biol 1010 Data Analysis Handout 3

4 Standard deviation is useful for giving you a measure of your data expressed in the original units of measurement. Section B. Simple line charts A line chart, sometimes called a line graph, is a type of chart which displays a series of measurement values on a chart connected by straight line segments. A line chart is often used to visualize a trend in data over intervals of time - for example, the changes in temperature over time. How to create a line chart or an x-y scatter chart A line chart provides a nice visual way to map two numerical variables. The line segment that connects the points on the graph expresses the trend of the data, but does not give a statistical equation to describe the relationship of the two variables. A line chart distributes data points evenly along the horizontal category axis (x-axis). Scatter charts are similar to line charts but can show more than a general trend. The individual points that appear on the chart can be interpreted to express a trend, or, that there is a lack of a trend. However, additionally, a statistical equation can be produced via use of the software to describe the relationship between the two variables and a line can be produced to show this relationship. Consider the following data showing heart rate for two subjects (Harry and Sally), measured at various times after the start of an exercise routine. Note that a few of the times recorded (minutes after starting the exercise) are slightly different for Harry versus Sally. Biol 1010 Data Analysis Handout 4

5 These data will be represented differently on a line chart (data points are assumed by Excel to have even spacing) than a scatter chart: HOW TO CREATE A LINE CHART: A) Arrange the data in columns. For this exercise, type the following data into a worksheet: Biol 1010 Data Analysis Handout 5

6 Note that the data in the column labeled "Exercise Time - minutes" are in ascending order. These data will be graphed as the x-axis. Data to be graphed in a line chart in Excel must be sorted in descending or ascending order. B. Select the data in the rows or columns to include in the line chart. To do this, click on the first cell you want included in your line chart and while holding down the mouse button, drag your mouse to highlight the rest of the data you want on your chart. C. From the top menu bar, click on "Insert" and select "Line" from the "Chart" options. Choose and click on the chart subtype you want from the pictures. D. You can move the chart to any location in your worksheet by clicking on it and dragging it when you see the four-way arrow. E. Adjust the size of the chart by moving each side, and the top and bottom in or out with your mouse. You can right click on the chart to obtain chart formatting options. HOW TO CREATE A SCATTER CHART: A. Steps "A" and "B" are identical to above section on how to create a line chart. For step "C", click on "Insert" and select "Scatter" from the "Chart" options. Choose and click on the chart subtype you want from the pictures. Steps "D" and "E" from above section are the same. Section C. Column or Bar Charts Column and bar charts (also called bar graphs) can be used to show how something changes over time or to compare different times. Column charts show your data as vertical columns, bar charts show your data as horizontal bars. Column charts are good for plotting data that spans many years (or days, weeks, etc...), has really big changes from year to year (or day to day...), or they can be used for comparing different items in a related category (for example: comparing the change in heart rate after exercise between athletes and non-athletes). They can also be used to show one or more independent variable, as outlined below. The following section describes how to make a column charts. Bar charts can be made using these same directions, just choosing the Bar option from the Excel Charts menu. A. Column charts are created in much the same way scatter plots and line graphs are. Arrange the data in columns as you did for line graphs and scatter graphs. The figure at the left below shows how to arrange the data for a single independent variable (the variable you are controllingexample - here, the variable is the type of mammals being counted). Biol 1010 Data Analysis Handout 6

7 Note that the independent variable is placed in the first column while the dependent variable is placed in the second column. The headers at the top of each column are not necessary, but they do help identify the variables. B. Select the data shown above as you did for line graphs. C. From the top menu bar, click on the Insert tab and choose the and then choose Column from the Charts option. Choose and click on the chart subtype you want from the pictures, keeping in mind that for most of the data we will collect the 2D side-by-side charts are likely to be the most useful and easiest to work with. D. You can move the chart to any location in your worksheet by clicking on it and dragging it when you see the four-way arrow. You may also choose to move the chart to its own worksheet by right clicking on the inserted chart and selecting Move Chart from the options list that comes up. Select New sheet and the chart will be moved to its own worksheet. Your chart should look like the one below: E. The title can be changed by clicking on the Count text at the top and adding more useful text such as Animal Count in Area 54. A title can also be added to your graph in Excel 2010 version by clicking on the chart and then choosing the Quick Layout- Chart Layouts option. Select from the options pictured there to add a title. F. A multiple bar graph depicting data using two independent variables is created in the same way as a simple bar graph. Enter your data as shown below. When ready, highlight the boxes that include all the boxes from A2 to C6, and insert a column chart as indicated above. For this chart, you will need to change the layout using the Quick Layout feature described in step E to insert a title that will make this chart more useful to convey the information. Note, however, that Excel has included a figure legend already that indicates the different colored columns refer to the data collected for the types of mammals during two different weeks. Biol 1010 Data Analysis Handout 7

8 Some things to note when creating this multiple column chart: The first independent variable, Mammal, is still in the first column, with the dependent variable values (Count) in columns two and three. The second and third columns represent dependent variable values at two different levels of the second independent variable, Week. Make sure to select all of the data when creating the graph. The graphing tool in Excel will automatically recognize you have a second independent variable. Section D. Pie charts Pie charts (also called pie graphs) are very difficult to do well and most pie charts are not useful for providing clear scientific information to the reader. We strongly discourage you from trying to make pie charts to show any type of scientific data. Biol 1010 Data Analysis Handout 8