Data Analysis Guidelines

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1 Data Analysis Guidelines DESCRIPTIVE STATISTICS Standard Deviation Standard deviation is a calculated value that describes the variation (or spread) of values in a data set. It is calculated using a formula that compares each piece of data to the mean. It is useful to think of this number as a plus or minus value, where a larger standard deviation indicates that the data are spread further from the mean and thus the mean is less reliable. In general, a large value of standard deviation indicates less confidence in the data set and its mean, while a small value of standard deviations suggests greater confidence in the data and its mean. To calculate standard deviation: 1. Calculate the mean. 2. Calculate the difference between the mean and each data value. 3. Square each difference. 4. Add the squared values together. 5. Divide the sum by the total number of data in the set. 6. The square root of the value calculated in the previous step is the standard deviation. 7. Record standard deviation as a ± value in the appropriate column of the data table. Summary: Standard deviation describes how far the majority of the data is from the mean. To calculate mean and standard deviation using a graphing calculator* (Texas Instruments): 1. Press the Stat key, then choose Edit and press Enter. 2. Enter data values in list one (L1). 3. Press the Stat key again, choose Calc, then choose 1-Var Stats and press Enter. 4. Choose 2, then nd L1 (the number 1 key) and press Enter. 5. The x value is the mean and the s x value is the standard deviation. *Any scientific calculator can calculate mean and standard deviation. Refer to the instructional manual for your scientific calculator for specific instructions. To calculate mean and standard deviation using a Texas Instruments Ti 36X Pro: 1. Press the DATA key. 2. Enter data values in list one (L1). 3. Press the 2 key followed by the DATA key, and scroll down to 1-Var Stats and press Enter. nd 4. Scroll down to CALC. 5. The x value is the mean and the s x value is the standard deviation. To calculate standard deviation using Microsoft Excel - Windows 1. Create a data table in an Excel spreadsheet complete with all relevant data values and columns headings for data analysis (ex. mean, standard deviation) 2. Highlight a cell where you want to add a calculation 3. Choose Formulas from the menu, and then Insert Function that appears on the far left Choose AVERAGE to calculate mean Choose STDEV.P to calculate standard deviation Note: There is no Function to calculate mode for qualitative values or frequency distribution. You will either need to determine frequency distribution and input the calculated value into the data table OR create a formula in Excel to calculate frequency distribution. 4. Select the cells with the appropriate data to be analyzed Either select and highlight the cells, or type the cell numbers into the window that appears. Note: When calculating standard deviation, do not include the mean value when selecting the data to be analyzed. To calculate standard deviation using Microsoft Excel - Mac

2 1. Create a data table in an Excel spreadsheet complete with all relevant data values and columns headings for data analysis (ex. mean, standard deviation) 2. Highlight a cell where you want to add a calculation 3. Choose Insert and then Function from the menu Note: There is no Function to calculate frequency distribution. You will either need to determine frequency distribution and input the calculated value into the data table OR create a formula in Excel to calculate frequency distribution. 4. Select the cells with the appropriate data to be analyzed Either select and highlight the cells, or type the cell numbers into the window that appears. Note: When calculating standard deviation, do not include the mean value when selecting the data to be analyzed. To calculate mean and standard deviation using Google Sheets 1. Create a data table in Google Sheets complete with all relevant data values and columns headings for data analysis (ex. mean, standard deviation) 2. Highlight a cell where you want to add a calculation 3. Choose Insert from the main menu, and then Function from the dropdown list Choose AVERAGE to calculate mean Choose STDEVP to calculate standard deviation, or Type an equal sign followed by STDEVP Note: There is no Function to calculate mode for qualitative values or frequency distribution. You will either need to determine frequency distribution and input the calculated value into the data table OR create a formula in Google Sheets to calculate frequency distribution. 4. Select the cells with the appropriate data to be analyzed Either select and highlight the cells, or type the cell numbers into the window that appears. Note: When calculating standard deviation, do not include the mean value when selecting the data to be analyzed. Standard Error Standard error is used instead of standard deviation with the number of data values in the data set is relatively small samples less than 25. It too describes the variation (or spread) of values in a data set, but eliminates the affect of outliers, which have a greater impact on a small data set as opposed to a large data set. It is calculated by dividing standard deviation by the square root of the sample size. Standard Error = Standard Deviation/ (Number of data values in the sample size) To calculate standard error using Excel or Google Sheets 1. Highlight a cell where you want to add a calculation for standard error. 2. To calculate standard error: Type an equal sign = Click the cell containing the standard deviation value you previously calculated. Type a forward slash / to indicate division Then type SQRT to calculate square root. Type the number of data values in the sample size within parentheses, (N) Press Enter or Return to complete the calculation. Frequency Distribution When using qualitative data, frequency distribution is a good expression of variation. Frequency distribution is a decimal that represents the number of times a particular data value occurs for each experimental group. It is calculated by dividing the number of times a particular data value occurs by the total number of data in the set. To calculate frequency distribution: 1. Identify and the number of times a particular data value occurs in a data set. 2. Divide this number by the total number of data in the set. 3. Report this value as a decimal. 4. Calculate and record frequency distribution for all data categories in the appropriate column of the data table.

3 INFERENTIAL STATISTICS To calculate inferential statistics using Google Sheets 1. Open a new spreadsheet in Google Sheets. 2. Under the Add-ons menu choose Get add-ons. 3. Type Statistics in the Search add-ons dialog box. 4. Click Free next to the XLMiner Analysis ToolPak. 5. Go back to the Add-ons menu, place the cursor over XLMiner Analysis ToolPak and choose Start. 6. A list of Analysis Tools should appear to the right of the sheet. t-test: Two Sample Assuming Equal Variance A standard t-test is used to compare two sets of data - control data and experimental data, in order to determine if there is an actual difference between the averages of both data sets. 1. Organize the data in two columns, one for the control and another for the treatment. 2. Choose t-test: Two Sample Assuming Equal Variance from the Analysis Tools on the right. 3. Click the dialog box for Variable 1 Range, then select the column of data related to your control data. Select the column heading too. Double check to be sure the range that appears in the dialog box corresponds to the control data. 4. Click the dialog box for Variable 2 Range, then select the column of Control Experimental data related to your experimental data. Select the column heading too. Double check to be sure the range that appears in the dialog box corresponds to the experimental data. 5. Select the Labels Option 6. Click the dialog box for Output Range and select a location on the spreadsheet for the statistical test results to appear. 7. Choose OK. 8. The test provides a lot of information, but you should focus on the p-values. Use the two-tailed p-value if your hypothesis predicted that the means would merely be different from one another. However, if you predicted one mean to be greater or less than the other, use the one-tailed p- value. ANOVA: Single Factor A single factor ANOVA test analyzes the effect of one independent variable. It indicates whether or not the variable being tested had a measurable effect. While it is true that all ANOVA tests are able to tell whether or not there are statistically significant differences somewhere in the data as a whole, it does not indicate where exactly those differences are. For example, if the various amounts of fertilizer are tested on plant growth. The ANOVA can suggest with a p-value less than.05 that fertilizer does in fact affect plant growth. It does not indicate which amount of fertilizer has the greatest effect. 1. Organize the data in two columns, one for each treatment or level of the independent variable. Fertilizer 0 ml 150 ml 300 ml 600 ml

4 Choose ANOVA - Single Factor from the Analysis Tools on the right Click the dialog box for Input Range, then select the columns of data related to your results. Select the column headings representing treatment too. Double check to be sure the range that appears in the dialog box corresponds to the control data. 4. Select the Labels Option 5. Click the dialog box for Output Range and select a location on the spreadsheet for the statistical test results to appear. Double check to be sure the location you prefer appears in the dialog box. 6. Choose OK. 7. The test provides a lot of information, but you should focus on the p-values. As stated above, a p- value of.05 or less represents data that is statistically significant, providing confidence that the variable you tested in fact had a measurable effect. ANOVA: Two Factor With Replication A two factor ANOVA test analyzes the effect of two independent variables. It indicates whether or not the variables being tested had a measurable effect. While it is true that all ANOVA tests are able to tell whether or not there are statistically significant differences somewhere in the data as a whole, it does not indicate where exactly those differences are. For example, if the various amounts of light and fertilizer are tested on plant growth. The ANOVA can suggest with a p-value less than.05 that light and fertilizer affected plant growth. It does not indicate which amount of light or fertilizer had the greatest effect. 1. Organize the data in two columns, one for each treatment or level of the independent variable. 2. Choose ANOVA - Two Factor with Replication from the Light Fertilizer Analysis Tools on the right. 3. Click the dialog box for Input Range, then select the rows and 0 ml 150 ml 300 ml columns of data related to your results. Select the column headings 8 hr representing the treatments too. Double check to be sure the range that appears in the dialog box corresponds to the control data. 4. Click the dialog box for Rows per Sample. Enter the number of rows containing data for the treatments organized in rows. For example, there are four rows for each light treatment in the table 16 hr above. 5. Click the dialog box for Output Range and select a location on the spreadsheet for the statistical test results to appear. Double check to be sure the location you prefer appears in the dialog box Choose OK. 7. The test provides a lot of information, but you should focus on the 24 hr p-values. As stated above, a p-value of.05 or less represents data that is statistically significant, providing confidence that the variables you tested in fact had a measurable effect Graphing Guidelines Computer Graphing Use the instructions below to enter, analyze, and graph data in Excel and Google Sheets. Graphing in Excel for Windows: 1. Create a data table in an Excel spreadsheet complete with all relevant data values. 2. Highlight data to appear on the y-axis (the DV). If appropriate, you can also highlight the data for the x-axis (the IV). Note: in many cases, this will be the values in the central tendency column 3. Select Insert from the menu Select the appropriate type of graph (recommended type for bar graphs is Clustered Column).

5 Choose Select Data under Chart Tools Design to change series titles and horizontal category axis if applicable. Note: category x axis labels represent the levels of the independent variable Click on the grid icon next to the window labeled horizontal category axis and then simply highlight the cells containing the levels of the IV on your data table. Click OK. Choose Chart Tools Layout from the toolbar and select Chart Title to title the graph. Choose Chart Tools Layout from the toolbar and select Axis Title. Choose Horizontal Axis Label to label the x- axis by typing the independent variable. Don t forget units! Choose Chart Tools Layout from the toolbar and select Axis Title. Choose Vertical Axis Label to label the y- axis by typing the dependent variable. Don t forget units! 4. Select Chart Tools Layout Move Chart and select New Sheet Note: Graphs can often better express the difference between data values by changing the scale of the y-axis. To do this, double click on the y-axis of your graph. Under scale, change the minimum value when appropriate. Graphing Error Bars (standard deviation) in Excel - Windows: 1. Choose Chart Tools Layout from the toolbar and select Error Bars. Note: This may not work if you created a 3 dimensional bar graph. Change the chart type to Clustered Column. 2. Choose the item titled More Error Bar Options from dialogue box. 3. Click the Both icon and select Custom. Click Specify Value. Click on the grid icon next to the window labeled Positive Error Value. Highlight the cells containing values for standard deviation on your data table. Click on the grid icon next to the window labeled Negative Error Value. Highlight the cells containing values for standard deviation on your data table. Click OK. Graphing in Excel Mac: 1. Create a data table in an Excel spreadsheet complete with all relevant data values. 2. Highlight data to appear on the y-axis (the DV). If appropriate, you can also highlight the data for the x-axis (the IV). Note: in many cases, this will be the values in the central tendency column 3. Select Insert Chart from the menu Select the appropriate type of graph (recommended type for bar graphs is Clustered Column). Select Chart Source Data to change series titles and category x- axis labels if applicable. Note: category x axis labels represent the levels of the independent variable Click on the grid icon next to the window labeled category x-axis labels and then simply highlight the cells containing the levels of the IV on your data table. Click OK. Choose Chart Layout from the toolbar and select Chart Title to title the graph. Choose Chart Layout from the toolbar and select Axis Title. Choose Horizontal Axis Label to label the x- axis by typing the independent variable. Don t forget units! Choose Chart Layout from the toolbar and select Axis Title. Choose Vertical Axis Label to label the y- axis by typing the dependent variable. Don t forget units! 4. Select Chart Move Chart and select New Sheet I: Graphs can often better express the difference between data values by changing the scale of the y- axis. To do this, double click on the y-axis of your graph. Under scale, change the minimum value when appropriate. Graphing Error Bars (standard deviation) in Excel - Mac: 1. If the graph is a bar graph, double click on one of the bars. If the graph is a line graph, double click on one of the data points in the graph. Note: This may not work if you created a 3 dimensional bar graph. Change the chart type to Clustered Column. 2. Choose the item titled Error Bars from dialogue box. 3. Click the Both icon and select Custom. Click Specify Value. Click on the grid icon next to the window labeled Positive Error Value. Highlight the cells containing values for standard deviation on your data table. Click on the grid icon next to the window labeled Negative Error

6 Value. Highlight the cells containing values for standard deviation on your data table. Click OK. Graphing in Google Sheets: 1. Create a data table in Google Sheets complete with all relevant data values. An effective method for organizing the data to graph is illustrated to the right. 2. Highlight the data to appear on the y-axis (the DV) and the treatments corresponding to those measured values. Select Insert Chart from the menu Under Chart Types, select the appropriate type of graph (recommended type for bar graphs is Clustered Column). Light (hours) and Mean (biomass, g) Use the preview to determine if the data is represented accurately. Select or deselect Switch rows / columns and Use column/row as label to change series titles and category x- axis labels if applicable. Choose Customization. Click on the dialog box next to Title to add a title. Scroll down to orient the legend if applicable. Scroll down to Axis and click on the drop down menu to select the horizontal axis. Type the axis label in the dialog box provided. Change the axis scale if necessary. Repeat for the vertical axis. Click Insert to finish the graph. To move the graph to a new sheet, click the arrow in the upper right hand corner of the graph and choose Move to own sheet from the drop-down menu. Graphing Error Bars (standard deviation and standard error) in Google Sheets: 1. Choose Advanced edit. Note: This may not work if you created a 3 dimensional bar graph. Change the chart type to Clustered Column. 2. Choose Customization. 3. Scroll down to Series and note the treatment selected. 4. Click on the dialog box next to Error bars. Choose Constant and type the standard deviation or standard error value in the corresponding dialog box for the selected treatment. 5. Click on the drop-down menu next to the Series and choose a different treatment. 6. Repeat the Error bar steps by choosing Constant and typing the standard deviation or standard error value in the corresponding dialog box for the selected treatment. 7. Continue until error bar values have been included for all treatments.

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