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First, make sure your data are entered appropriately in a spreadsheet. For an example, you may use the mountain lion weight data found here.
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Go to the Data tab, Data Analysis, then select "t-Test: Two Sample Assuming Equal Variances." (If you don't have a Data Analysis option under your Data tab, see directions for installing the ToolPak here.) Your screen should look like this:
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Click in the Variable 1 Range box, then click and drag to highlight the data for your first variable.
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Next click in the Variable 2 Range box, then click and drag to highlight the data for your second variable.
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Important: If you include the column headings (such as northern and southern in this example), make sure the Labels box is checked.
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Click OK. You should see output that looks like this:
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Congratulations - you just successfully completed a t-Test! Now for the hard part - formatting and interpreting your table.
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First, make sure you're seeing all of the output. Sometimes the columns need to be widened so that you can see everything. To automatically make a column wide enough to show all information, place your cursor between the letters of the column heading (where the red circle is located between A and B in the screenshot above) and double click. You should now see all of the information.
Formatting Your Statistical Table
You will need to modify your output table before presenting it in a paper or talk. Some information can be deleted; other information needs to be re-labeled.
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Highlight and delete the rows titled Pooled Variance, Hypothesized Mean Difference, and t Stat. To delete a row, click on the row number on the left so that the entire row is highlighted, then right click and select Delete. (For a full explanation of what all t-Test output means, see Appendix IX of the online Stats Manual).
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Next you need to know whether to use a one-tailed or two-tailed t-Test. If you're simply comparing mean values of two groups and are not predicting which group should have a greater mean value, use a two-tailed p-value (as in this example). If you're predicting which group should have a greater mean value, use a one-tailed p-value.
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Because in this example we're just comparing mean values (and not predicting which should be greater), we're using a two-tailed test. Highlight and delete the rows titled P(T<=t) one-tail, t Critical one-tail, and t Critical two-tail. Highlight the cell called "P(T<=t) two-tail" and re-name it simply "p-value".
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You need to highlight and re-name the columns headings above your output titled "Variable 1" and "Variable 2" (or titled with the headings from your raw data sheet). Type in something accurate and meaningful, such as n. mtn. lion population and s. mtn. lion population. Also, change the font so that it doesn't appear in italics.
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Clarify the row titled Mean by adding words so that it reads "Mean Weight (kgs.)".
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Reporting Digits: You need to reduce the number of decimal places reported for some of the output variables. Report all zeros to the right of the decimal point until a digit with a value greater than zero is reached, then report the next two following digits with a value greater than zero. (For example, report 5.07832 as 5.078, 0.00012497333 as 0.00012. Also, round up if the digit to the right of the last digit you report is 5 or greater. For example, report 32.34511 as 32.35, 0.2053921 as 0.21, 0.0030821 as 0.0031.). If you get a number in scientific notation such as 1.87283E-06, it means 1.87283 x 10-6 (so the decimal place should be moved to the left 6 places for non-scientific notation). You should report that number either as 1.87 x 10-6, or as 0.0000019.
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For papers and presentations, it's important to give tables a clear title and description. Table titles and descriptions always appear above the table (Figure titles and descriptions always appear below the figure). Here you could change the title to read "Table 1. Results of t-Test comparing weights of mountain lions captured in northern and the southern Rockies during the fall of 2004".
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To make a lot of text fit into one cell at the top of your table, you can use the "Merge and Center" button (it looks like a 3 with arrows pointing to the side). Highlight the cells you wish to merge, then click the button. To make the text appear on several lines, go to the Home tab, Alignment, and make sure the Wrap text box is checked.. To change the height of the row, click and drag on the lower border below the row number.
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Your table should now look similar to this:
Interpreting Your Output
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Mean: These values are the calculated averages or arithmetic means for each of the two groups of numbers.
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Variance: This is a measure of the variation within each group of numbers. The greater the value for variance, the greater the variation. It's also helpful to know that the variance = the standard deviation squared. If you wanted to know the standard deviation, you could take the square root of the variance.
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Observations: This is simply the sample size or the number of data points within each group.
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df: This stands for "degrees of freedom" and is related to sample size. It is necessary when you use a statistical table to find your p-value. Even though you have used the computer to find p, it's still important to report df. In general, the greater your df, the better you are able to detect differences between means.
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p-value: This is the "punch-line" - the output that tells you whether the difference between the means in the two groups of data is statistically significant. If p < 0.05, then the difference between the means is statistically significant. If p > 0.05, the difference between the means is not statistically significant. It is also helpful to know precisely what p stands for — it is the probability that the difference between the means is due random chance. The lower the probability that the difference is due to random chance (the lower the value of p), the more likely that something non-random (and possibly biologically or ecologically interesting) is causing the difference between the means. In the comparison of the weights of mountain lions, the p value is 0.20 (which is greater than 0.05) meaning there is a 20% chance that the difference in weight between the two populations is due to random chance. Therefore, there is not a meaningful difference between the two groups of numbers; the difference is not "statistically significant."