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Sample T-Test Spreadsheet: Comparing Soil Arsenic Between Two Different Regions
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In this example, ten soil samples were collected in Sweet Home, and ten more in Corvallis. All soil samples were analyzed by instrumental neutron activation analysis (INAA) at OSU to determine arsenic content on a ppm basis.
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Is the average soil arsenic really different as suggested by the averages, or only different because we could only take and then analyze a finite number of samples? (INAA is expensive!)
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On this spreadsheet, a T-test is used to compare the average arsenic content in soil between Sweet Home and Corvallis.
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When opened in Excel or Google Sheets, click on a yellow highlighted cell and look at the box below the tool bar at the top of the screen to see the formula used to compute the average, standard deviation, and T-test.
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Soil Arsenic Content (ppm)
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Sample #Sweet Home SoilsCorvallis Soils
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10.230.1
How a T-test result is used:
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20.430.15
T-test results will always range from 0 to 1.0
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30.120.07
(1-(T-test result))x100% = the percent confidence we have in any difference seen between an average value between the two populations.
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40.220.11
A low t-test result means there is high confidence that the difference in the average values of the two populations is real and exists.
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50.330.23
In contrast, a high t-test result means there is less confidence that the difference in the average values of the two populations being compared really exists. Instead, random error in measurements might be the reasons the difference was calculated.
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60.240.04
There is one HUGE assumption being made here: the populations of measurements or samples come from a normally distributed population.
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70.420.1
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80.320.11
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90.330.16
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100.110.21
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Average:0.2750.128
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St. dev.:0.11088031590.05959119995
Standard deviation gives you a sense for the variation between a sample in a SINGLE group or population.
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T-test Results:0.002465686041
So . . . this T-test result indicates that there is a 99.75% chance [(1-.002465) x100%] that we can believe what we are seeing, that the average aresenic content is different between the two locations.
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FORMULA FORMAT TO USE:
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=average(F5:F14)
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=stdev(F5:F14)
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=ttest(F5:F14,G5:G14,2,3)
F5:F14 and G5:G14 represent the two sets of data -- these will be different for your spreadsheet
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HOW TO INTERPRET YOUR T-TEST RESULT:
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A T-test result helps you determine whether or not any difference between the means of two populations is statistically significant.
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If the T-test result is 0.05, there is a 95% chance (often stated as having a 95% confience level . . . ) that a difference in the averages (aka means) seen for these two sets of data is real.
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If the T-test result is less than 0.05, there is more than a 95% chance that a difference in the averages seen for these two sets of data are real. We might say the populations are different.
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If the T-test result is greater than 0.05, there is less than a 95% chance that a difference in the averages seen for these two sets of data is real. We become less confident in saying there is a difference between these two populations.
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The above T-tests suggests a 99.75% chance that the arsenic values are actually different, and it was calculated as follows: [(1.0 - (T-test result)) x 100%]
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Higher t-test results suggest that our sampling or sampling methods might be causing our averages to be different rather than the averages truly being different.
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