Experimental error: Under "Analytical resources," review "error analysis and significant figures" and "error representation and curvefiting."
Statistical tests: [Unpaired (independent) t test] [paired t test] [Chi-squared test] [sample problems] [solutions to sample problems]
Tables: ['Student's' t distribution] [Chi-squared critical values]

'Student's' t Test (For Paired Samples) Use this test to compare two small sets of quantitative data when data in each sample set are related in a special way. Criteria The number of points in each data set must be the same, and they must be organized in pairs, in which there is a definite relationship between each pair of data points If the data were taken as random samples, you must use the independent test even if the number of data points in each set is the same Even if data are related in pairs, sometimes the paired t is still inappropriate Here's a simple rule to determine if the paired t must not be used - if a given data point in group one could be paired with any data point in group two, you cannot use a paired t test Examples The paired t test is generally used when measurements are taken from the same subject before and after some manipulation such as injection of a drug. For example, you can use a paired t test to determine the significance of a difference in blood pressure before and after administration of an experimental pressor substance. You can also use a paired t test to compare samples that are subjected to different conditions, provided the samples in each pair are identical otherwise. For example, you might test the effectiveness of a water additive in reducing bacterial numbers by sampling water from different sources and comparing bacterial counts in the treated versus untreated water sample. Each different water source would give a different pair of data points. The value of the paired t test is best demonstrated in an example. Suppose patient 1 responds to a drug with a 5 mm Hg rise in mean blood pressure from 100 to 105. Patient 2 has a 30 mm Hg rise, from 90 to 120. Likewise for several other subjects. The response to the drug varied widely, but all patients had one thing in common - there was always a rise in blood pressure. Some of that experimental error is avoided by the paired t test, which likely will pick up a significant difference. The independent test, which would be improperly applied in this case, would not be able to reject the null hypothesis. Be certain that use of the paired t test is valid before applying it to real data. An applied statistics course or supervision of a qualified mentor may provide the experience you need. Some spreadsheet programs include the paired t test as a built-in option. Even without a built-in option, is is so easy to set up a spreadsheet to do a paired t test that it may not be worth the expense and effort to buy and learn a dedicated statistics software program, unless more complicated statistics are needed.