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The t-test is a statistical method used to compare the sample mean with a population mean or compare two means from two data sets. The test statistic is calculated from the standard deviation, mean, and number of measurements in the data set at a selected confidence interval and then compared to a table of critical values at this confidence level. If the test statistic is smaller than the critical value, the null hypothesis is accepted. In this case, we state that the difference between the means is not statistically significant and therefore comes from indeterminate (random) errors. If the test statistic is higher than the critical value, the null hypothesis is rejected. In this case, we state that the difference between the means is statistically significant and cannot be explained by random errors. The difference comes from errors in the method, sampling, the analysts themselves, or true phenomenological differences. In statistics, t-tests can be performed on unpaired as well as paired data. Unpaired data are two sets of replicate measurements from the same source; paired data refer to data taken on the same samples or subjects from two different methods or at two different time points for comparison. When only one side of a normal distribution curve is used in the t-test, it is a one-tailed test. If both sides of the distribution are used in the t-test, the test is two-tailed.

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T testStatistical MethodSample MeanPopulation MeanTest StatisticStandard DeviationConfidence IntervalNull HypothesisCritical ValueStatistical SignificanceUnpaired DataPaired DataOne tailed TestTwo tailed Test

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1.15 : Comparing Experimental Results: Student's t-Test

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1.1 : SI Units: 2019 Redefinition

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1.2 : Degrees of Freedom

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1.3 : Statistical Analysis: Overview

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1.4 : Types of Errors: Detection and Minimization

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1.5 : Systematic Error: Methodological and Sampling Errors

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1.6 : Random Error

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1.7 : Standard Deviation of Calculated Results

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1.8 : Introduction to z Scores

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1.9 : Uncertainty: Overview

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1.10 : Propagation of Uncertainty from Random Error

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1.11 : Propagation of Uncertainty from Systematic Error

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1.12 : Uncertainty: Confidence Intervals

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1.13 : Significance Testing: Overview

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1.14 : Identifying Statistically Significant Differences: The F-Test

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