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- https://chem.libretexts.org/Bookshelves/Analytical_Chemistry/Instrumental_Analysis_(LibreTexts)/35%3A_Appendicies/35.03%3A_Critical_Values_for_t-TestIn the first approach we choose a value of \(\alpha\) for rejecting the null hypothesis and read the value of \(t(\alpha,\nu)\) from the table below. In the second approach, we find the row in the tab...In the first approach we choose a value of \(\alpha\) for rejecting the null hypothesis and read the value of \(t(\alpha,\nu)\) from the table below. In the second approach, we find the row in the table below that corresponds to the available degrees of freedom and move across the row to find (or estimate) the a that corresponds to \(t_\text{exp} = t(\alpha,\nu)\); this establishes largest value of \(\alpha\) for which we can retain the null hypothesis.
- https://chem.libretexts.org/Bookshelves/Analytical_Chemistry/Analytical_Chemistry_2.1_(Harvey)/04%3A_Evaluating_Analytical_Data/4.06%3A_Statistical_Methods_for_Normal_DistributionsThis page discusses the use of statistical tests to compare means and variances in analytical chemistry. Key methods include the t-test for comparing sample means, the F-test for variances, and signif...This page discusses the use of statistical tests to compare means and variances in analytical chemistry. Key methods include the t-test for comparing sample means, the F-test for variances, and significance tests for outliers like Dixon's Q-test, Grubb's test, and Chauvenet's criterion. The tests help determine if observed differences are significant or due to chance, aiding in validating analytical methods or identifying errors in analyses.
- https://chem.libretexts.org/Bookshelves/Analytical_Chemistry/Analytical_Chemistry_2.1_(Harvey)/16%3A_Appendix/16.04%3A_Critical_Values_for_t-TestThe page describes two approaches to interpreting a t-test once t_{exp} has been calculated. The first approach involves selecting an alpha value to reject the null hypothesis and comparing t_{exp} ag...The page describes two approaches to interpreting a t-test once t_{exp} has been calculated. The first approach involves selecting an alpha value to reject the null hypothesis and comparing t_{exp} against the critical t-values from a table. If t_{exp}) is greater, the null hypothesis is rejected.
- https://chem.libretexts.org/Courses/Los_Angeles_Trade_Technical_College/Analytical_Chemistry/2%3A_Analytical_Chemistry_2.0_(Harvey)/05%3A_Evaluating_Analytical_Data/5.05%3A_Statistical_Analysis_of_DataA confidence interval is a useful way to report the result of an analysis because it sets limits on the expected result. In the absence of determinate error, a confidence interval indicates the range ...A confidence interval is a useful way to report the result of an analysis because it sets limits on the expected result. In the absence of determinate error, a confidence interval indicates the range of values in which we expect to find the population’s expected mean. When we report a 95% confidence interval for the mass of a penny as 3.117 g ± 0.047 g, for example, we are claiming that there is only a 5% probability that the expected mass of penny is less than 3.070 g or more than 3.164 g.
- https://chem.libretexts.org/Bookshelves/Analytical_Chemistry/Analytical_Chemistry_2.1_(Harvey)/04%3A_Evaluating_Analytical_Data/4.05%3A_Statistical_Analysis_of_DataThis page discusses the concept of confidence intervals and significance testing in statistical analysis. Confidence intervals are used to estimate the range of values within which a population mean m...This page discusses the concept of confidence intervals and significance testing in statistical analysis. Confidence intervals are used to estimate the range of values within which a population mean may lie, providing a probabilistic basis for making inferences. Significance testing, or hypothesis testing, involves comparing sample results to determine if differences are due to random error or significant factors.
- https://chem.libretexts.org/Courses/Lakehead_University/Analytical_I/4%3A_Evaluating_Analytical_Data/4.05%3A_Statistical_Analysis_of_DataA confidence interval is a useful way to report the result of an analysis because it sets limits on the expected result. In the absence of determinate error, a confidence interval indicates the range ...A confidence interval is a useful way to report the result of an analysis because it sets limits on the expected result. In the absence of determinate error, a confidence interval indicates the range of values in which we expect to find the population’s expected mean. When we report a 95% confidence interval for the mass of a penny as 3.117 g ± 0.047 g, for example, we are claiming that there is only a 5% probability that the expected mass of penny is less than 3.070 g or more than 3.164 g.
- https://chem.libretexts.org/Bookshelves/Analytical_Chemistry/Analytical_Chemistry_2.1_(Harvey)/04%3A_Evaluating_Analytical_Data/4.11%3A_Chapter_Summary_and_Key_TermsThe page discusses the characterization of data by central tendency and spread, involving measures like mean, median, range, and standard deviation. Errors affecting accuracy and precision are address...The page discusses the characterization of data by central tendency and spread, involving measures like mean, median, range, and standard deviation. Errors affecting accuracy and precision are addressed through propagation of uncertainty. The page covers probability distributions, normal distribution confidence intervals, and statistical analysis techniques such as t-tests and F-tests for comparing data sets.
