(Basic Statistics for Citizen Data Scientist) Power of One Sample Variance Testing Let represent the hypothetical variance and s2 the observed variance. Let x+crit be the right critical value (based on the null hypothesis with significance level α/2) and x-crit be the left critical value (two-tailed test) , i.e. x-crit = CHIINV(1−α/2,n−1) x+crit = CHIINV(α/2,n−1) Let δ = /s2. Then the beta …
(Basic Statistics for Citizen Data Scientist) One Sample Hypothesis Testing of the Variance Based on Theorem 2 of Chi-square Distribution and its corollaries, we can use the chi-square distribution to test the variance of a distribution. Example 1: A company produces metal pipes of a standard length. Twenty years ago it tested its production quality and found that …
(Basic Statistics for Citizen Data Scientist) Chi-square Distribution Definition 1: The chi-square distribution with k degrees of freedom, abbreviated χ2(k), has probability density function k does not have to be an integer and can be any positive real number. Click here for more technical details about the chi-square distribution, including proofs of some of the propositions described below. Except for the proof …
(Basic Statistics for Citizen Data Scientist) Equivalence Testing (TOST) The objective of a two-sample equivalence test is to determine whether the means of two populations are equivalent based on two independent samples from these populations; here “equivalent” means that the two means differ by a small pre-defined amount. This margin of equivalence is determined by …
(Basic Statistics for Citizen Data Scientist) Coefficient of Variation Testing One Sample Testing In Measures of Variability, we describe the unitless measure of dispersion called the coefficient of variation. It turns out that s/x̄ is a biased estimator for the population coefficient of variation σ/μ. A nearly unbiased estimator is where n is the sample size. When the coefficient of variation …
(Basic Statistics for Citizen Data Scientist) Paired Sample t Test In paired sample hypothesis testing, a sample from the population is chosen and two measurements for each element in the sample are taken. Each set of measurements is considered a sample. Unlike the hypothesis testing studied so far, the two samples are not independent of one another. …
(Basic Statistics for Citizen Data Scientist) Two Sample t Test: unequal variances Theorem 1: Let x̄ and ȳ be the sample means and sx and sy be the sample standard deviations of two sets of data of size nx and ny respectively. If x and y are normal, or nx and ny are sufficiently large for the Central Limit Theorem to hold, then the random variable has distribution T(m) where Observation: The nearest integer to m can be …
(Basic Statistics for Citizen Data Scientist) Two Sample t Test: equal variances We now consider an experimental design where we want to determine whether there is a difference between two groups within the population. For example, let’s suppose we want to test whether there is any difference between the effectiveness of a new drug for …
(Basic Statistics for Citizen Data Scientist) One Sample t Test The t distribution provides a good way to perform one-sample tests on the mean when the population variance is not known provided the population is normal or the sample is sufficiently large so that the Central Limit Theorem applies. It turns out that the t distribution provides good results even …
(Basic Statistics for Citizen Data Scientist) Basic Concepts of t Distribution The one sample hypothesis test described in Hypothesis Testing using the Central Limit Theorem using the normal distribution is fine when one knows the standard deviation of the population distribution and the population is either normally distributed or the sample is sufficiently large that the Central Limit …