Sampling Distribution, Central Limit Theorem, and Unbiasedness in Behavioral Statistics, Study notes of Statistics for Psychologists

Download Sampling Distribution, Central Limit Theorem, and Unbiasedness in Behavioral Statistics and more Study notes Statistics for Psychologists in PDF only on Docsity! Basic Statistics for The Behavioral Sciences LECTURE NOTES 1 Docsity.com Ch. 7. Sampling Distribution, Central Limit Theorem, and Unbiasedness. I. Three different distributions A. Population dist; usually large, infinite, and hypothetical dist consisted of raw scores (X) with parameters as summary characteristics. B. Sample dist; small, finite, and empirical dist consisted of raw scores(X) with statistics as summary characteristics. C. Sampling dist; a hypothetical, theoretical, and probability dist consisted of a statistic. II. Sampling distribution A. Definition: A theoretical distribution of a statistic computed across all possible samples (usually infinite) of a given size n drawn from a given population. (e.g.) B. Properties of sampling distribution. 1. There are infinitely many sampling distributions depending on different statistics computed from different sample sizes. 2. A theoretical, probability distribution. 10 C. Notation 1. Population dist.; μ σx² 2. Sample dist.; M sx² 3. Sampling dist.; Mµ , 2 Mσ 2sµ ² 2 2sσ III. Sampling distribution of sample means A. Definition; a particular sampling dist consisted of sample means. B. For a population dist of X with mean of μ, and variance of σ², the sampling distribution of sample means is normally distributed with the mean of μ, and variance of σ²/n, if 1) the population distribution is normally distributed, or 2) the sample size (n) approaches infinity. C. The case of 2) is called Central Limit Docsity.com