1 / 4

STAT 3120 Statistical Methods I

STAT 3120 Statistical Methods I. Lecture 6 The Central Limit Theorem. STAT3120 - Central Limit Theorem. Before we get into a discussion of the Central Limit Theorem, lets take a minute to talk about the differences between Descriptive and Inferential statistics:.

ellema
Télécharger la présentation

STAT 3120 Statistical Methods I

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. STAT 3120Statistical Methods I Lecture 6 The Central Limit Theorem

  2. STAT3120 - Central Limit Theorem Before we get into a discussion of the Central Limit Theorem, lets take a minute to talk about the differences between Descriptive and Inferential statistics: Analysis of a SAMPLE of data – population is unavailable because of time, cost, access, etc. Results are NEVER 100% accurate. Analysis of ALL available data of interest. Results are ALWAYS 100% accurate. Descriptive Statistics • Descriptions of central tendency and variation; • Visualizations through tables and graphics. Inferential Statistics • Drawing an inference onto a population through Confidence Intervals, Hypothesis Testing, Statistical Models, etc.

  3. STAT3120 - Central Limit Theorem When we draw a sample (>30) because we cannot access the entire population, the descriptive measures of the sample (specifically the mean) will not equal the descriptive statistics for the population. Sample statistics will follow a distribution – which is normal. This concept forms the basis for the Central Limit Theorem – which forms the basis for why statistics “works”. Take a look at this applet: http://www.ruf.rice.edu/~lane/stat_sim/sampling_dist/index.html

  4. STAT3120 - Central Limit Theorem Important concepts to remember about the Central Limit Theorem: • The distribution of sample means will, as the number of samples increases approach a normal distribution; • The mean of all sample means approximates the population mean; • The std of all sample means is the std of the population/the SQRT of the sample size; • If the population is NOT normally distributed, sample sizes must be greater than 30 to assume normality; • If the population IS normally distributed, samples can be of any size to assume normality (although greater than 30 is always preferred). • The CLT DOES NOT provide that any individual sample will be normally distributed.

More Related