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# Satterthwaite Pooled Standard Error

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## T-test Pooled Vs Satterthwaite

Sampling in Statistics Famous Mathematicians and Statisticians Calculators Variance and Standard Deviation Calculator Tdist satterthwaite approximation degrees of freedom Calculator Permutation Calculator / Combination Calculator Interquartile Range Calculator Linear Regression Calculator Expected Value Calculator Binomial Distribution Calculator Statistics Blog Calculus satterthwaite approximation calculator Matrices Practically Cheating Statistics Handbook Navigation Satterthwaite approximation Probability and Statistics > T-Distributions > Satterthwaite approximation Before you read this article, you may want to read this one first: Pooled standard error (how to find

## Satterthwaite Approximation In R

it). Watch the video or read the article below: What is the Satterthwaite Approximation? The Satterthwaite approximation is a way to account for two different sample variances. Basically, there are two ways to account for two sample variances: Use the pooled standard error formula: Sp √ (1/n1 + 1/n2) Use Satterthwaite's: Se = √ (s12/n1 + s22/n2) The two formulas are essentially equivalent -- they will both give exactly the same

## Satterthwaite Approximation T-test

answer. However, there are significant differences when the variances for the two samples are different. The pooled SE can only be used when your variances are equal -- which almost never happens in real life. When your variances are not equal, use the Satterthwaite approximation. In fact, the Satterthwaite is always correct, so you may want to consider always using it over the pooled SE. Satterthwaite Approximation: Steps Sample problem: Use the Satterthwaite approximation for the following sample data: Sample 1: s=20, n=50. Sample 2: s=15, n=40. Step 1: Insert your data into the formula. Note that: n1 is the sample size from the first sample; n2 is the sample size from the second sample; s1 is the standard deviation from the first sample; s12is the variance. s2 is the standard deviation from the first sample; s22is the variance. Se = √ (202/50 + 152/40) Step 2: Solve: Se = √ (8 + 5.625) ≈ 3.691 The Satterthwaite approximation is roughly equal to 3.691. That's it! Satterthwaite approximation was last modified: February 5th, 2016 by Andale By Andale | November 26, 2013 | T-Distribution | 2 Comments | ← Middle Fifty in Statistics: What is it? Choose Bin Sizes for Histograms in Easy Steps → 2 thoughts

## Two Sample T Test Sas

Cross Validated Questions Tags Users Badges Unanswered Ask Question _ Cross Validated is a question and answer site for people interested in satterthwaite approximation excel statistics, machine learning, data analysis, data mining, and data visualization. Join them; it only takes a minute: Sign up Here's how it works: Anybody can ask a question Anybody can answer The best answers are voted http://www.statisticshowto.com/satterthwaite-approximation/ up and rise to the top Satterthwaite approximation vs Pooled Sample Standard Error up vote 1 down vote favorite Udacity gives two equations for standard error, and calls the second (pooled) one "corrected" without proof. At 2:30, the narrator states that the following is the Standard Error for Independent Samples, after going through some kind of informal semantic explanation: $$SE = \sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}$$ $s_1$ and $s_2$ are the sample standard http://stats.stackexchange.com/questions/232817/satterthwaite-approximation-vs-pooled-sample-standard-error deviations. Later in the lesson though, in a 14 second video, the narrator blithely replaces these individual sample variances with the pooled variance: $$SE = \sqrt{\frac{s_p^2}{n_1} + \frac{s_p^2}{n_2}}$$ The narrator specifically uses the word "corrected", implying that the first is biased...? Udacity has yet to use the word "biased" though, so perhaps I'm focusing too much on specific word choice. Some googling led me to this video which states that the first SE formulation is the Satterthwaite approximation. It states that the Satterthwaite approximation may be always used instead of the pooled variant, which makes sense to me because it is more general. Can I ignore the word "corrected" and always use the Satterthwaite approximation? standard-error pooling inferential-statistics share|improve this question asked Sep 1 at 9:11 DharmaTurtle 1727 add a comment| 1 Answer 1 active oldest votes up vote 1 down vote accepted They are the same thing. Let's rephrase what we want to do here. We want to use two samples t-test for statistical testing, and we have two groups. Each group has it's own variance. The variance of the two groups can be anything. This makes your first formula, where you have s1 and s2. So far, we have not assumed anything other than the sample size of two groups is

performs t-tests for one sample, two samples and paired observations. The single-sample t-test compares the mean of the sample to a given http://www.ats.ucla.edu/stat/sas/output/ttest.htm number (which you supply). The dependent-sample t-test compares the difference in the means from the two variables to a given number (usually 0), while taking into account the fact that the scores are not independent. The independent samples t-test compares the difference in the means from the two groups to a given value (usually 0). In other words, it tests satterthwaite approximation whether the difference in the means is 0. In our examples, we will use the hsb2 data set. Single sample t-test For this example, we will compare the mean of the variable write with a pre-selected value of 50. In practice, the value against which the mean is compared should be based on theoretical considerations and/or previous research. proc ttest data="D:\hsb2" satterthwaite pooled standard H0=50; var write; run; The TTEST Procedure Statistics Lower CL Upper CL Lower CL Upper CL Variable N Mean Mean Mean Std Dev Std Dev Std Dev Std Err write 200 51.453 52.775 54.097 8.6318 9.4786 10.511 0.6702 T-Tests Variable DF t Value Pr > |t| write 199 4.14 <.0001 Summary statistics Statistics Lower CL Upper CL Lower CL Upper CL Variablea Nb Meanc Meand Meanc Std Deve Std Devf Std Deve Std Errg write 200 51.453 52.775 54.097 8.6318 9.4786 10.511 0.6702 a. Variable - This is the list of variables. Each variable that was listed on the var statement will have its own line in this part of the output. b. N - This is the number of valid (i.e., non-missing) observations used in calculating the t-test. c. Lower CL Mean and Upper CL Mean - These are the lower and upper bounds of the confidence interval for the mean. A confidence interval for the mean specifies a range of values within which the unknown population parameter, in this case the mean, may lie. It is given by

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