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How To Calculate The Pooled Standard Error

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When To Use Pooled Variance

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Pooled Variance T Test

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when they are assumed to have a common standard deviation. The pooled standard deviation is the average spread of all data

Pooled Two Sample T Test

points about their group mean (not the overall mean). It is when to use pooled t test a weighted average of each group's standard deviation. The weighting gives larger groups a proportionally greater pooled t test formula effect on the overall estimate. Pooled standard deviations are used in t-tests, ANOVAs, control charts, and capability analysis. Example of a pooled standard deviation Suppose your https://www.youtube.com/watch?v=kkEszcVaWhA study has the following four groups: Group Mean Standard Deviation N 1 9.7 2.5 50 2 12.1 2.9 50 3 14.5 3.2 50 4 17.3 6.8 200 The first three groups are equal in size (n=50) with standard deviations around 3. The fourth group is much larger (n=200) and has a higher standard http://support.minitab.com/en-us/minitab/17/topic-library/basic-statistics-and-graphs/introductory-concepts/standard-deviation-variance-and-the-normal-distribution/pooled-sd/ deviation (6.8). Because the pooled standard deviation uses a weighted average, its value (5.486) is closer to the standard deviation of the largest group. If you used a simple average, then all groups would have had an equal effect. Manually calculating the pooled standard deviation Suppose C1 contains the response, and C3 contains the mean for each factor level. For example: C1 C2 C3 Response Factor Mean 18.95 1 14.5033 12.62 1 14.5033 11.94 1 14.5033 14.42 2 10.5567 10.06 2 10.5567 7.19 2 10.5567 Use Calc > Calculator with the following expression: SQRT((SUM((C1 - C3)^2)) / (total number of observations - number of groups)) For the previous example, the expression for pooled standard deviation would be: SQRT((SUM(('Response' - 'Mean')^2)) / (6 - 2)) The value that Minitab stores is 3.75489. Minitab.comLicense PortalStoreBlogContact UsCopyright © 2016 Minitab Inc. All rights Reserved.EnglishfrançaisDeutschportuguêsespañol日本語한국어中文（简体）By using this site you agree to the use of cookies for analytics and personalized content.Read our policyOK

draw conclusions about populations. Related Articles How to Convert Quadratic Equations From Standard to Vertex Form How to Solve Cubic Polynomials How to Calculate the Carbon Footprint of Your Lawn Mower How to Calculate Vector Cross Product Statisticians often http://classroom.synonym.com/calculate-pooled-standard-error-2686.html compare two or more groups when conducting research. Either because of participant dropout or funding reasons, the number of individuals in each group can vary. In order to make up for this variation, a special type of standard error http://stattrek.com/statistics/formulas.aspx is used which accounts for one group of participants contributing more weight to the standard deviation than another. This is known as a pooled standard error. Step 1 Conduct an experiment and record the sample sizes and standard deviations t test of each group. For example, if you were interested in the pooled standard error of the daily caloric intake of teachers versus school children, you would record the sample size of 30 teachers (n1 = 30) and 65 students (n2 = 65) and their respective standard deviations (let's say s1 = 120 and s2 = 45). Step 2 Calculate the pooled standard deviation, represented by Sp. First, find the numerator of Sp²: (n1 -- 1) x (s1)² pooled t test + (n2 -- 1) x (s2)². Using our example, you would have (30 -- 1) x (120)² + (65 -- 1) x (45)² = 547,200. Then find the denominator: (n1 + n2 -- 2). In this case, the denominator would be 30 + 65 -- 2 = 93. So if Sp² = numerator / denominator = 547,200 / 93 ≈ 5,884, then Sp = sqrt(Sp²) = sqrt(5,884) ≈ 76.7. Step 3 Compute the pooled standard error, which is Sp x sqrt(1/n1 + 1/n2). From our example, you would get SEp = (76.7) x sqrt(1/30 + 1/65) ≈ 16.9. The reason you use these longer calculations is to account for the heavier weight of students affecting the standard deviation more and because we have unequal sample sizes. This is when you have to "pool" your data together to conclude more accurate results. Things You Will Need Calculator References Fayetteville State University: Independent Samples t-test; David S. Wallace Ph. D.University of New Mexico: Variations of the t-test; Marcus Hamilton About the Author Sky Smith has been writing on psychology, electronics, health and fitness since 2002 for various online publications. He graduated from the University of Florida with honors in 2005, earning a Bachelor of Science in psychology and statistics with a minor in math. Photo Credits chocolates image by Renata Osinska from Fotolia.com Related Searches Higher Education Prep How to Calculate Marginal P

 

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