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## STATISTICAL METHODS

by: Celestino Bergnaum

18

0

1

# STATISTICAL METHODS STAT 303

Marketplace > Texas A&M University > Statistics > STAT 303 > STATISTICAL METHODS
Celestino Bergnaum
Texas A&M
GPA 3.5

Staff

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COURSE
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Staff
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Class Notes
PAGES
1
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KARMA
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## Popular in Statistics

This 1 page Class Notes was uploaded by Celestino Bergnaum on Wednesday October 21, 2015. The Class Notes belongs to STAT 303 at Texas A&M University taught by Staff in Fall. Since its upload, it has received 18 views. For similar materials see /class/225758/stat-303-texas-a-m-university in Statistics at Texas A&M University.

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Date Created: 10/21/15
2 Test of Independence Hypotheses Ho the row and column variables are independent HA the row and column variables are related Assumptions Each expected count must be at least 5 for a 2x2 tables For larger ones the average of the expected counts must be 5 and every cell must have at least 1 count df rlcl Type I error We claim that the variables are related when they actually are independent Type II error We fail to prove there is a relationship between the variables even though it does exist pvalue interpretation How often we see at least this strong of a relationship between the two variables when they are actually independent Conclusion If pvalue lt on we reject H0 and conclude that there is a statistically significant relationship between the two variables If pvalue NOT lt on we fail to reject H0 and cannot prove that there is a statistically significant relationship between the two variables Oneway AN OVA F test Hypotheses Ho pl u pk there is no effect on the means due to the categorical variable HA the means are NOT all equal the effect due to the categorical variable is stat sig F test statistic has 2 dfs k l and N k where k is the number of groups means being tested and N is the total number of obs Assumptions 1 Each of the k population or group distributions is normal check with a Normal Quantile Plot or boxplot of each group 2 These distributions have identical variances standard deviations check if largest sd is gt 2 times smallest sd or use Levine s test skip MSE pooled variance and is the estimate of the true variance within each group 3 Each of the k samples is a random sample 4 Each of the k samples is selected independently of one another These assumptions are exactly the same as the pooled l test Type I error We claim that there is a stat sig effect when there actually is not one We claim the means are not all the same when actually they are Type II error We fail to prove there is a stat sig effect even though it does exist We fail to prove the means are not all the same even though they are not all the same pvalue interpretation How often we see at least this strong of an effect when there actually is not one Conclusion If pvalue lt on we reject H0 and conclude that there is a statistically significant effect If pvalue NOT lt on we fail to reject H0 and cannot prove that there is a statistically significant effect Linear Regression ttest Hypotheses Ho 31 0 use 9 7 to predict y there is no linear relationship between x and y HA 31 i 0 use 3 be b1 x to predict y there is a stat sig linear relationship between x and y Assumptions 1 There is a true or population line or equation yx 30 31x g where 30 is the yintercept and 31 is the slope which defines the linear relationship between the independent variable x and the dependent y The random deviations e s allow the points to vary about the true line The estimated line is j be bx 2 The s have mean zero ue 0 3 The standard deviation of the s is constant 02 is not dependent on the x s 4 The afs are independent of each other 5 The afs are normally distributed We use the residuals e s to estimate the g s Combined this say each of the as are independently identically distributed NO 02 or g iid NN0 oz This means that the y s are also normal and each y N N 30le oz NOTE we now have 2 parameters 30 and 31 we have to estimate The sole purpose of residual plots is to check these assumptions I I I Type I error We claim there is a stat sig linear relationship between x and y when actually there isn t any linear relationship Type II error We fail to prove there is a stat sig linear relationship betweenx and y when actually there is a linear relationship pvalue interpretation How often we see at least this strong of a linear relationship between x and y when there really isn t a linear relationship at all Conclusion If pvalue lt on we reject H0 and conclude that there is a stat sig linear relationship between x and y If pvalue NOT lt on we fail to reject H0 and cannot prove that there is a statistically significant linear relationship between x an y

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