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Two sample t-test

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Stephen Lange

The document discusses comparing measurements from two physicians who measured tumor volumes. A paired t-test was used to test if the measurements significantly differed. The t-test showed no significant difference between physicians. Additionally, two sample t-tests were used to compare tumor volumes between different cancer types, finding significant differences between brain and breast cancers and brain and liver cancers.

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Comparison of two samples Summer program Brian Healy
Previous classes ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
What are we doing today? ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Big picture ,[object Object],[object Object],[object Object]
Example ,[object Object],[object Object],[object Object]
Available data ,[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],19.7 20.5 10 27.5 29.3 9 25.4 23.0 8 20.3 21.8 7 24.8 24.0 6 28.0 26.8 5 18.5 15.7 4 14.2 14.5 3 20.3 22.3 2 17.2 15.8 1 Dr. 2 Dr. 1 Tumor
Dependent sample ,[object Object],[object Object],[object Object],19.7 27.5 25.4 20.3 24.8 28.0 18.5 14.2 20.3 17.2 Dr. 2 0.8 1.8 -2.4 1.5 -0.8 -1.2 -2.8 0.3 2.0 -1.4 Difference 20.5 10 29.3 9 23.0 8 21.8 7 24.0 6 26.8 5 15.7 4 14.5 3 22.3 2 15.8 1 Dr. 1 Tumor
Differences ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Distribution of differences ,[object Object],[object Object],[object Object]
Picture ,[object Object]
Paired t-test ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Confidence interval ,[object Object],[object Object],[object Object],[object Object]
Paired t-test in R ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Practice
Extensions ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Unpaired samples ,[object Object],[object Object],[object Object],[object Object],[object Object]
Example ,[object Object],[object Object],[object Object]
Null hypothesis ,[object Object],[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Difference in the sample means ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Equal variance ,[object Object],[object Object],[object Object],[object Object]
Equal variance continued ,[object Object],[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object],6.0 3.49 s 2 17.5 cm 3 16.2 cm 3 xbar 28 20 n Breast Brain
Hypothesis test ,[object Object],[object Object],[object Object],[object Object],[object Object]
R code ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
R output ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Unequal variance ,[object Object],[object Object],[object Object]
[object Object],[object Object]
Example ,[object Object],[object Object],14.4 3.49 s 2 19.35 cm 3 16.2 cm 3 xbar 20 n Liver Brain
Example ,[object Object],[object Object],[object Object],[object Object],[object Object]
R output ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Practice ,[object Object],[object Object]
Can we test if the variances are equal? ,[object Object],[object Object],[object Object],[object Object]
Equality of variance ,[object Object],[object Object],[object Object],[object Object]
Test of equality ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
F-distribution ,[object Object],[object Object]
Example ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Power and sample size ,[object Object],[object Object],[object Object]
One sample case (review) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Two sample case ,[object Object]

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Two sample t-test

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