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--- rem4:t-tests_and_linear_models [2008/10/15 14:46] – thorisson
+++ rem4:t-tests_and_linear_models [2024/04/29 13:33] (current) – external edit 127.0.0.1
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 | Sample  | 20 individual fish are tested.   |
 | Variables  | Dependent: Health.  Independent: Oceanic area (N,S).  Dependent variable is measured with the "famous Health Probe".  |
-| Subject pool  | N=20; random sample.  |
+| Subject pool  | N=20; random sample. Specify by which means/method the randomness is generated and followed.  |
 | Gathering data  | Repeated measures: 20 measurements for indexes of health: \\ North:97,99,88,77,99,20,87,88,89,65; \\ South:66,48, ....   |
 | **What we have so far**  | Basically, we have a bunch of measurements which came from two different parts of the country. They will probably have a different mean, median, etc. -- it's unlikely that they will be equal. This difference, we would like to find out -- is it a true representation of the actual fish population in each of these two different locations?  |
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-=== T-Tests ===
+=== t-tests ===
 | A.k.a.  | "Student's t-test"  |
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 | One-sample and two-sample t-test  | In the fish example above we have two separate sample populations, hence we use two-sample t-test.  |
 | One-sample alternative names  | Matched-sample t-test, Paired t-test, Repeated-measures t-test.  |
-| Formula for t-test  | http://upload.wikimedia.org/math/f/a/c/fac1832e2955cb829f855fd36736ab9a.png  |
+| More information  | http://biology.nebrwesleyan.edu/courses/labs/biology_of_animals/t-test_flash.html  |
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+=== Linear Models: Regression Analysis ===
+| Purpose of Regression Analysis  | Discover a function that allows prediction of the values of dependent variable y based on values of independent variable x  |
+| Scatterplot  | Shows the distribution of y-values for given (sampled) x-values  |
+| First-order linear function  | Y = A + bX \\ Provides us with a single, straight line that gets as close to all the points in the scatterplot as possible (given that it is straight)  |
+| Residual  | For each x,y point, the distance to the line   |
+| How do we find the line?  | Least Squares Criterion: We select the linear function that will yield the smallest sum of squared residuals  |
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+===Linear Correlation===
+| Given a linear function  | Given an X-score, the predicted Y-score is given by the line. However, in reality the Y-score rarely falls straight on the line.   |
+| Need estimate of error  | We must estimate how closely real Ys (Y) follow the predicted Ys (Y')  |
+| The measure most commonly used  | Standard Error of Estimate  |
+| Formula for Std. Err. of Est. | http://cs.gmu.edu/cne/modules/dau/stat/regression/multregsn/mreg_2_frm.html   |
+| What it tells us  | How far, on average, real Ys fall from the line  |
+| The smaller the Std. Err. of Est. is ... | ... the better a predictor the line is  |
+| Main limitation of linear models  | Assumes -- apriori! -- a linear relationship  |
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+EOF