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--- public:rem4:rem4-20:design_of_comparative_experiments_ii [2020/03/25 19:33] – thorisson
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 | One dependent variable, multiple independent variables, each with two or more levels  | ANOVA - Analysis of variance   |
 | Many dependent variables, many independent variables  | MANOVA (multiple analysis of variance)  |
+| REF for M/ANOVA | https://www.statisticshowto.datasciencecentral.com/probability-and-statistics/hypothesis-testing/anova/  |
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 | Two-tailed t-test  | If your hypothesis only says that your dependent variable will be affected, but does NOT specify how.   |
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+=== Example of an Experiment: Fish ===
+| Theory   | Temperature has an effect on cell growth of animals. This goes for fish as well.    |
+| Motivation   | If we can find evidence for this we might be able to grow larger fish in captivity; larger fish means fewer people starving (or more revenue - or both). \\ Fishing further South might be better for everyone, even those living in the North.   |
+| Hypothesis  | That size of fish varies with ocean temperature. \\   |
+| Experiment   | Comparing the size of fish in the Atlantic Ocean by taking a sample from various latitudes. Argument: Temperature falls the further North one goes; thus, fish at higher latitudes should be smaller.  |
+| Sample | 100 fish south of Iceland. 100 fish north of Iceland.  |
+| Dependent variable  | Size of fish (continuous).   |
+| Independent variable  | Latitude (two levels - South and North).   |
+| Statistics  | Linear regression.    |
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+=== Example of an Experiment: Routers ===
+| Theory    | Congestion on networks gets worse the smaller "visibility horizon" <m>H_v</m> each node <m>N_i</m> in a network has about traffic on other adjacent nodes. \\ <m>H_v</m>: Information about traffic, including past, present, and predicted.       |
+| Motivation   | Knowing whether nodes from router manufacturer X or Y are a better purchase might be decided by looking at their implemented routing methods. \\ Knowing how to set parameters on already-purchased routing nodes might be put on a more scientific ground.   |
+| Experiment   | Comparing routers from ZYX and Cis. The former advertise their routers to be "network-aware" whereas the latter brag about being "perfect for P2P networks" because each node doesn't need to know anything about the rest of the network.     |
+| Hypothesis   | Routers from ZYX will perform better at handling congestion than routers from Cis.     |
+| Independent variables   | 1. Router type. \\ 2. Traffic. \\ 3. Network size.    |
+| Dependent variables    | 1. Congestion. \\ 2. Congestion recovery. \\ 3. Routing efficiency.    |
+| Statistics    | MANOVA   |
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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. | https://www.youtube.com/watch?v=r-txC-dpI-E (walk-through video)   |
+| 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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