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19 Cards in this Set
- Front
- Back
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What is SS What is residual? |
SUM OF SQUARES Residual is the unexplained data --> the fact that all the dots does not fall exactly on the line |
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What does the F-value and the MS tell us in an ANOVA? |
If MS for regression and residual are the same (around 1) --> H0 is true The null hypothesis is rejected if the F calculated from the data is greater than the critical value of the F-distribution for some desired false-rejection probability |
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What is the benefit of an ANOVA? |
It can test multiple samples
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What affects the ANOVA? |
Sample size and numbers of levels Type I Error: will be less of you have many samples! |
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What degrees of freedom would the following have (Treatment, residual and total) if there was 2 levels of diets and 4 replicated aquarias? |
Treatment= 1*2 = 2
Total = 4*2 = 8 DEPENDS ON THE OVERALL MEANS FROM THE TREATMENTS! |
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Which 4 assumptions is there for the ANOVA? |
1. Independent observations 2. Homogenous variances 3. Balanced samples 4. Normal distributions |
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How can we test for homogeneous variances? |
Cochran’s C test. The C test detects one exceptionally large variance value at a time Means from every treament If your C-value is higher than Ccrit --> reject H0 (Take largest S^2 of the treatments/The sum of all the means in the treatments) |
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What is an SNK-test and why is it good? |
The SNK test is a method of stepwise multiple comparisons procedure used to identify sample means that are significantly different from each other --> Finds out which treatment differs from each other (Does this by ranking the treatments) KEEP in mind: this test is less powerful than ANOVA |
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What is a Nested ANOVA? |
Use nested anova when you have one measurement variable and more than one nominal variable, and the nominal variables are nested (form subgroups within groups). It tests whether there is significant variation in means among groups, among subgroups within groups, etc. Content within each group are more similar to each other than the rest (nested to exposure) |
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Why should you use a nested design? |
• Ensure independent replicate units • Quality control of experiments • Cost-benefit analysis • Insurance |
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What is a Multi-factor model? |
A model that detects: |
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What is Orthogonal factors? |
Crossed factors Ex, Grazors and no grazors vs. toxin level Nutrients*Grazors shows the interactions If more than 2 orthological factors: nested factor ex aquaria |
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MAIN MESSAGE |
Playing with different designs you can get a good idea of flaws, powers of the tests |
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Why is a power analysis important? |
Tells us: We need to: * Formulate H1 and H0
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Topics discussed 1 |
• The scientific loop of observation, model,hypothesis and test • Finding confidence intervals of the true mean from a sample • Understanding how to construct probability distributions of statistics like tand F • The logic behind statistical models wherethe variation is explained by factors |
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Topics discussed 2 |
• Linear regression • Fixed and random factors • Analysis of variance (ANOVA) • Nested factors • Orthogonal factors • Complex designs analysed by multifactorial ANOVA • Power analysis |
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Think about when doing an experimental design |
• Adequate controls • Draw graphs of results that support yourhypotheses • Write down the ANOVA and check that it will really test your hypothesis • Power analysis before conducting the study • Cost-benefit analysis |
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Likely questions from Per |
*Difference between SE and SD |
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Why is randomization important? |
To avoid bias --> push the uncertainty back into the residual where it should be, but the power goes down |
