Cheatography
https://cheatography.com
OneWay ANova
TwoWay ANova
Simple Linear regression
Proportions
This is a draft cheat sheet. It is a work in progress and is not finished yet.
Comparison Procedures
LSD Requires knowing the global F test is significant before any testing should be done. More powerful than Bonferroni, but can lead to inflated Type I error rate. Not recommended 
TUKEY Controls experimentwise Type I error rate exactly if sample sizes between groups are equal More powerful than Bonferrroni Use when only interested in all (or most) pairwise comparisons of means(unplanned comparisons) 
BONFERRONI Very conservative Use when only interested in a small number of planned comparisons Use when making comparisons other than between pairs. 
Individual Vs Family CI
**Individual confidence level (comparisonwise,πΌππ€): Success rate of a procedure for constructing a single confidence interval (or conducting a single hypothesis test) 
Familywise confidence level (experimentwise,πΌππ€):Success rate of a procedure for constructing a family of confidence intervals (or a family of hypothesis tests) A βsuccessfulβ usage is one in which ALL intervals in the family capture their parameters 
Pairwise Example
Nematodes in tomato plants How do nematodes affect plant growth? 12 identical pots, Different# of nematodes per pot; 0, 1000, 5000, Measure increase in tomato seedling height (cm) 16 days after planting 
Hypothesis Test: Ho:u1=u2=u3 vs Ha: Not all of the u are equal 
Overall F test significant (pvalue = 0.0027) > not all of the group means are equal 
Hypo for pairwise comparisons H0: uiuj=0 Ha: uiujβ 0 β iβ j 
How many pairwise comparisons are there for this example? 
How many pairwise comparisons are there for this example? K=K=I(I1)2β 3(31)2= 3 
Levels not connected by the same letter are significantly different 
Ordered Differences Report for lower CL and upper Cl= difference of growth 
Which nematode groups have significantly different ang growth? 05000 (p value = 0.0045)and 50001000 (0.006) are significantly different Difference in growth between 0 and 5000 will be between 1.83 cm and 8.27 cm more than 5000 


Factor Effects Model
ππππ = π+πΌπ +π½π +(πΌπ½)ππ+ππππ 
Response = overall avg growth + main effects +interaction effect 
Assumptions: ππππ~N(0,π2) are independent Errors are normal, independent, with constant variance 
Constraints: ΟπΌπ =Οπ½π =Ο(πΌπ½)ππ =0 Required to keep model from being overparameterized 
# of test = factoralevels X factorblevels 
Assumptions Errors are
Normal 
Normal Probability Plot 
Constant Variance 
Predicted Residual vs Fitted and Residual vs Factor Levels 
Independence 
Usually Assumed and typically assumed 
Main Effects and Interaction Plot
Main Effects Plot Separate plot for each factor Plot of mean response for each level of the factor Gives an indication of whether a factor is important Horizontal line indicates means are the same for both levels of the factor and thus factor is not important 
Interaction Plot Plot means for each treatment combination against levels of one factor, with different lines for the other factor Parallel Lines β No Interaction Crossing Lines  Interaction 


Simple Liner Regression Vocal
Least Squares Regression 
standard approach for estimating the line The line is chosen, so that the sum of squared vertical distances between points and the line is minimized. 
correlation coefficient r 
A measure of association for two quantitative variables is the 
predicted or fitted values. 
The points that lie on the regression line vertically above (or below) an observed value Notation ^yi 
residuals. 
(vertical) distances between observed and predicted values notatio: ei=yi^yi 
FTests
First: Test for Interaction β’ π»0: (πΌπ½)ππ=0 for all i,j vs. π»π: πππ‘ πππ (πΌπ½)ππ equal zero 
pvalue <a =Reject HO or pvalue>a = fail to reject H0 This means that both factors are important (even if main effects not significant) β’ We may need to interpret in terms of the interaction since we may not be able to separate out the main effects for individual interpretation 
Then: Test Main Effects Factor A π»0:πΌπ =0 for all i vs. π»π:πππ‘ππππΌπ equal zero β’ Main Effect of Factor B π»0:π½π =0 for all j vs. π»π:πππ‘ππππ½πequal zero 
H0: factorAi= 0 for all i (no effect) reject H0 if pvalue<a 
Model parameters(unknown)
Assumprions
Linear relationship between X and Y 
Model assumes that the error terms are 
Independent, Normal, Have constant variance. 
Residuals may be used to explore the legitimacy of these assumptions. 
