Research Statistics Central

Objective :  You are running ANOVAs or regressions in SAS, and wish there was a way to avoid writing the dozens of commands needed to conduct the analysis and generate recommended diagnostics and summary of results, not to mention the hundreds of possible options that might be needed to access recommended methods.  A possible solution is to download a copy of danda.sas below, and use this macro collection to run the dozens of commands with one statement.  We will also have future posts covering various uses of danda.sas, giving examples as always. danda.sas is under continued development, check this page for updates. Date                       Version               Link 2021/03/15             2.12.030          danda.sas 2021/03/15       ...

Objective :  You are running a linear model, for example ANOVA or regression, and are using the "ANOVA table" to decide which terms in the model are influencing the dependent variable.  You check the numerator and denominator degrees of freedom, as recommended , to guard against modeling errors and use of wrong error terms.  Reported values disagree with what you expected, so now what? Make sure your expected numbers are calculated correctly : An example model is (last term is the residual error) [Model 1]       y = u + block + treat + block*treat + rep(block*treat) If numbers of levels are b=2 for blocks, t=2 for treats, and r=5 for reps, then we expect degrees of freedom (DF) to be DF[block] = b-1 = 1 DF[treat] = t-1 = 1 DF[block*treat] = (b-1)*(t-1) = 1*1 = 1 DF[rep(block*treat)] = (r-1)*(b)*(t) = 4*2*2 = 16 Number of observations is b*t*r = 20, and DF add to 19, which is 20 minus the one DF for the intercept, as expected. DF rules are: ...

Objective :  Individuals are measured for several characteristics, and we want to group the individuals based on similarities across all characteristics. Statistical options are cluster analysis, principle components (PCA), and biplots.  PCA has the advantage of combining correlated variables together, reducing the complexity of explaining why individuals cluster together.  And biplots adds some nice features to PCA.  This post compares these choices. Example :  10 farms measured for nutrients in grass, and the primary question is to see if/which farms have similar nutrient profiles. Create a random dataset with 4 nutrients measured on 4 pastures in each of 10 farms. Run the SAS code for producing biplots.  Here we restrict the number of PC to 2 (n=2), in general you would use PCA to decide how many components are needed.  Prinqual requires all variables to be processed by a Transform statement, here we use the identity transformation so the variab...

Objective : We are comparing means using ANOVA, and our treatment levels are amounts of something.  Thus regression hypotheses may shed light on how the treatments differ, for example is there an overall linear trend for the response variable to increase or decrease with treatment level.  This is addressed by adding orthogonal polynomial contrasts to our ANOVA, which may require that we add contrast coefficients. Example :  Treatments are amounts of corn in the diet, specifically 62%, 65%, 68%, 71% and 74%. SAS :  IML product has an orthogonal polynomial calculator.  Additional code here attempts to make the coefficients whole numbers by dividing by the smallest non-zero number.  Note IML may not be available, depending on your license. proc iml; trtlevels={0.62, 0.65,0.68,0.71,0.74}; **this is only user input; ntrt=nrow(trtlevels); coeff=orpol(trtlevels); coeff = coeff[,2:ntrt]; div=abs(coeff); zerloc=loc(div<1e-14); if n...

Objective :  We need to know how many observations to collect so our estimate of the mean has a useful precision.  For example, how many animals should be measured in order to have an 80% chance that the 95% confidence interval for weight will be no wider than 20 kg?  In addition to those 3 numbers, we also need an estimate of the std. deviation.  Suppose the best situation expected has SD=20kg, but we also want to see what changes if SD=40kg, SAS:   Run this code proc power;    onesamplemeans ci=t       alpha = 0.05       halfwidth = 10       stddev = 20 40       probwidth = 0.80       ntotal = .; run; data adjust;  samplesize=22;  population=1200;  adjsamplesize=ceil(samplesize/(1 + ((samplesize-1)/population))); run; proc print; run; The 95% confidence interval is requested by setting alpha=0.05. The 80% chance that our experiment will satisf...

 In our role as statisticians, we see many identical questions from researchers on how to perform common statistical methods.  Rather than repeatedly give the same answers, we plan to post the current recommended practice for each type of problem, and update as needed.  Our focus will be on R and SAS software, widely used and what we have the most experience with.  Like most statistical consultants, we are educators, hoping to teach you how to think about and do statistics.    Statistics is a broad topic, reaching into almost every area of science.  Since the different sciences have different types of data, different sources of variation, statistical methodology can be area specific.  The questions we see mainly come from agriculture, so there will be a bias towards methods most widely used there. We will strive to place sufficient key words in the posts to enable searches to uncover appropriate material.    Time permitting, we will p...