Scope of inference

 The scope of any inferences is constrained based on whether there is a random sample (RS) and/or random assignment (RA). 

Table 1-1 contains the four possible combinations of these two characteristics of a given study. 



Random assignment allows for causal inferences for differences that are observed - the different in treatment levels causes differences in the mean responses. 

Random sampling (or at least some sort of representative sample) allows inferences to be made to the population of interest. 

If we do not have RA, then causal inferences cannot be made. 

If we do not have a representative sample, then our inferences are limited to the sampled subjects.


Reference

Hypothesis testing (general) - Statistics with R (montana.edu)


Comments

Post a Comment

Popular posts from this blog

Clear Understanding on Sin, Cos and Tan (Trigonometric Functions)

Image
  Clear Understanding on Sin, Cos and Tan (Trigonometric Functions) Trigonometry  (from  Ancient Greek   τρίγωνον  ( trígōnon )  'triangle', and  μέτρον  ( métron )  'measure')  is a branch of  mathematics  concerned with relationships between  angles  and side lengths of triangles.  All trigonometric formulas are divided into two major systems: Trigonometric Functions Trigonometric Identities In particular, the  trigonometric functions    relate the angles of a  right triangle  with  ratios  of its side lengths. Also, called as trigonometric rations. Trigonometric functions  are also known as  Circular or cyclic Functions. Trig functions  can be simply defined as the functions of an angle of a triangle. It means that the relationship between the angles and sides of a triangle are given by these trig functions. There are basically 6 ratios used for finding the elements in Trigonometry, those are  sine(sin), cosine(cos),  tangent(tan),  cotangent(cot), secant(sec) and co
Read more

Clear Understanding on Mahalanobis Distance

Image
  Clear Understanding on Mahalanobis Distance In multivariate/ multicharacteristics data, a measure of divergence or distance between groups in terms of  multiple characteristics is required. Lets consider, you are interested in measuring the difference (distance) between groups G1 and G2 (each of p-dimensional). A common assumption is to take the p-dimensional random vector X  , from each group, as having same variation about its mean within either group. The difference between the groups can be considered in terms of difference between mean vectors of X, in each group relative to the common within-group variation  (using common (pooled) covariance matrix). The most often used measure for multiple characteristics data is, Mahalanobis distance (Mahalanobis  Δ , where  Δ  is Uppercase Delta). The square of Mahalanobis distance is given by,  Δ 2 =  (µ 1 -µ 2 ) T Σ -1 (µ 1 -µ 2 ) or          Δ 2 =  (µ 1 -µ 2 ) ′ Σ -1 (µ 1 -µ 2 ) where the superfix T or  ′  denotes matrix transpose,   
Read more

Vignettes for Matrix concepts, related operations

  Geometric Transformations, compute the matrix of a rotation transformation and visualize it. Wolfram|Alpha Examples: Geometric Transformations (wolframalpha.com) Reference Change of Basis – GeoGebra Eigenvalues of a Matrix Calculator - Online Eigen Values λ Finder (dcode.fr) Eigenvectors of a Matrix Calculator (with Eigenvalues) - Online (dcode.fr) Matrix Visualization | Sarah Greer (sygreer.com)   Matrix visualizer (utexas.edu)  gives rotation by angle. Eigenvalue Calculator: Wolfram|Alpha (wolframalpha.com) Determinant Calculator: Wolfram|Alpha (wolframalpha.com)
Read more