#### Sampling and non sampling error and Types of sampling.

A small portion of the population is taken as a sample and then studied. So that the results from the sample may not exactly some results from the population and certain amount of errors. This error is called sampling error.There are several methods of population units to be included in the sample on the basis of probability. The particular units of the universe for constituting a sample on the basis that the small mass that they so select out of a huge one will be typical or representative of the whole.

#### Random sampling.

This type of sampling has to be used to make the inference of the study valid and reliable.Multistage sampling is less accurate than a sample of the same size which has been selected for the size which has been selected by some suitable single stage method. In the case of cluster sampling, the total population is divided into a number of relatively small subdivisions which are themselves the cluster of still smaller units and then some of this cluster are randomly selected for inclusions in the overall sample.

#### Numerical related to validity and length of test.

The increase in length of a test not only increases its reliability but also increases its validity. The effect of increase in length upon the validity coefficient is estimated by the formula $$r_{n(cx)}=\frac{nr_{(cx)}}{\sqrt{n+n(n-1)_{rw}}}$$ $$r(cx)=The\,coefficient\,of\,correlation\,between\,the\,criterion\,c\,and\,the\,given\,test\,x$$ $$r_w=THe\,realibility\,of\,coefficient\,of\,the\,test\,x$$ $$n=number\,of\,parallel\,forms\,of\,the\,test\,c\,or\,the\,number\,of\,items\,it\,is lengthened$$

#### Miscellinous numerical

$$Z=\frac{X-\overline{X}}{σ}$$ $$=Mean\,of\,standard\,score\,+s.d\,of\,standard\,score$$ $$\frac{iN {100}=\frac{(Pi-L)×f}{h}+c.f$$ $$\frac{iN}{100}=Percentile\,rank\,of\,given\,solve$$