Characteristics of scale.

Characteristics of a Scale.

A Good scale should have a defined continuum , should be reliable and valid.

Continuum.

The various factors to be measured must be logically interrelated and should be in the form of continued measurement rather than stray facts here and there. Care has to be taken to include only such items facts which are clear, unambiguous and falling on different points of a continuum. The items (facts ,statement) should not be the duplicate expression/statement falling on the same point. The continuum to be defined depends upon the nature of the phenomenon and the nature of the factors to be included.

Reliability.

A measurement instrument is reliable if it provides consistent results. The reliability is an indication of the stability and consistency with which the instrument measure the concept and helps to assess the goodness of measure. Reliability means an absence of the error of measurement in the measuring instrument. A scale should be reliable I,e should be the same measurement under similar conditions. For example, an economic status scale is reliable only if two persons with apparently same economic status show the same scores. Reliability means dependability,stability, consistency, predictability and accuracy of the scale used.

There are the different definition of reliability They are.

1. If we measure the same set of objects again and again with the same or comparable measuring instruments and us get the same or similar results, then the measurement is called reliable.
2. Reliability means measures obtained from a measuring instrument I,e the true measures of the property measured. This definition implies the accuracy of the scale.
3. Reliability means the absence of errors of measurement in measuring instrument. This definition helps to solve both theoretical and practical problems associated with the definition of reliability.

Tests of Reliability

The methods used to test the reliability of a scale are:

1. Retest(Test-Retest) Method:

According to this method , the same scale is applied twice to the same population and the results obtained are compared by computing a correlation between the first and second set of scores.Whenever applications at different times are not possible , the technique of control group is also used.To avoid the effects of causative factors in the prolonged period of two test , two similar groups are used to test a scale. Although this method is sometimes the only available procedure , the method ids open to several serious objections . Immediate memory, practice and the confidence induced by familiarity with the material are some of the effects that affect scores when the test is taken for the second time. The reliability coefficient obtained in this method is called “stability coefficient”.

2. Alternative or parallels from a method:

According to this method , two forms of a scale;e are constructed and are administered to the same population . If the results obtained by methods show the high degree of similarity then the scale is considered reliable. Hence the degree of similarity is measured by the correlation coefficients. The correlation coefficient is called self-correlation and indicates the degree of equivalence of the two form of attest. Parallel forms are usually available for standard psychological and educational achievements.

3.Split-half method:

Here, the test is first divided into two equivalent halves and the correlation coefficient is calculated for these half tests.From this correlation coefficient, the self-correlation of the whole test is then estimated by using spearman-Brown prophecy formula. The procedure is to make up two sets of scores by grouping alternate items in the test . The first set of scores represents performances on the odd-numbered items. i.e 1,3,5,7…..etc. and the second set of scores representing the performances on the even numbered items i.e 2,4,6…etc. The test could alternatively be divided into more parts three, four etc or even into individual items . The reliability coefficient for t6he whole test also called stepped up reliability is calculated by the spearman-Brown formula.

$$R_w= \frac{nr_p}{1+(n-1)r_p}......(i)$$

Where

$$R_w=Cofficient\,of\,reliability$$

$$n=number\,of\,parts\,of\,whole\,observation\,dvided$$

$$r_p=Correlation\,between \,any\,two\,parts$$

$$If\,R_w>0.5\,then\,the\,scale\,is\,reliable$$

$$If\,R_w=-Ve\,,it\,is\,not\,reliable\,so\,new\,scale\,has\,to\,be\,adopted$$

Example.

A test is divided into two parts / halves and the correlation coefficient between these halves is found to be 0.68. Then the reliability coefficient of the whole test by using the formula is 2x0.68/(1+0.68)=0.8095

The split half method is used when it is not feasible to construct parallel forms of the test or not advisable to repeat the test itself.

Example as.

Suppose in a group of two college students the reliability coefficient of an achievement test is 0.70. What will be the effect upon the test of reliability if the length of the test is triple?

Solution.

$$r_p=0.70$$

$$n=3$$

$$We\,have$$

$$R_w= \frac{nr_p}{1+(n-1)r_p}......(i)$$

$$R_w= \frac{3×0.70}{1+(3-1)0.70}$$

$$R_w=0.85$$

4)Rational-equivalance method:

Generally , two data qualitative and quantitative are exchanged and we apply formula,

$$R_w= \frac{n}{n-1}\frac{(σ^2-\sum{pq)}}{σ^2}$$

$$Where\, Rw = Reliability \,coefficient \,of \,the \,whole \,test.$$

$$N= number\, of \,items \,in\, the \,test.$$

$$σ= standard \,deviation\, of \,the \,test \,scorre$$

$$P= proportion \,of \,bthe\, group \,answering \,a \,test \,item \,correctly.$$

$$Q= The\, proportion \,of\, the \,group \,answering \,a \,test\, item \,incorrectly.$$

The approxamate to the formula (i) is

$$a),R_w=\frac{nσ^2-M(n-M)}{(n-1)σ^2}$$

$$m=mean\, of \,the \,test \,score.$$

Two forms of a test are defined as equivalent when corresponding items A, a;B,b etc . are interchangeable and when the inter-items correlations are same for both forms. This method of rational equivalence emphasises on the inter-correlations of the test and the correlations of the items with the test as a whole.

Important question.

A test of 40 multiple choice items is administrated to small class students. An item correctly answered is scored 1 and not correctly answered also. The mean test score is found as 24.45 and the s.d as 6.00. Find the reliability coefficient.

Solution.

No of items (n)=40.

Mean test score (M)=24.75

Standard deviation(σ=6.00

We have,

$$R_w=\frac{nσ^2-M(n-M)}{(n-1)σ^2}$$

$$R_w=\frac{40×σ^2-24.75(40-24.75)}{(39×36)}$$

$$R_w=0.7584$$

Reference

Kerlinger, F.N. Foundation of Behavioural Research. New Delhi: Surjeet Publication, 2000.

Kothari, C.R. Research Methodology. India: Vishwa Prakashan, 1990.

Singh, M.L. and J.M Singh. Understanding Research Methodology. 1998.

Singh, Mrigendra Lal. Understanding Research Methodology. Nepal: Natiocentreok centre, 2013.