What do you understand by the word ‘ **Reliable**‘? the dictionary meaning of it is Trustworthy, Dependable, stable , etc. If you have any meaning of it, you are right! Congratulations!! In Psychometry or Psychological testing, Ratability as noun has a little different meaning, lets understand that.

In Psychometry, Reliability means the **Consistency of scores** of the same person on same test on different occasions. Reliability refers to the accuracy, dependability, consistency, or repeatability of test results.

It refers to **the degree to which test scores are free of measurement errors**. Psychological Tests that are relatively free of measurement error are considered to be reliable, and tests that contain relatively large measurement error are considered unreliable.

In psychological testing, the word ** ‘error**‘

**. Though it has a negative connotation,**

*does not imply*a mistake*error*implies that there will

**always be some inaccuracy**in our measurements. Our task is to find the magnitude of such errors and to develop ways to minimize them.

Contents

**History of Reliability in Psychometry**

**Charles Spearman **was the early psychometrician who gave contribution to the development of **reliability assessment**. He gave ‘**Classical test theory**‘. Spearman worked out most of the basics of contemporary reliability theory and published a article entitled “** The Proof and Measurement of Association between Two Things.**’’

In 1733, Abraham De Moivre introduced the basic notion of ** ‘sampling error** ‘.

**Karl Pearso**n (1896) developed the ‘**Product Moment Correlation.’**

**What is Test reliability?**

Test reliability Indicate; How much individual differences in test score causable to ‘True’ differences on the characteristics And how much they are causable to change errors.

### What is Random Error?

*▫Obtained score(Xi) = true score(T i) + random error(E i).*

▫Random error of 2 individual can’t be same.

### What is Error Variance?

*•Total variance= true variance + error variance *

**Error variance** –Any condition that is irrelevant to the purpose/

•Error variance for one purpose would be classified under true variance for another.

**For Illustration –**

- Purpose 1 –measuring fluctuation of mood . ▫
**True variance – day to day mood changes**in score on a test of cheerfulness- depression.- Purpose 2 – measuring permanent personality characteristics . ▫
**Error variance –day to day mood**fluctuations.

- Purpose 2 – measuring permanent personality characteristics . ▫

So, **To reduce error variance** and to bring more reliability in test scores . The examiner try to maintain **uniform condition** –testing environment, instructions, time limit, rapport, etc.

**What is Correlation Coefficant (r)? **

Reliability i.e. consistency of score or agreement between two scores expressed in term of **correlation coefficient**(r). Correlation Coefficient (r) is mathematical index that **describes the direction & magnitude of a relationship**. It express the **degree of correspondence** or relationship, between two sets of scores.

Correlation Coefficient range form -1 to 0 to +1.

**Positive Correlation (0.00 to +1.00)**•means that high scores on Y are associated with high scores on X, and low scores on Y correspond to low scores on X.**Negative correlation (-1.00 to 0.00)**-means higher scores on Y are associated with lower scores on X, and lower scores on Y are associated with higher scores on X. •Ex – the higher the drug dose, the less active the patients are.**No correlation**(0.00) •The variables are not related. •Here, scores on X do not give us information about scores on Y. •Ex – correlation between shoe size and IQ.

**How to Calculate Correlation Coefficient (r)?**

There are two ways to compute/ Calculate correlation coefficient (r).

**Pearson product moment correlation**-To find out followings- Persons position in group .
- Amount of his/her deviation above(+) or below(-) the group mean like SS
- Correlation between two continuous variables such as height, weight, and intelligence.

**Spearman’s rho / The rho coefficient (**▫for finding*r)*- the association between two sets of ranks.
- used when the individuals in a sample can be ranked on two variables but their actual scores are not known or have a normal distribution.

*Testing the Statistical Significance of a Correlation Coefficient*

*Testing the Statistical Significance of a Correlation Coefficient*

- If we have r=0.40 means moderate positive degree between X n Y for that sample.
- But we want to apply this (r=0.4) to population .
- for that we need significance level.
- We check its Significance level from tables (significance of correlation in any stat book) depending up on sample size .
**Significant at the 1%(****0.01)**= means chances are no grater than 1 out of 100 that the population correlation is zero. Hence two variables are truly correlated .**level****Significant at the 5%(****0.05)**= means chances are no grater than 5 out of 100 that the population correlation is zero. Hence two variables are truly correlated.**level**- Significance level- risk of error we are willing to take in drawing conclusions from out data.

**What is Reliability coefficient?**

- it is a application of correlation coefficient(r).
- Reliability coefficient provide test users with some information concerning the magnitude of the error that is likely to enter into scores from various resources.
- It the correlation of the test with itself.
- It is based on data such as
**two administrations of the same test,****two versions of the same test**,**inter item correlations**and so on, that*ought to be*highly consistent. - In most of the cases it is considered as higher the coefficient, better the reliability.
**Approximate minimal satisfactory coefficient**is considered to be**.70**and/ or higher that that by many researchers.- The r
**eliability coefficient**is the**ratio**of the v**ariance of the true scores**on a test to the v**ariance of the observed scores.**