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solved assignments for mba 4th sem Q1.What are the different types of Reliability estimates? What are the important components of retest reliability?

There are several types of reliability estimates, such as:
Inter-rater reliability is the difference in measurements when undertaken by different people but with the same method or instruments.

Test-retest reliability is the difference in measurements undertaken by a single person or instrument on the same item and under the same conditions. This is called intra-rater reliability.

Inter-method reliability is the difference in measurements of the same target when undertaken by a different methods or instruments, but with the same person. It is termed as parallel-forms reliability.

Internal consistency reliability, measures the consistency of results across items within a test.

Most common form of reliability is the retest reliability, which refers to the reproducibility of values of a variable when the measurement is done more than once on the same product. Here, we take the example of 10 people weighed twice with a gap of two weeks between tests. This example is used to explain the three important components of retest reliability: change in the mean – typical error, retest correlation – kappa coefficient and alpha reliability.

1. Change in the Mean
The difference between the two tests conducted is the change in the mean. The change consists of two components: a random change and a systematic change.

Random change in the mean is due to the sampling error. This kind of change arises from the typical error, which is like a randomly selected number added to or subtracted from the true value every time the measurement is conducted.

Systematic change in the mean is a systematic change in the value between two measures. This variation in the mean value is an important issue when subjects perform a series of trials as part of a tracking the program. The subjects are usually tracked to determine the effects of an intervention (example, a change in diet or training), so it is important to perform trials to make learning effects or other systematic changes insignificant before applying the intervention.

Typical Error of Measurement
In the above example, the first few weights show a slight trend downwards – it shows that the subjects lose a bit of weight, so there is a random variation of about a kilogram. This random variation is the typical error. It is quantified as the standard deviation in each subject’s measurements between tests, after any shifts in the mean have been taken into account. The variation/error is also known as the within-subject standard deviation, or the standard error of measurement.

Coefficient of variation is an important form of typical error. This is the typical error is expressed as a percentage of the subject's mean score.
Another form of within-subject variation is reliability limits of agreement, which represent the 95% likely range for the difference between a subject's scores in two tests4.

2. Retest Correlation
When the test and retest values are determined, it is obvious that the closer the values are to the true value, the higher is the reliability. Therefore, a retest correlation is one way to quantify reliability. A correlation of 1.00 represents perfect agreement between tests, whereas 0.00 represents no agreement whatever. In our example the correlation is 0.95, which represents very high reliability.

Kappa Coefficient: Reliability of Nominal Variables
Reliability can also be defined for supposed variables, to represent the constancy with which something is classified on several occasions. The best measure is something called the kappa coefficient. It is equivalent to a correlation coefficient and has the same range of values (-1 to +1).

3. Alpha Reliability
The alpha reliability of the variable is derived by assuming that each item represents a retest of a single item. For example, if there are five items, it is as though the five scores are the retest scores for one item. But reliability is calculated such that it represents the reliability of the mean of the items and not the reliability of any single item. Hence, the alpha reliability of 10 items would be higher than that of 5 similar items.5
Alpha reliability is regarded as a measure of internal consistency of the mean of the items at the time of supervision of the questionnaire. It refers to the ability to reproduce the results whenever it is required. This is essentially enhances faith in the statistical analysis and the results obtained.


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