2.1 Random Samples

For a sample to be random, it must have been obtained in such a way that each possible sample of the same size has an equal probability of being selected from population. Characteristic of random samples drawn from a given population will vary from sample to sample (due to chance), but the result obtained from larger random samples tend to vary less than those from smaller samples.

2.2 Variables and Constants

A variable is characteristic that may take on different values. Typical examples are intelligence test scores, height, number of error on a spelling test, eye color, marital status, and sex.

Constant, on the other hand, remain the same in a given study. Constants define the boundaries of a study and also limit the generalizability of the results. In the school nurse’s situation, for example, the sex of the students (male), the school (Lincoln), and the grade level (seventh) are all constants.

2.3 Scales of Measurement

Measurement is the process of assigning numbers to observations. The several scales of measurement and their characteristic are:

a. Nominal Scale

Mutually exclusive categories differing in some qualitative aspect. Examples: eye color, types of cheese, etc.

b. Ordinal Scale

Scale has a property of a nominal scale (Mutually exclusive categories) and in addition has observations ranked in order of magnitude. Ranks, which may be numerical, express a “greater than” relationship, but with no implication about how much greater. Example: workers sorted according to order of merit.

c. Interval Scale

Scale has a property of an ordinal scale and in addition numerical values indicate order of merit and meaningfully reflect relative distances between points along the scale. A given interval between measures has the same meaning at any point in the scale. Example: temperature in degrees Celsius.

d. Ratio Scale

Scale has a property of an interval scale and in addition has an absolute zero point. Ratio between measures becomes meaningful. Examples: length, weight, temperature in degrees Kelvin.

2.4 Scales of Measurement and Problems of Statistical Treatment

Most psychological and educational tests lack equal intervals and absolute zero point. Although these shortcomings do not ordinarily prevent us from using statistical procedures, scales problems can lead erroneous research conclusions.

2.5 Computational Accuracy With Continous Variables

Discrete variables hava exact values, like the number of subjects in an experiment. Continous variables can take on any value, but the process of measurement always reduces them to discrete variables. Thus, measurement of a continous variables give us approximate values, like the length or weight of a object. When computations involve both approximate and exact numbers (as is typical in calculating an average), the approximate numbers dictate the accuracy of the outcome.

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