The four levels of measurement in statistical research

¶ … Measurement and Precision

There are many types of variables that a researcher may want to study. These variables are typically classified into the four levels of measurement (scales) namely nominal, ordinal, interval and ratio. The nominal scale is the simplest of the four which divides the population into different categories (e.g. gender, nationality or original hair color). The ordinal scale is the same as nominal but with categories that can be arranged into a specific order such as socio-economic class (basically divided into the upper class, middle class and lower class). The interval scale is the same as the ordinal scale but the specific order (or ranking) of the variable measured has equal-appearing intervals. An example of which is temperature where the difference between 1 degree Celsius and 10 degrees Celsius is the same as the difference between 11 degree Celsius and 20 degrees Celsius. The ratio scale is the same as the interval scale but with an absolute zero measurement which signifies absence of the variable. For example, in measuring distance traveled, zero distance traveled means the entity stayed at its starting point the whole time; as opposed to the interval scale variable temperature, where zero degrees Celsius does not signify absence of temperature (but rather, freezing point temperature).

Defining the levels of measurement of each variable in a research study is important in order to determine the appropriate statistical tests to be used for diagnostics. As a rule of thumb, non-parametric tests are suitable for nominal and ordinal scale variables while parametric tests are fitting for interval and ratio scale variables. Consequently, using the appropriate statistical tests will ensure results relevant to proving the hypothesis and will enable the researcher to yield precise conclusions.

II. Random Sampling

In experimental research design, one of the trickiest things the researcher has to decide on is sampling. Since in statistics, we are always dealing with estimates, a good sample is pre-requisite to an estimate that is closer to the true value. Conversely, a poor sample will give you estimates that are inaccurate and misleading. Thus, the need for a genuine random sample is essential in every research design. Random sampling is a method that gives each member of the population equal chances of being included in the study with the end goal of having a sample that accurately represents the population. There are basically two kinds of random sampling, Simple Random Sampling, or simply, Random Sampling, and Stratified Random Sampling.

With Random Sampling, members of the population are included in the sample if their corresponding pre-assigned numbers is picked via the table of random numbers. Nowadays, there are many variations to this method. You may select the sample by doing a raffle (whether manual or electronic) or you may even use statistical software for the purpose.

Meanwhile, Stratified Random Sampling is also Random Sampling but done within known groups of the population which the researcher wants to explore. For example, among teenagers, the average height of males is to be compared with the average height of females. Random Sampling should be done separately among males and among females such that the sample sizes of the two groups are equal (or whichever the true proportion is). Simple Random Sampling is not advisable because the proportion of males and females cannot be controlled in that process.

III. Quasi-Experimental Design

Quasi-experimental design is closer to true experimental design compared to pre-experimental design because it has a means of comparing groups (i.e. It utilizes the control group concept). However, it uses convenience and judgment sampling instead of random sampling and therefore runs the risk of having a biased sample. There are three types of quasi-experimental design according to Barry Gribbons and Joan Herman namely nonequivalent groups -- posttest only, nonequivalent groups -- pretest-posttest and time series designs.

Nonequivalent groups -- posttest only applies different treatments to two groups and compares the variable under study between the two groups after the treatment. The major limitation of this design is it does not take into account the difference between the two groups prior to the treatment. On the other hand, nonequivalent groups -- pretest-posttest eliminates this major limitation by testing the differences between the two groups prior to the treatment. However, this still does not guarantee that the difference in results may be attributed to the different treatments applied between the two groups. Lastly, time series designs calls for two or more pretest and posttest to provide a better picture of the results through trends.

Quasi-experimental designs are used when a true random sample is either impractical to do or impossible to attain. This problem usually arises if the target population has rare qualities. For example, if the research involves people born as triplets, the researcher will probably include all triplets encountered to attain a fairly sized sample. In addition, budget and timing should also be considered in deciding which approach to take since quasi-experimental design is obviously cheaper and can be accomplished faster than a true experimental design. Nevertheless, the accuracy and precision that a true experimental design offers is paramount.