What are important concepts of research? - Chapter 1

In this chapter, we will use an empirical example to illustrate some of the issues involved in designing and analyzing research. This example will also help you to become familiar with the basic statistical concepts of research. The example concerns a group of educators who developed a course that is designed to teach high school students how to manage stress and the effect of self-management on self-esteem. This group of educators asked an outside investigator, to tell them how well the course is working and whether students who took the course have higher self-esteem that students who did not take the course. 

What are the basic concepts?

It goes beyond human capacity to study the entire population of high school students in the country. Therefore, it is common practice to draw a sample from the population, preferably a random sample. To draw such a random sample from the population, one should follow a set of procedures to ensure that each student has an equal opportunity to be selected. Although theoretically feasible, one should be aware that truly random samples are normally very impractical if not impossible. After having drawn a random sample of students, it is common practice to assign half of the students to a group that will receive the intervention program and half to a group that will not receive the course.

population is the entire collection of events in which one is interested. In the current example, the event of interest is the self-esteem score of students. A population can be of any size. Unfortunately, the population is often very large, making it impossible to measure the entire population. Therefore, as introduced in the prior paragraph, we draw a sample of observations from that population and use that sample to infer something about the characteristics of the population. The generalizability of the results from the sample to the population depend on the randomness of the sample. If the sample was not so random, it is less likely that the results form a proper reflection of the results for the entire population. 

Randomness has two important parts we need to consider. The first part that we need to consider is external validity. External validity refers to the question whether the sample reflects the population and, hence, whether the results from the sample can be used to infer something about the population. A sample drawn from Utrecht University would not produce an external valid result for the effectiveness of the course for all students in the country. Although the results may still be useful for us, we should not conclude that this sample is representative for the entire population of students in the country. Thus, our ability to draw inferences is limited in this case.

The second important aspect of randomness concerns interval validity. Whereas external validity refers to the source of our data and the generalizibility to the population, internal validity refers to the random assignment of subjects (once selected) to different (treatment) groups. A random assignment to different groups is fundamental for the integrity of an experiment. We want to ensure that potential differences between groups are truly caused by the course and are not because, for example, students could assign themselves to the course. 

What are variables and what variable types exist?

After selecting the students and assigning them to one of the groups, it is time to consider how we treat each group and how we will characterize the resulting data. A variable is a characteristic of an object or event that can take on different values. An example of a variable is hair color, which can take on the values (among others): blond, brown, red, and black. In our example, variables are: self-esteem, gender, social support, and treatment condition. 

Variables can be dependent or independent. An independent variable is a variable that is being controlled for or manipulated by the researcher. In our example, the independent variable is group membership (receiving the course or not receiving the course). We determine who receives the course and who does not receive the course. Gender, for instance, is not a variable that we can control for, but we can however choose which gender we want to examine or whether we want to examine the difference between men and women. Hence, when it is part of the research question, gender could be an independent variable. On the other hand, the data that result from the study, such as self-esteem scores and scores on personal control, are dependent variables

Discrete variables are variables with a limited set of possible values, such as gender and school grade. Continuous variables can, in theory, take on every value between a lowest and highest point on a scale, such as gender and self-esteem scores. 

Quantitative data (sometimes called measurement data) is the result of any sort of measurement, such as grades on a test, weight, or scores on a scale of self-esteem. 

Qualitative data (sometimes called frequency data or categorical data) results from categorizing things or individuals and our data consists of frequencies for each category. For instance, there are 34 boys and 26 girls in our sample. 

Dependent variables usually are quantitative and continuous. Independent variables can be either qualitative or quantitative and either discrete or continuous.

What are the two primary divisions in the field of statistics?

After collecting the data, we are left with the raw data. There are two primary divisions in the field of statistics that are concerned with how these data are used and reported. 

  1. Descriptive statistics are used to merely describe a set of data. We can compute means, visualize the scores in a graph and look for outliers. For a long time, this field was regarded as rather boring. John Tukey, however, showed that exploratory data analysis (EDA) is fundamental before invoking more technically demanding analyses.
  2. Inferential statistics refers to making inferences about the population based on the sample. Most of the content in this book deals with inferential statistics. A measurement that concerns the entire population is called a parameter. A measurement that refers to the sample is called a statistic. Hence, statistics are estimated of parameters.

What are the four measurement scales?

  1. Nominal scales are not really scales at all; they do not scale items along any dimension, but only label them. For instance, gender is a nominal variable. A participant can be male or female, but none of the options is better than the other. Most categorical data are measured on a nominal scale.
  2. Ordinal scales are the simplest true scales. They order people, objects, or events, along some continuum without the possibility to say anything about the distance between different intervals on that continuum. For instance, there is no reason to think that the difference between a commander and a captain is the same as the distance between a captain and a rear admiral. 
  3. Interval scales have a measurement scale for which we can truly speak of differences between scale points. For instance, a 10-point difference in temperature has the same meaning anywhere along the scale. Thus, the difference between 10 and 20 degrees Celcius is the same as the difference between 20 and 30 degrees Celcius. Note, however, that this does not mean that 40 degrees Celcius is twice as hot as 20 degrees Celcius.
  4. Ratio scales have a true zero point (in contrast to temperature as illustrated above, which has an arbitrary zero point). An example of a variable with a ratio scale is a person's weight.

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